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A methodology for derivation of marginal costs of hospital cases and application to estimation of cost… Barer, Morris Lionel, 1951- 1977

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A METHODOLOGY FOR DERIVATION OF MARGINAL COSTS OF HOSPITAL CASES, AND APPLICATION TO ESTIMATION OF COST SAVINGS FROM COMMUNITY HEALTH CENTRES A Thesis Submitted in P a r t i a l Fu l f i lment o f the Requirements f o r the Degree of Doctor o f Phi losophy in the Department of Economics. The U n i v e r s i t y o f B r i t i s h Columbia March 1977 We accept t h i s t h e s i s as conforming to the requi red standard. Morris Lionel Barer, 1977 by Morr is L ionel Barer In presenting th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f r ee ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f i n a n c i a l gain sha l l not be allowed without my wri t ten permission. Department of Economics  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date April 26, 1977 ABSTRACT Considerable attention has been devoted in the past to documenting the impact of prepaid group practices and community health centres on inpatient hospital utilization. The thesis develops and applies a methodology designed to allow estimation of the fiscal implications of such evidence. An equation relating average hospital inpatient costs to a number of explanatory variables is specified. The maximum likelihood estimation technique is employed in a time-series/cross-section analysis to determine parameter estimates for that equation over the period 1966-73. The variables are constructed from data deriving from eighty-seven British Columbia public general hospitals. Empirical results indicate the importance of case mix, average length of inpatient stay, rate of case flow and education-related hospital activities in explaining the variance across the eighty-seven hospitals in average cost per separation. The parameter estimates derived in the unit cost analysis are utilized in a comparative static determination of the implications for unit costs of changes in a hospital's case mix. The impact of case-specific case mix changes on unit (per separation) costs is determined, from which analysis case-specific marginal costs are derived.. •< Finally, the marginal case costs are combined with utilization statistics from matched population studies involving community health centres or prepaid group practices. This allows determination of the expenditure implications of the utilization differentials reported in that literature. A subsequent extrapolative and conjectural analysis considers the cost implications of more widespread use of community health centres as a mode of medical care delivery in British Columbia. The conclusions suggest that the fiscal impact on the overall medical care budget in B.C. would be minimal i n the absence of corresponding reductions in numbers of hospital beds. A number of other applications of the case cost derivation methodology are suggested. i v TABLE of CONTENTS Page Li s t of Tables v i Li s t of Figures ix Li s t of Commonly Used Abbreviations x Acknowledgements x i Chapter 1: Introduction, Scope and Methodology 1 Chapter 2: Medical Care Delivery - Taxonomy and U t i l i z a t i o n Experiences 21 2.1 The Organizational Spectrum 22 2.2 Comparative Hospital U t i l i z a t i o n Experience -A Selective Review 28 Chapter 3: Hospital U t i l i z a t i o n - Behavioural Considerations 58 3.1 Patient, Physician or Hospital: Who 'Generates' the Data? 58 3.1.1 - Patient Factors 59 3.1.2 - Physician Factors 65 3.1.3 - Hospital Factors 72 3.1.4 - Summary 75 3.2 Economic Modelling of Physician Objectives 76 3.2.1 - Income/Profit Maximization 77 3.2.2 - U t i l i t y Maximization 82 3.2.3 - Non-Maximizing Models 92 3.3 Summary of Physician Modelling 95 3.4 Conclusion 96 Chapter 4: A Hospital Average Cost Equation - Theoretical Specification 102 Appendix 4A: Expected Occupancy Rate Options 126 Chapter 5: From Theory to Practice - Data Compilation and Variable Creation 128 Appendix 5A: B.C. Acute Care Public General Hospitals 153 Appendix 5B: Deflation of Dependent Variable 157 Appendix 5C: Canadian Hospital Morbidity Lists 164 Appendix 5D: Hospital Statistics 184 Chapter 6: Econometric Analysis - From OLS to MLE 193 Appendix 6A: Testing for Time Sta b i l i t y of Parameter Estimates 222 Page Chapter 7: Marginal Case Costs - Application of a Behavioural Hospital Average Cost Equation 227 Appendix 7A: 1970 Inpatient Share of Hospital Gross Expenditures 253 Chapter 8: The Canadian Clinics 256 8.1 Sault Ste. Marie C l i n i c 256 8.2 Saskatchewan Cl i n i c s 261 Appendix 8A: Conversion From Case Costs to Broad Diagnostic Category Costs 269 Appendix 8B: Saskatchewan CHA Cl i n i c s ' 1972-73 Hospital U t i l i z a t i o n Experience 276 Appendix 8C: Saskatchewan CHA Clinics ' 1972-73 Ut i l i z a t i o n and Cost Differentials 283 Chapter 9: The American Experience 295 9.1 GHI vs. HIP 295 9.2 HIP vs. D i s t r i c t 65 Retail, Wholesale and Department Store Unions 305 9.3 GHA vs. Blue Cross - Blue Shield 309 Appendix 9A: Calculation of Case Cost for "Other Diseases of Breast and Female Genital System" 318 Chapter 10: Summary and Discussion of Expenditure Estimates .. 321 Chapter 11: Summary, Implications and Potential Research Extensions 335 11.1 Summary 335 11.2 Policy Implications 341 11.3 Further Extensions and Applications 349 Bibliography 359 v i LIST of TABLES Table Page 1.1 Health Care Expenditure i n Canada - Selected Statistics 2 2.1 Summary of Hospital U t i l i z a t i o n Data 48 3.1 Admissions Per 1000 Population to Canadian General and Al l i e d Special Hospitals, 1967-1973 62 3.2 Percentage Changes in Average Net Fee-Practice Physician Incomes, 1966-1971 85 3.3 Percentage Changes in Estimated Number of Active Fee-Practice Physicians, 1966-1971 86 5.1 Correlation of Case Complexity Vectors 139 5.2 Aggregated Yearly Case Complexities 140 5.3 Distribution of Principal Components Variance 146 5A B.C. Acute Care Public General Hospitals 153 5B.1 Percentage Distribution of Inpatient Expenditures -1966-1968 158 5B.2 Percentage Distribution of Inpatient Expenditures -1969-1973 159 5B.3 Price Indices 160 5B.4 Deflators 163 5C.1 98 Diagnostic Category Canadian Hospital Morbidity L i s t 164 5C.2 188 Diagnostic Category Canadian Hospital Morbidity L i s t 170 5C.3 Aggregation Formula For Compatibility of 188 and 98 Diagnostic Category Canadian Hospital Morbidity Lists .. 180 5D.1 Selected Hospital Statistics - 1970 184 5D.2 Hospital Complexity Measures 187 5D.3 Hospital WAGE1 and WAGE2 Values, Selected Years 190 6.1 OLS Estimation Results 195 6.2 Maximum Likelihood Estimation Results (1) 200 6.3 Residual Correlation Matrix - Unrestricted MLE 202 6.4 Maximum Likelihood Estimation Results (2) 205 6.5 OLS Estimation Results From Test For Heteroskedasticity 208 6.6 Maximum Likelihood Estimation Results (3) 210 6.7 Residual Correlation Matrix - Unrestricted MLE After Data Transformation 212 v i i Table Page 7.1 1966 Case Costs - Selected Hospitals 232 7.2 1970 Case Costs - Selected Hospitals 236 7.3 Aggregated Yearly Case Costs 242 7.4 Marginal Cost By Diagnostic Category 249 7A 1970 Inpatient Share of Hospital Gross Expenditures ... 253 8.1 Comparative U t i l i z a t i o n Experience of Dual Choice Population: GHA versus Prudential 257 8.2 Aggregation of Case Costs to Form Diagnostic Category Cost for Neoplasms 259 8.3 Diagnostic Category Cost Differentials 260 8.4 Hospital U t i l i z a t i o n by G.H.A. Members and Prudential Beneficiaries (other than Newborns) who were Attended To by a Physician at Least Once, and Cost Implications 265 8A.1 Diagnostic Category Cost - Aller g i c , Endocrine, Metabolic 269 8A.2 Diagnostic Category Cost - Mental 270 8A.3 " " " - Nervous System 270 8A.4 " " " - Circulatory 271 8A.5 " " " Respiratory 271 8A.6 " " " - Digestive 272 8A.7 " " " - Deliveries, complications .. 272 8A.8 " " " - Genitourinary 273 8A.9 " " " - Musculoskeletal 273 8A.10 Diagnostic Category Cost - Symptoms, Senility and I l l -Defined Conditions 274 8A.11 Diagnostic Category Cost - Accidents, Poisoning, Violence, Etc 274 8A.12 Diagnostic Category Cost - Balance of Cases 275 8B Number of Separations per 1000 Population for Saskatchewan CHA Clinics and Comparison Populations (1972-1973) 276 8C.1 U t i l i z a t i o n and Cost Differentials - Regina CHAC ...... 283 8C.2 U t i l i z a t i o n and Cost Differentials - Saskatoon CHAC ... 287 8C.3 U t i l i z a t i o n and Cost Differentials - Prince Albert CHAC 291 9.1 Annual Hospital Admission Rates by Diagnosis, July 1956 to June 1957, Adjusted for Age and Union Local Within Each Sex 296 viii Table Page 9.2 Diagnostic Category Cost Differentials Between GHI and HIP Subscribers: Female 299 9.3 Diagnostic Category Cost Differentials Between GHI and HIP Subscribers: Male 303 9.4 Annual Hospital Admission Rates, and Cost Differentials for 1958, by Diagnostic Category, By Insurance Status (HIP and Union Fee-For-Service Plan) 306 9.5 Admission Rates per 1000 Member Years, and Expenditure Differentials, for Selected Diagnostic Categories: BC - BS and GHA 310 9A Calculation of Case Cost For "Other Diseases of Breast and Female Genital System" 318 10.1 Summary of Expenditure Differential Statistics 322 11.1 Hospital Expenditure Savings From Bed Stock Reduction . 346 11.2 Estimates of Net Savings for B.C. Population From Substitution of CHC's for Private Practitioners ($1970) 348 ix LIST of FIGURES Figure Page 3.1 Utility as a Function of Income in a Target Income Model 94 4.1 Geometrically Declining Treatment Costs Per Day 112 4.2 Gamma Distribution 114 X LIST of COMMONLY USED ABBREVIATIONS ALS - Average Length of Stay BC - Blue Cross BS - Blue Shield CHAC - Community Health Association Clinic CHC - Community Health Centre (Clinic) FEHBP - Federal Employees Health Benefits Program GHA - Group Health Association, Incorporated, Washington, D.C. GHI - Group Health Insurance HIF - Health Information Foundation HIP - Health Insurance Plan of Greater New York HMO - Health Maintenance Organization ICDA - International Classification of Diseases Adapted for Use in the United States MLE - Maximum Likelihood Estimation OCC . - Occupancy Rate PGP - Prepaid Group Practice xi ACKNOWLEDGEMENTS The extensive use of the first person plural throughout the thesis is intentional. An undertaking of this magnitude inevitably benefits from the insights, support and time of many individuals. The contributions of my thesis supervisor, Robert G. Evans, will be self-evident to all who read the manuscript. His unceasing drive, willingness to give generously of that most valuable of resources - time, and endless insights prevented the project from faltering under its own weight on numerous occasions. During those other spells when anything appeared more desirable than writing a thesis, his communicable enthusiasm ultimately prevailed. The additional members of my thesis committee, Ernst Berndt, Russell Uhler and Donald 0. Anderson contributed timely suggestions and solutions to specific obstacles at various critical points in the analysis. To Greg Stoddart and Hugh D. Walker, a special note of thanks for their careful reading of, and comments on, an earlier draft of the study. And to Brenda Lundman, Donald Paterson, Samuel Ho, Jon Kesselman and David Donaldson, who persevered through 350 pages and in some cases two thesis defenses, my apologies for the length and my thanks for numerous incisive queries and suggestions. Keith Wales, Lewis James and Frank Flynn merit special thanks for their many hours of assistance with computing problems when I found myself in over my head. Without their support I might yet be staring at a Vucom screen in the U.B.C. Statistical Centre. Despite the valiant efforts of these numerous individuals, this thesis would not have been completed without the assistance of my wife, Rachel. Her xii unflinching moral support and friendship were the catalysts which enabled me to utilize the diverse talents noted above to my best advantage. For her perseverance throughout the typing of this manuscript, and in particular her favourite pages - the tables, many thanks to Carol Menzies. The financial support offered by Health and Welfare Canada, through Student Fellowship No. 610-1044-22, is gratefully acknowledged. Tempting as it may be to share the blame for the final product with some or all of the above, I am reluctantly forced by logic and convention to accept responsibility for any errors which remain. 1 Chapter I t Introduction, Scope and Methodology The cost of health, care has received increasing attention during the past decade. Recent rapid increases in an already high"1" level of expenditures have prompted much of the economic research, applied to the medical care delivery system during that period. The underlying motivation is articulated throughout the introductions of many research projects devoted to the investigation of specific problems within the broad frame-work of health care delivery: "The cost of health services has risen so rapidly in Canada in recent years that three alternatives are now imminent..." (Health and Welfare Canada, Task Force Reports, 1970,1); "The most pressing problem of Ontario's Health care system is the', rapidly rising levels of expenditure and unit costs" (Ontario Economic Council 1976,1); "The rapid increases in health services costs in Canada in recent years are now matters of urgent public concern" (Evans, 1973a,1); "The containment of rapidly increasing medical care costs has become a dominant policy objective, not just for the federal government, but for many state and local governments as well" (Rafferty, 1974,xxi). One could extend this list, but to no apparent advantage. The message is clear. We undertake no marked departure from tradition here. Rather it was the extraordinary growth in expenditures within one sector of the delivery framework, the hospital, which provided the initial raison d'etre for this project. Hospital expenditures held the ignominious distinction of out-growing all other sectors (physician services, dental services, pharma-ceuticals etc.) for a number of years in the past decade, as indicated by the figures in Table 1.1. While expenditures on general and allied 2 special hospital care have been declining as a percentage of gross national product in recent years, as recently as 1973 this sector was still displaying a rate of growth in excess of the other health care components noted above. TABLE 1.1: Health Care Expenditure in Canada-Selected Statistics 2 TOTAL EXPENDITURE, MILLIONS OF DO '{Current Dollars) LLARS % O f GNP 1960 % of GNP 1971 % of GNP 1973 1960 1965 1970 1971 1972 1973 Total health care 2113 3336 6025 6843 7462 8220 5.5 7.3 6.9 General and allied Special hospitals 641 1144 2303 2587 2862 3216* 1.7 2.8 2.7 Physicians' services 355 545 1029 1236 1369 1471 0.9 1.3 1.2 Dentists' services 110 160 263 298 329 363 0.3 0.3 0.3 Drugs and appliances 313 454 776 868 932 1035 0.8 0.9 0.9 Rest of health sector 694 1033 1654 1854 1970 2188 1.8 2.0 1.8 AVERAGE ANNUAL % INCREASE IN EXPENDITURES .1960-1965 1965-1970 1970-1971 1971-1972 1972-1973 Total health care 9.4 12.6 13.6 9.0 10.2 General and allied Special hospitals 12.2 15.2 12.3 10.6 * 12.4 Physicians' services 8.9 13.8 20.1 10.7 7.5 Dentists1 services 8.1 10.6 13.5 10.0 10.4 Drugs and appliances 7.7 11.5 11.8 7.4 11.1 Rest of health sector 12.1 6.3 11.1 SOURCE: "National Health. Expenditures in Canada 1960-1973"/Health and Welfare Canada, 1975. * The above source indicates expenditure of $3163 million. However, recent correspondence with Health and Welfare Canada officials has indicated that this figure will be revised upward to the figure appearing in the table. Note, however, that the total health care figure has not been revised upward, as no more reliable data were available. If we add the $53 million difference to total health care as well, it turns out that those expenditures were closer to 7.0% of 1973 GNP, and that the % increase, 1972-'73, was 10.9% rather than 10.2%. This upward trend has been superimposed on a level of expenditure which embodied 38% of total health, care costs in 1973 and constituted 43% of 3 "personal health care expenditures". More recent, as yet unpublished, statistics indicate that as a % of GNP total health care expenditures continued their decline in 1974, measuring 6.7% However, preliminary indications are that 1974 may represent the trough for that statistic. In addition, we note that despite this turnaround, general and allied special hospitals have maintained their share of GNP; the unofficial figure for 1974 indicates approximately 2.7% ($3922 million - general and allied special; $144616 million GNP; preliminary 1974 figures). Even more dramatic is the fact that, after reaching an apparent low of 10.6%, annual percentage increases for this sector rose to more than 12% for 1972-'73 and, if preliminary figures are to be believed, underwent an increase of almost 22% from 1973 to 1974. Regardless of the degree of reliability of these latest figures, we can state unequivocally that hospital expenditure growth is still very much in evidence. In addition to the figures presented in Table 1.1, it is also interesting to note that while Canadian GNP increased by approximately 210% between 1960 and 1973, the comparable figure for general and allied special hospitals is 393%, a rate considerably in excess of the physician and dentist figures which are, respectively, 314% and 230%. To summarize, then, the figures in Table 1.1 illustrate that the rate at which expenditures for such hospital care, have grown has generally exceeded the comparable rates for other components of health care services. This growth has seen hospital expenditures rise from 1.7% of GNP in 1960 to figures in the neighbourhood of 2.7% in recent years. The level and growth of Canadian hospital expenditures has prompted considerable research into means of curtailing, or even reversing, the trend. Much of this research involves investigation of the behavioural influences underlying the statistics and formulation of policies directed toward any isolated causal factors. Thus, we see 'experiments' with 4 alternative methods of hospital reimbursement , supposedly directed at a behavioural entity called the hospital which is purported to behave in a technically inefficient manner. The problem with this approach is that it does not come to grips with the fact that such a homogeneous behavioural entity does not exist. Designers of such experiments appear seldom, if ever, to address themselves beforehand to the question of whom the changes in budgeting are directed at - what are the built-in incentives, and from which objective functions are they likely to prompt a response? 5 Growing pressure for new health care delivery organizations is aimed primarily at physicians - the dominant primary care providers - and in an. indirect manner at misuse of hospitals. In particular, it is argued that since physicians are important decision-makers within the hospital, attempts to re-organize the financial and physical . characteristics of their practices will have repercussions on hospital utilization, and thus on hospital expenditures. Finally, economists are continually attempting to develop an empirically testable model of the economic behaviour of the 6 'hospital unit'. In this pursuit, they are primarily interested in determining the nature of the causality itself - which decision-maker(s) should policy be directed toward, and what form of policy is most likely to be successful? Our present research could be considered to span all three of the above areas of interest, in that (i) it provides the methodology necessary to operationalize a potentially new means of reimbursing hospitals; 5 (ii) it applies this methodology to a segment of the literature devoted to the discussion of community health centres and prepaid group practices. In particular, it provides quantitative estimates of the potential fiscal impact of such 'alternative' institutions; and, (iii) it discusses the behavioural entities involved in 'generating' hospital expenditures, with the aim of delineating the causality behind the magnitude and growth of such expenditures. In that regard, we are implicitly assuming an "exchange" model (Jacobs, 1974, 83) of hospital behaviour, wherein "the performance of the ... (hospital) ... is a means to an end- the ends of the individuals who use it to achieve their ...goals." Thus, the project's scope spans a number of distinct but inter-related areas. Any attempt to mitigate the pace of hospital expenditures, either through direct policy measures or by first investigating the underlying processes and decision-making is predicated upon a belief that present levels and/or growth rates are in some way inappropriate. In assessing degree of 'appropriateness', analyses of the latter type commonly commence with an attempt -to disaggregate the expenditure data into price and quantity components. This, method is adopted for two reasons- First, the causal relationships governing the movement of each may be quite different. In particular, different sets of personnel involved in the.physical confines of the hospital 'unit* may.interact to 'produce' the statistics we observe. Second, two distinct sets of policy decisions may be appropriate (one for each of the price and quantity effects) although elements of eaeh set may 6 be formulated to affect, both halves of the expenditure process. Dis-aggregation of expenditure data often facilitates this task of identification and the subsequent designation of policy instruments to effect change. Turning specifically to the hospital setting we first consider the price component of the expenditure equation. If it is possible to dichotomize price and quantity trends, and if evidence of price increases is indicated, an identification problem remains, since such potential influences as factor price (and in particular wage rate) increases, general inflationary trends and improvement in quality of the product may all claim partial responsibility. If the disaggregation indicates a price decline, one would again be faced with the same choice of explanatory variables (working in the opposite direction) with the addition of increases in factor productivity. In either case, it would be necessary first to adjust both factor prices and 'hospital product' prices for general inflation, and then to concentrate on allocating any remaining price level changes across residual factor price shifts, quality of care changes and other identified explanatory variables. A more detailed analysis is unnecessary here, as subsequent attention is devoted exclusively to" the quantity/output side of the expenditure equation, for reasons noted below. Increases in quantity of output (measurement problems aside for the moment) might lead to investigation of changes in per capita income or in insured benefit coverage, number of physicians and other medical personnel, growth in population or particular disease incidences. However, the delineation of (and subsequent investigation into) changes in quantity of output naturally hinges upon an appropriate means of measuring that output. Ideally one might wish to utilize a measure of the change in a person's health status as a result of medical care received. However, no universally adopted measure has been developed^ , and much of the research 7 requiring measures of output falls back on the more readily available utilization proxies. Thus, we find number of office visits (perhaps weighted by price), number of procedures, etc., used in measuring physician practice output. In a similar vein, hospital days or cases, quantity of.. x-rays or laboratory tests may be employed, after various degrees of standardization, as hospital throughput indicators. Not only could it be argued that this type of data more closely measures factors of 'production' than the product itself, but such usages are further complicated by ambiguities which arise as a.result of the "intermediate product" problem. For example, two possible proxies for physician care output might be number 8 of office visits or number of episodes of illness treated. Clearly, the two measures will provide conflicting output levels for a patient who is recalled a number of times for the monitoring of a certain condition, within a single illness episode, although any change in the patient's health status is clearly independent of the measure employed. Similar incongruities arise as a result of patients, being readmitted to hospital for treatment of one condition, or of patients being transferred between hospitals. As noted above, the intent here is to focus on an investigation of possible trends in hospital output. The price side is largely ignored for a number of reasons. First, in Canada output prices have only minimal effect on the demand side of the market. Second, output is likely to be more readily vulnerable to change (if it is established that change is desirable) than either factor, or product, prices, in the absence of a complete restructuring of the entire health care sector. Even this drastic measure would likely be insufficient, as the personnel within this sector are inescapably intertwined with those outside the 'medical care industry' when it comes to bargaining for fee schedules or wage rates. And finally, in the absence of adequate health status indices, it would be 8 impossible to differentiate quality of care price effects from alternative causal factors. Thus, i f hospital care expenditures are to be affected, at least i n the short run, the target i s l i k e l y to be the input-output side. It would be heartening, but misleading, to suggest that we have found a novel measure of output which circumvents the above-noted d i f f i c u l t i e s . For our purposes, the number of hospital admissions or separations, suitably standardized for complexity, w i l l be employed as the unit of hospital output. Alternative measures have frequently appeared i n the literature. The advantages and disadvantages of a number of alternatives, as well as of the unit employed here, are discussed in a subsequent 9 chapter. Given this operational, albeit not ideal, measure of hospital output, we address ourselves once again to the c r i t e r i a by which we might judge appropriateness of both output levels and changes in those levels. If i t is established that output has increased over some specific time period we would naturally be interested i n determing whether such increases were warranted, from a social welfare perspective. But even in the absence of such a trend (i.e., i f i t turns out that output levels have been relatively stable or have declined) i t may s t i l l follow that the absolute output level i s too 'high', again i n a social or paternalistic sense. The order of investigation would therefore appear to require us f i r s t to establish the acceptability of output levels, prior to any attempted isolation of growth trend.causality. Thus we have, in a sense, come f u l l c i r c l e . Our departure point was the suggestion that expenditure growth rates were alarming. And, indeed, i t was the growth rates, together with, absolute expenditure levels, which prompted the delineation of this particular project. We proceeded from the premise that growth in expenditures implies growth in price levels and/or in output levels, to look, briefly at some of the factors which we would expect to influence these respective components. Deriving from that discussion was the fact that identification problems not only complicate any price/quantity disaggregation, but that they render any further allocation of weights to potential contributory factors an almost impossible task. We return, therefore, to output levels, as measured by hospital throughput. There is a fairly extensive body of literature which implicitly (if not explicitly) supports the notion that excess hospital utilization exists in Canada and the U.S. This literature will be discussed and reviewed in the following chapter. In the meantime we might briefly consider the implications of such evidence. In almost any other 'industry', output (or at least productivity) increases are desirable and, indeed, the same would likely be true for medical care, if an appropriate measure of output were being employed. In fact, no health economist would dispute the desirability of increases in productivity. However, more hospital cases, days and the like, are clearly not unambiguously better than less. Alternatively, the marginal social utility of such output is likely often small and perhaps even negative. Advocates of a consumer sovereignty model would argue that patients who increase consumption of medical services are doing so because consumption of additional units of care at the margin provides sufficient utility. The counter-argument (and, we contend, a more satisfactory position in view of the fact that, in Canada, medical care is 'purchased' privately but largely funded from the public purse), is based upon an implicit model in which health status and medical services are both arguments in the consumer's utility (preference) function. Denoting these, respectively, by HS and MS, let us consider 1 0 the marginal effect of medical service consumption on a consumer's u t i l i t y , U = U(.HS,MS...) where HS = HS(MS...) dU_ = 3 U _ 3HS + 3U dMS 3HS ' 3MS 3MS The motivation for contacting some member of a medical care delivery organization must derive from a prospective patient's perception that the medical services received w i l l have a positive effect on his/her u t i l i t y . Thus, the consumer who expects dU to be > 0 w i l l be equipped dMS with a rational reason for approaching a medical practice. With the possible exception of some misguided hypochondriac, no one i s l i k e l y to argue with the assertion that 3u > 0. These same hypochondriacs 9 H S 10 provide the only l i k e l y resistence to a suggestion that 3U < 0. To 3MS the majority of us, the v i s i t to the hospital, the medical laboratory or the physician's office i s at best distasteful and something to be concluded with minimum elapsed time. We are l e f t with placing a sign on 3HS , a parameter unrelated to 3MS the individual consumer's u t i l i t y considerations - in effect a technical, production-process determined term which the consumer believes to be suffi c i e n t l y positive as to yield the expected dU > 0. It i s this term dMS which i l l u s t r a t e s the distinction between the standard u t i l i t y maximizing model and the present representation of the purchasing process. The former model asserts that consumers w i l l purchase additional units of medical care so long as dU i s suff i c i e n t l y large (and positive) that, in dMS conjunction with the price of that good, U /P i s not equal to the MS MS ^ equivalent ratio for a l l other goods and services in the u t i l i t y function. But that model relies on the assumption that the consumer-patient i s able to determine, with certainty, the value of U = dU The model MS —'— dMS suggested above, on the other hand, i s based on the premise that the consumer believes dU to be > Q, as a result of believing that 3HS is dMS 3MS of some specific magnitude, > 0. Clearly, an overestimate of 3HS (and 3MS we have suggested-above that this may take on zero, or even negative, values! has potentially serious connotations. While the patient.may believe dU to have one value, an over-estimate, either by patient or dMS provider, of the value of 3HS may result in the consumption of medical 3MS" goods and services which would not have been purchased in a market characterised by perfect information. Note that, while the consumer's utility considerations initially determine entry into the system, the provider's valuation of expected 3HS may prompt further 'purchases'. 3MS At this point, two effects should be distinguished. First, this 'market' is not only characterized by consumer ignorance and uncertainty and an information gap between consumer and supplier, but its functioning is further hindered by lack of product knowledge on the part of the supplier. In particular, the physician may be unable to determine (with any significant degree of certainty) the effect of a prescribed set of procedures on a patient's long-run or short-run health status. It is the information gap which gives rise to the so-called agency, physician-patient, relationship wherein the consumer relies to a great extent on the physician for guidance. But it is the combination of consumer and provider uncertainty, and the resulting potential bias in the expected value of dU/dMSwhich undermines the usefulness of standard utility maximizing theory. The sovereign consumer who is posited to be the main actor in that utility theory of demand, is subjected to seemingly inescapable damage when we introduce the supplier influence, agency, relationship and, as Culyer (1973) points out,, there are also certain clear-cut cases (mentally-ill patients, 12 emergency cases) where the consumer sovereignty concept is a sham. It would appear, then, that the existence of consumer and supplier uncertainty, 1 2 and a resulting potential legitimate over-estimation of the value of 3HS/3MS, may lead to excess Cor unnecessary) utilization. Second, it is the actual Cand hence unknown, at least in the short run) value of 3HS which we might consider to be a proxy for the effect 9MS upon social welfare of additional medical care industry output. But note that, in addition to legitimate overestimates of 9 H S by provider and 8MS patient, unnecessary utilization may also derive from supplier conflict 13 of interest. For the supplier of care, increases in hospital output (to the extent that they do not conflict with other parameters in his/her utility function) are desirable as they facilitate a net income, or practice revenue, maximization objective. Thus, the scope for a potential conflict between social utility and supplier utility emerges and is further enhanced by the uncertainty on the part of consumer and producer which affects output decisions. This model clearly illustrates the pervasiveness of uncertainty in the determination of utilization levels. In particular, lack of information may lead to 'consumer abuse' as manifested through (for example) numerous consultations, dissatisfaction with an office visit which does not provide some concrete 'cure' (i.e. a prescription), and the like. It may also give rise to two distinct provider-motivated excess 'demand' channels. In addition to the above-noted legitimate uncertainty, 'producer abuse' may appear in the guise of 'marginally-needed' recall visits, unnecessary or incorrect pharmaceutical prescribing, or recommendations to the patient to undergo 'elective' surgical procedures. In the latter instance, the patient's actual health status may not be affected, irrespective of his/her . . 14 ultimate decision. Chapter 3 is devoted to the disentanglement of the various factors which may affect hospital utilization. While some authors have strongly suggested that the supplier derived form of abuse dominates the 'market', we leave further discussion of the matter to that chapter, wherein we investigate a potential spectrum of causal variables underlying hospital utilization.15 The crucial point to be derived from this discussion is that the behavioural potential exists for the incidence of excess, or unnecessary, hospital utilization in Canada. Unnecessary hospital utilization may take on many guises. In a hospital with low occupancy, patients may be encouraged to extend lengths of stay, especially in light of at most a nominal point-of-service cost to the patient in Canada. In addition, admissions for conditions treatable on an ambulatory basis, but more conveniently handled through in-patient care, may be encouraged. Finally, physicians may hospitalize patients and utilize hospital facilities for diagnostic analysis where alternative . settings for laboratory and radiology 'work-up' exist. The evidence cited in the following chapter points to the admissions phenomenon as playing a large part in excess hospitalization. The rather crude model discussed above suggested that unnecessary care is often the result of incorrect expectations on the part of provider and patient. If there is, indeed, evidence suggesting that unnecessary hospitalization does exist, the implication is that the patient affected would derive at least equal utility, through change in health status, from an alternative (or no) treatment. (In:the absence of a change in the focus of public health education, however, expected utility may remain higher through the hospitalization route). In addition these ambulatory options are almost always.less expensive, not only due to the elimination of in-patient care related costs but also as a result of a reduction in the risk of iatrogenic illness. A brief account of the intended scope of the thesis was provided earlier in this chapter. The discussion below expands on what we perceive 14 to be the major contributions of the remaining chapters. In that regard, the discussion may be subdivided into three subsections: (i) hospital cost reimbursement (ii) substitution of ambulatory for hospital care (iii) behavioural structure underlying hospital utilization. Needless to say, the three areas of focus are inter-related and are treated that way: (i) It has been suggested that, as opposed to global or line budgeting, a reimbursement scheme which involved payment to hospitals on a per-standardized-case basis would embody an inherent incentive structure 17 essential to containing hospital expenditures. The intent in this thesis will not be to suggest, or sit in judgement on, any detailed reimbursement scheme, but rather to set out and operationalize a particular methodology which could provide the prerequisite case costs for such a plan. This potential application is one of a number to which the methodology developed in this project might be applied. In particular, a hospital average cost per case equation is specified and estimated. The resulting parameter estimates are employed to determine the comparative static implications for cost per hospital case, of changes in the hospital's case mix. The result of this cost analysis is a vector of cost per case figures, by diagnosis, and the methodology is applicable to any selected diagnostic breakdown. The list employed here is the 98 category Canadian list, based 18 on the ICDA, seventh revision. (ii) Our attention here will be devoted first to a detailed review of the numerous hospital utilization studies in which patient populations have been compared for trends in the volume of hospitalization 'consumed'. These particular studies have focused on situations wherein patients received primary care either through a prepaid group practice (PGP) or 1 5 community health centre (CHC)f or from the more traditional (and more common) private practitioner. The data compiled by certain of these studies will then provide the basis for one application of our estimated case costs. These data have consistently illustrated that subscribers to group practice or CHC plans utilize hospital facilities to a lesser extent than their matched population counterparts receiving 'traditional' care. We will be particularly interested in those settings wherein the populations are matched (to the extent that the available data permits) for age and sex composition, socio-economic factors and geographic location. This subset of studies can be pared further for the case cost application by eliminating those not providing a diagnostic disaggregation of the hospital utilization experience. What remains is a small number of studies (Densen et al. (1960,1962), Riedel et al. (1975), Hastings et al. (1973a), McPhee (1973)) in which such a breakdown is provided, or from which the data may be obtained. By applying the case cost figures to the reported utilization differentials, we obtain estimates of the expenditure magnitude of 'excess' hospital care. In doing so, we attempt to estimate the fiscal impact (on hospital expenditures) of a hypothetical situation in which care is provided to all British Columbians through an integrated clinic-type setting (to be described in the following chapter). As a by-product, it will be possible to ascertain for which diagnostic categories the impact would likely be greatest. (iii) To complete the analysis we devote some attention to an investigat-ion of the segment of the medical care market responsible for 'generating' hospital utilization data. Thus, in an extension of the discussion of this chapter, each set of actors - patients, physicians, and hospital setting - will be considered in turn, in an attempt to pinpoint the likely 16 cause for the data described in (ii), and we will make a brief foray into physician behaviour modelling as part of this investigation. The following chapter of the thesis provides a brief background on the modes of medical care delivery in use in Canada and the United States today. This is followed by the presentation and discussion of the data described briefly in (ii) above. Chapter 3 devotes its attention to item (iii), while chapters 4 to 7 contain the cost analysis outlined in (i). This block of chapters, which comprises the major analytical section of the project, is then followed by three chapters in which the above-discussed application to the PGP and CHC data is undertaken and analyzed. The thesis closes with a setting out of major conclusions, possible extensions, and potential policy applications of the methodology and results. 1 7 Chapter 1^  - Footnotes 1. The 'high.' reference is to the level of per capita expenditures relative to per capita dollars spent on other goods and services. In particular, we will contend in the project that not only are present absolute expenditure levels excessive, but the rampant increases of late in this area are unwarranted in that little concomitant increase in 'output' is evident. 2. Our hospital reference throughout this thesis will be to General and Allied Special hospitals. This involves the exclusion of all Mental, Tuberculosis and Federal hospitals. The latter three categories accounted for only slightly more than 17% of total hospital expenditures in Canada in 1973 (Health and Welfare Canada, 1975, 11). 3. These figures are computed from Table 1, page 11 of the source for our Table 1.1 statistics. Personal health care expenditures differ from total health expenditures in that the former do not include expenditures arising from prepayment and administration, government public health, voluntary organizations and research and construction. 4. For example, emphasis has been shifting from line budgeting to glohal budgeting in certain areas. Milne (1977) describes (and investigates the degree of success of) changes in the Ontario hospital budgetary system in the period 1968-74. 5. Portions of the vast literature on community health centres and prepaid group practices will be considered in subsequent chapters. 6. For a recent review of such modelling, see Jacobs (1974). 7. Two volumes devoted to this issue are Berg (1973) and Culyer (1977). 8. For a delineation of the 'episode of illness' usage, the reader might consult Stoddart (1975). 9. Yet another measure of health output, and one perhaps more closely linked to attempts at quantifying health status, is that of 'good health' or 'healthy days' such as one might expect to find used in a health capital model the likes of Grossman (1972). However, these concepts are nebulous and difficult, if not impossible, to quantify. 1 8 9. (.cont'd) Furthermore, it is not clear that this is, in fact, what medical care produces. 10. I am indebted to Robert Evans for clarifying the partial/total dichotomy of MS effects on U, 11. If this bias is upward, we are likely to observe unnecessary utilization, as described subsequently. This, rather than a downward biased estimate of the value of dU/dMS, is the more likely phenomenon. If downward bias were prevalent we would observe neither evidence of excess utilization, nor such rampant increases in the utilization of health services for very little resultant effect on health status. 12. It is interesting to consider other, seemingly analogous, consumer-supplier interactions. If we consider the purchase of medical care as an attempt to upgrade health status, one immediate analogy which comes to mind is the repair of a 'sick' automobile. Again the consumer often has little knowledge as to the quality of the producer (the mechanic), and is generally incompetent to judge the effect of the production process on his/her automobile's long term 'health status* (except in severe cases where there is an obvious improvement, or in cases of clear neglect in which the car's post-care operation is inferior to its original state of well-being). Thus, both the information gap and the consumer-supplier agency relationship exist. However, there is likely to be more 'shopping around' in this market, prices play a rationing role and are often advertised, the supplier is usually aware of the effect of prescribed treatment on the condition of the automobile, and ailments are not of a life threatening nature (unless, for example a brake line springs a leak or a steering column or axle suffers a severe fracture). A somewhat closer approximation to the health care situation is provided by the interaction of a university faculty with graduate students. Supplier, influence on course of 'treatment' is prevalent. There may be consumer and supplier uncertainty as to the long-run effect of additional consump-tion of courses on the student's human capital stock. The consumer often relies rather heavily on the supplier for advice as to the most appropriate mode of treatment for the 'insufficient education' condition. In this market, however, there may be advertising 1 9 12. (cont'd) (recruiting of students), the situation analogous to the emergency case never appears, and one suspects that the effect of additional education consumption on human capital stock is far less uncertain than the analogous medical 'care consumption situation. The most important distinction concerns the complete lack of life threatening situations. In any event, we suggest that the collapse of the assumptions underlying the consumer sovereignty-utility maximizing model is more severe in the case of health care consumption than in either of these analogous cases. 13. This phenomenon is not a distinguishing characteristic of medical care consumption. A similar conflict of interest clearly confronts the automobile mechanic (Toronto Star, 1976). The educator, to the extent that student numbers secure his/her position, is also confronted with a similar conflict of interest. If there is any characteristic which sets medical care providers apart from both these others with respect to conflict of interest, it is that over-zealous adherence to the financial side of the dichotomous considerations may have life-threatening consequences for the consumer. Society's judgement as to the relative values of life, good health, good education and a finely tuned car, ultimately determines the degree of severity of the respective conflicts of interest. 14. This discussion is based on more than random theorizing. Evidence from the drug sector indicates that "adverse drug reactions - due in large part to well-intentioned but irrational prescribing - are now responsible for a million or more hospital admissions annually in the U.S. alone, tens of millions of days of prolonged hospitalization, thousands of preventable deaths, and the resultant expenditure of billions of dollars each year" (Silverman and Lee, 1974, 2). 15. A well-known, but perhaps rather extreme, view is that of Illich (1975). He argues, in a fashion consistent with the data and thrust of the thought in this project, but on a somewhat more provocative level, that the medical care establishment in general is counter-productive in that it tends to atrophy our inherent self-healing powers, while concurrently failing to significantly increase its own capacity to heal. In the same flavour, Gertman (1974) concludes a discussion on 15. (cont'd) the role of the physician by suggesting that "if our society wishes to have control over utilization of health care, it seems imperative to develop a better understanding of the mysterious behaviour of that key decisionmaker - the physician - and the rationale he employs in guiding.the use of health services" (p. 378). 16. Iatrogenic illness refers, in the broad sense, to medical care delivery system initiated illness. Thus, although "Iatrogenesis is composed of the Greek words for 'physician' (iatros) and for 'origins' (genesis) ... In a more general and more widely accepted sense, clinical iatrogenic disease comprises all clinical conditions for which remedies, physicians or hospitals are the pathogens or 'sickening' agents" (Illich, 1975, 22). 17. See, for example, the Ontario Economic Council's 1976 publication, Issues and Alternatives 1976 - Health, pp. 17-19. 18. A number of diagnostic category breakdowns exist. We employ the International Classification of Diseases, Adapted for Use in the U.S., 7th revision. In addition, for 1969-73 data, we commence with diagnostic data coded according to the 8th revision of the same coding, and employ a meshing described in Chapter 5 to ensure compatibility of diagnostic categories over time. The methodology would be equally applicable to the Ontario Broad Code or the fine I.CD.A. breakdown. 21 Chapter 2: Medical Care Delivery - Taxonomy and Utilization Experiences In the introductory chapter we outlined reasons for focusing on hospital output levels rather than on growth in those levels, or on prices. It was also suggested that there existed evidence which supported an excess hospital utilization hypothesis, and the implications of such evidence were briefly discussed. This chapter reviews and assesses that evidence after first providing a medical care delivery mode taxonomy as background. In particular, the chapter is comprised of two sections: (i) given that alternative means of delivering medical care exist, in what form are the alternatives manifested, and what are their apparent distinguishing characteristics? (ii) what is the evidence which suggests that these alternatives may induce a lower volume of hospital throughput? The relevant literature is reviewed. With regard to (i), we will be particularly interested in attempting to isolate the economic processes underlying the various practice modes. However, before proceeding we should define our use of the phrase 'medical care delivery' with a brief explanation of this terminology. Medical care is often subdivided into primary and secondary care, the major distinction between the two being that the latter is commonly thought of as "a resource to the primary care sector" (Mustard et al., 1974, 15). Thus, primary care institutions serve the function of providing "not only those first contact between the patient and health professional, but also responsibility for promotion and maintenance of health and for complete and continuous care for the individual, including referral when required" (Mustard et al., 1974, 11). Within this particular framework, then, general practitioners would provide primary care services, as would specialists, emergency departments etc., so long as they provided 2 2 the f i r s t patient-medical care system contact for an il l n e s s episode. Secondary care would be provided by hospitals and specialists to whom patients are referred. Our attention i n this, and the following, chapter i s devoted to alternative medical care delivery organizations and their effects on one element in the secondary care spectrum, the acute care hospital. In that regard, we are not considering 'health care delivery' which i s generally broader ranging in i t s scope, implying the receipt by patients of any and a l l services related to their health status. 2.1 The Organizational Spectrum A wide variety of medical care practice settings exists within Canada and the United States. Although similar i n function, these practices d i f f e r with respect to the resources they embody, their physical settings, the means by which they finance themselves, and the means by which their labour inputs are remunerated. It i s particularly important here to highlight the i n t r i n s i c differences between American and Canadian i n s t i t u t i o n s . 1 As with any spectrum, the distinguishing features of two similar institutions are often i l l - d e f i n e d or imprecise. We no doubt miss mentioning some forms of practice. However, any such omissions w i l l l i k e l y be minor variants of one or more organizations discussed below. The 'spectrum' employed here uses, as i t s implicit primary cataloguing element, the number and/or mix of physicians practicing within an organization's confines. Thus, at one end of the band we observe the common single physician practice; at the other, a multi-functional, multi-specialty group practice or c l i n i c . Some f a c i l i t i e s , such as a hospital-based outpatient department, are d i f f i c u l t to place precisely within the spectrum. However, such exact placement i s not our major concern 2 3 here- What follows, then, i s a "descriptive analysis' of the various modes of primary care delivery. Single physician practices are s t i l l , i n Canada, the most common form 2 of medical practice. This group of practices may. be partitioned into solo general practitioners and solo specialists. In general, these practices are reimbursed (either directly or through a third party) on a fee-for-service basis. In Canada, fees for various procedures are determined through the setting of fee schedules - the result of negotiation between the provincial governments and the relevant medical associations. Thus, one may think of the physician as not only the primary labour input within the practice, and accordingly collecting a salary based on an imputed wage rate, but also serving as entrepreneur who receives any 3 residual income or p r o f i t deriving from the practice. In parts of Canada (i.e. B r i t i s h Columbia) the solo specialist depends primarily on general practitioner and fellow specialist referrals for clientele. In other provinces direct patient-specialist contacts may be more common, although they are not necessarily the rule. Consultation with five different students of health care delivery could conceivably result in five different opinions as to just which forms of practice are embodied in the group practice concept. One might consider any practice employing more than a single physician as a group practice. But where does that leave the medical arts building, which consists of a multitude of practices, or the hospital out-patient department? Clearly, the matter i s one of semantics, or degree of organization. The medical arts building i s primarily a means of housing numerous diverse single and/or group practices in a centralized location. Thus, rather than being a form of practice organization, i t i s a physical (as opposed to legal or financial) 2k entity comprised of medical and support personnel. There are a number of conceivable variations here. The building i t s e l f could be owned by the practices, or each practice might rent floor space from either a physician or group of physicians from within the group of practices, or from an autonomous person or organization. These buildings usually contain laboratory and radiology practices, a pharmaceutical outlet and other health f a c i l i t i e s in addition to the general practitioner and specialist practices. However, each practice within the physical confines of the building is a separate financial and legal entity. Most, i f not a l l , hospitals contain emergency departments which, while not forms of medical practice as we are thinking of them here, are nevertheless sources of primary care. They w i l l not concern us further, however. Many hospitals also boast well-organized out-patient departments which w i l l tend to various ambulatory care needs of a non-emergency nature. The physicians staffing such departments may be salaried employees of the hospital, interns, or physicians from the community f u l f i l l i n g an obligation to the hospital in return for admitting privileges. In that regard such f a c i l i t i e s are d i f f i c u l t to envision as any particular generalized form of practice. One might think of the partnership as the most fundamental form of group practice. Partnerships often involve two physicians of a common specialty, although such an arrangement i s not necessary. At any rate, office space and receptionist are commonly shared expenses of what i s otherwise very similar to the private practice - each practice w i l l generally charge for services on a fee basis, and a l l income w i l l accrue to the practice deriving i t . Clearly, revenues could also be pooled and allocated according to some pre-arranged formula. 2 5 The natural extension of the common specialty partnerships is what might be referred to as the single specialty groups. The usage here implies three or more physicians of common specialty sharing facilities and/or labour inputs while concurrently utilizing one of the two financial options described in the context of the partnership. Although income sharing is not necessarily a characteristic of such practices, "waiting rooms, receptionists, telephone service, laboratory, record rooms, and business services are frequently shared..." (Roemer, 1965, 1155). When referring to group practice, one commonly envisions a setting wherein three or more physicians of different specialties utilize a single location. That is not to say that the single specialty group is not a 'group', but rather that the more common usage refers to the multi-specialty organization. The group, as a practice, is paid on a fee-for-service basis while member physicians will arrange an income sharing scheme so that they share in the profits from the 'joint practices'. Size, as defined by number of participating physicians, will vary from groups of three or four physicians who might utilize a common list of non-group specialists for referral purposes and who send diagnostic work outside the group, to comprehensive groups. The latter, described by Roemer (1965, 1157) as "the classical model of group practice, for which praises are sung or epithets hurled..." still charge patients a fee-for-service, but now embody the facilities and personnel enabling them to provide a much broader range of services, commonly including many laboratory and radiology services as well as a wide spectrum of specialists. Physicians may engage in teaching and/or research within the group setting and, whereas smaller groups may, in certain cases, utilize some part-time members, the comprehen-sive groups generally employ full-time general practitioners, specialists 2 6 and paramedical personnel. At the other end of the spectrum we find comprehensive prepaid group practices (PGP) and community health centres (CHC). Although the two are not identical, they are similar, their major difference being primarily a function of their locale (PGP's being found in the U.S., CHC's 4 in Canada). Again, a comprehensive and varied slate of facilities and services is offered to the patient in a single locale. In the prepaid setting, a specified population combines financial arrangements with access to medical care, prior to the occurrence of any need for such care. Thus, rather than having patients pay for care as it is consumed, the prepaid group pools medical risks by requiring each member to prepay for the majority of care to be consumed in a future stipulated time period (commonly one year). In this way, such organizations combine an insurance function with the availability of a large number of 'benefits' to the subscriber population. In such settings, the group itself may be thought of as the entrepreneur (paid by capitation) and thus the claimant of residual profits, while member physicians may be reimbursed by salary or some other non-fee-for-service income sharing arrangement. A major distinguishing feature of the Canadian community health centre is the fact that there is no need for patients either to pay for services on a fee basis, or to prepay for such services. Public health insurance, which reimburses all provider agencies on behalf of the patients, precludes any patient financial involvement, other than payment of yearly premiums in some provinces and various cases of relatively insignificant copayments. Thus, the primary difference between community health centres and prepaid group practices is that the former bill a third party (the provincial and federal governments) for all medical expenses incurred by enrollees, or 2 7 are paid by the third party on a capitation or global budgeting basis. The member physicians are, as above, paid by salary or pre^set income sharing. When considering u t i l i z a t i o n data arising from community health centres, however, one must keep in mind that, unlike the U.S. situation involving comprehensive prepaid group practices, there i s no financial constraint binding a subscribing patient to the centre. Regardless of the patient's source of care, the b i l l w i l l be taken care of. Thus, u t i l i z a t i o n data may not represent total u t i l i z a t i o n of medical care f a c i l i t i e s by the community health centre subscribers unless care received outside the c l i n i c i s allocated back to the c l i n i c for roster definition purposes. In the United States, on the other hand, patients seeking care outside their PGP setting must bear the financial consequences, a disincentive which suggests a lesser bias i n the U.S. prepaid group practice data. There i s l i t t l e evidence available to suggest the extent to which the alternative financing arrangements d i f f e r e n t i a l l y bias the Canadian, vis a vis American studies. With this range of medical care f a c i l i t i e s i n mind, we are now equipped to proceed with an examination of a selective portion of the hospital u t i l i z a t i o n literature. Reference i s to that segment of the literature devoted to an examination of comparative u t i l i z a t i o n experiences for patients receiving care from different points on the spectrum. In particular, attention w i l l be focused on those settings involving PGP's or CHC's on the one hand, and private fee-for-service practitioners on the other. 2 8 2.2 Comparative Hospital Utilization Experience - A Selective Review There is, in general, no lack, of available hospital utilization data. It should, and does, follow that assemblage and comparison of various bodies of this data is a straightforward process. Unfortunately that is where the simplicity ceases. Interpretation of such comparisons is fraught with attendant ambiguities, as is repeatedly illustrated below. Our aim is to compare hospital utilization experiences reported by "alternative combinations of medical care organization and financing" (Klarman, 1969, 179). Interpretative difficulties are a result of the myriad of factors which determine utilization patterns. In order to compare utilization experiences of two organizational modes of delivery, one would ideally wish to have the study populations standardized for such potential contributory factors as age, sex, geographic location, marital status, accessibility of hospital facilities, extent of hospital and medical benefits, etc. The exact factors for which standardization is desired will be dependent on the questions being addressed (clearly geographic standardization would be undesirable in a study which attempts to identify locational differences in utilization). The studies reviewed below, however, embody differences in at least one, and commonly more, of the above factors. Needless to say, this undermines cause/effect identi fication. Our.aim in the following discussion is to present a summary of the utilization data which have appeared over the past three decades, while concurrently examining the degree to which the comparison populations were 'matched'? This will facilitate a determination of the relevant explanatory variables, a subject taken up in the next chapter. However, before we proceed with this review a few further qualifying remarks are in order. 29 The majority of the studies cited below are of American origin. In particular, the earlier studies Cpre-197Q1 are exclusively from the United States. Due to the difference In the medical insurance situations which existed at the time of the various studies, one must exercise caution in transporting results across the border for comparative, or application, purposes. It is also essential to recall the source of diagnostic utilization data. Unfortunately, physicians and hospitals use various procedures for reporting patient diagnoses and, in particular, the disease classification lists used may not be comparable over time. It is also not inconceivable that, where fee schedules are operative, economic motivation may give rise to erroneous diagnostic or service reporting. We assume bias of this nature is minimal, since there is in any case no means of purifying the data of this type of influence. Finally, inter-study comparisons of admission, discharge or average length of stay data tend to be unenlightening because of methodological, geographic and/or other differences embodied in the analyses. We are primarily concerned with intra-study comparisons, although a summary table of the studies reviewed here is provided, at the end of this chapter, for quick reference. (i) President's Commission on the Health Needs of the Nation (1952) . One of the earliest, if not the earliest, sources of evidence regarding comparative hospital utilization rates, arose out of the research undertaken by the above-named U.S. government appointed body. Figures from that study indicated that, while three prepaid group practices reported between 70 and 104 admissions per 1000 population., Blue Cross plan subscribers were admitted to hospital at a rate of 122 admissions per 10QQ person-years. In addition, although not showing as marked a differential, average length of stay (hereafter ALS) statistics, of 6.2 - 7.0 days vs 7.4 days, respect-30 ively, produced the same ordinal relationship. It is also worth noting that the PGP reporting the highest ALS (7.0 days) also indicated the lowest admission rate (70 per 1000).. The differences are, thus, most evident when comparison of total patient days per 1000 persons is made for the 8 two groups: 490 - 685 for the PGP's, 888 for Blue Cross. One must recall, of course, that geographic locations varied markedly, and no other standardization (i.e. for age/sex sample composition) of any sort was undertaken. (ii) Committee for the Special Research Project in the Health  Insurance Plan of Greater New York (HIP)9 (1957). This study, based on a 1951 household survey, compared hospital utilization by members of HIP (who were insured for medical care in and out of hospital) with utilization by a representative sample of New York city households (of which approximately one-half had no medical insurance coverage at all). It has been been reviewed in at least three articles, two (Donabedian (1965,1969)) of which indicate that the study found admission rates of 81 and 74 per 1000 subscribers for HIP and New York City respectively. The third (Klarman (1963)) review reported rates of 74 and 67 respectively. The latter review reproduces the crude, unadjusted rates, whereas the two Donabedian studies quote rates adjusted for deaths (based on estimate of admissions who subsequently died and were thus not reported in the survey). The ordering is thus independent of standardization.. In light of the disparity in insurance benefits between the two populations, we should perhaps not be surprised at the difference in utilization rates. However, as both Donabedian (.1965) and Klarman (.1963) point out, the uninsured segment of the New York City sample had, at the time, a higher hospital 3 1 utilization rate than the insured. Donabedian has suggested the readily accessible free care in.New York during.the time of the survey as a possible explanation for this latter phenomenon, but the HIP vs New York City rates remain largely unexplained. Average length, of stay statistics indicated that HIP subscribers stayed, on average, a day less than their New York (non-HIP) counterparts, the rates being 10.6 days and 11.6 days respectively. Finally, Donabedian isolates one diagnosis, tonsillectomies, for further scrutiny, reporting admission rates of 3.4 per 1000 persons and 4.9 per 1000 persons for HIP and N.Y. City respectively. (iii) Densen et al. (1958): HIP vs BC-BS11 Based on 1955 data (not survey data), this study compares HIP sub-scribers with a population insured for medical services through Blue Shield. Both study groups obtained hospital insurance from Blue Cross. The medical benefits available through the HIP plan were more extensive than those provided to Blue Shield subscribers, primarily in that the latter group were, in general, covered only for in-hospital medical care (in some cases only surgical hospital care). Thus, the populations were not matched with respect to extent of benefits. The reported admission rates were 77.4 (HIP) and 95.8 (BC-BS), while the ALS was similar for the two groups: 7.6 for HIP, 7.2 for BC-BS. Inspection of the above admission rates indicates that the latter group were being admitted to hospital in excess of 20% more frequently, and it has been estimated that, based on HIP membership of 500,000 at the time, these figures translated into a gross expenditure saving of approximately 12 $1,550,000 and a possible reduction in bed supply of 137 beds. When standardized for age-sex population distributions, the admission rates 3 2 become 81.1 and 93.9 respectively, still close to a 16% differential. Certain surgical procedures (tonsillectomies, appendectomies etc.) showed marked differences in admission rates, but the differences in coverage, and the subsequent possible incentives (to both consumer and provider) to substitute in-hospital surgery for ambulatory treatment, renders the diagnostic data from unsuitable for providing diagnostic information usable in our intended application. (iv) Anderson and Sheatsley (.1959) : HIF-NORC Household Survey: HIP vs GHI. Commencing in, and subsequent to, 1953 the Health Information Foundation (HIF) conducted a number of joint household surveys with the National Opinion Research Centre (NORC). One of these surveys, undertaken in 1955 in New York City, focussed on the membership of three trade unions. This was a dual choice situation, insofar as the union members were allowed a choice of membership: HIP or Group Health Insurance Plan (GHI).1^ The major difference between this and the earlier HIP study arose from the benefit structure of GHI which eliminated the greater part of the disparity in coverage for the populations under consideration. Thus, it would appear that the elimination of benefit discrepancies reduced the factors potentially accountable for any admission rate differentials to one, or more, of: organization and facilities; method of provider remuneration; physician access to hospital beds; particular incidence of illness patterns. The age-sex adjusted admission rates were, respectively, 63 and 110 for the HIP and GHI subscribers, while the ALS rates, similarly adjusted, were reported as 6.5 and 8.0, Striking differences were also observed in surgical admission rates; the rates were 43 per 1000 persons and 76 per 1000 persons, respectively, a remarkable 43% differential. 3 3 This study did appear to indicate that the extent of medical care coverage was not, as proposed by the authors of the previous study (iii), a significant explanatory variable for hospital utilization rate differentials. 14 (v) Falk and Senturia (I960): United Steelworkers of America. This study compared Kaiser Foundation Health Plan subscribers with populations insured through either BC-BS or a commercial plan in 1958. The populations were composed of steelworkers from various locales. Due to this lack of geographic standardization, the results must be interpreted 16 with extra caution. Reporting unadjusted admission rates, the authors showed Kaiser with a rate of 98 per 1000 population, as opposed to 135 17 for BC-BS and 150 for commercial insurance plans. The Kaiser rate of 98 is reduced to 90 upon deletion of one Kaiser group comprised largely of retirees. It is perhaps significant (see Roemer (1961a)), that Kaiser plans provide fewer acute care hospital beds per subscriber (approximately 2.0 per 1000 - Williams (1971) reports 1970 figures ranging from 1.4 in Ohio to 2:8 in Hawaii) than the U.S. average (approximately 4 per 1000). Unlike HIP and many other group plans, Kaiser owns and operates its own hospitals. One might be inclined to a prima facie conclusion that the lower bed/ population ratio inhibits admissions, some of which could be of the 'necessary' variety, with obvious implications for quality of care. However, the alternative direction of causality, which would argue that lower admissions give rise to a need for fewer beds, is supported by the evidence from other prepaid group practices. It is also interesting to note that Kaiser reported a lower average length of stay (6.4 days) than both BC-BS (7.6 days) and the commercial 3«t plan (.7.8 days) . (vi) Densen et al. (19601 ; HIP vs-GHI Like study Civ), this study compared Blue Cross members of HIP with their counterparts in the GHI plan. Unlike the former study, however, the data produced here were not based upon a household survey. Again, this was a dual choice situation, wherein members of the International Ladies Garment Workers Union were given the choice of HIP and GHI. The authors utilized 1956-1957 data, and again found a significantly lower utilization rate (70.2 admissions) for HIP members than for GHI enrollees (88.3 admissions; rates age-sex adjusted). There was little difference in ALS, and the difference in admission rates was largely derived from the female patients. As mentioned in the first chapter, this study provides the type of diagnostic disaggregation of utilization necessary for use with our estimated case cost figures. Thus, the data from the study receive further scrutiny in a later chapter. At this stage it is worth mentioning briefly that the authors reported a tonsillectomy rate for GHI subscribers of approximately double that for HIP members, and admissions for cases likely to involve surgery such as hernia, gall bladder, hemorrhoids and varicose 18 veins were also substantially lower for the latter group. (vii) . Densen :et al. (1962): HIP vs District 65 Unions This is the third of the HIP series and differs from the previous two primarily in that no significant differences were found in admission patterns. The study groups were all members of the District 65 Retail, Wholesale and Department Store Unions in New York who were, once again, in a dual choice situation: HIP or a union-sponsored fee-for-service plan covering both medical and hospital care. 3 S The age-sex adjusted admission rates were 64.3 for HIP, 63,9 for the union plan, while the comparable non-obstetrical rates were 49,3 and 51.6 respectively. Again, a, breakdown by diagnostic category is provided, and these data are utilized later. The rates reported in this study are in marked contrast to those in the majority of the research which preceded it. In particular, no significant utilization differential emerged. The study also generated doubts as to what, in fact, does lie behind the earlier significant differentials. However, the union differed from the BC-BS, GHI and other commercial plans in that, along with offering benefits coverage, it undertook (through a continuous education program aimed at both physicians and patients) to maintain effective control on utilization by stressing awareness of use and costs of facilities available, and by emphasizing the need for conservative use of resources. It would appear, then, that rigid surveillance of expenditures, combined with an ongoing educational program, was propounded as a viable alternative where group practice was not feasible. The expense entailed in the administration and operation of such a program (over and above medical expenses) was, however, not estimated, or at least was not reported. (viii) Williams et al. (1962); Columbia University Survey: Kaiser  vs BC-BS vs Commercial^  Employing 1958 household survey data (unstandardized for geographic locale) the authors found remarkably invariant admission rate experiences. The BC-BS sample was from the Newark, N.J. area, while the commercial subscribers were from various U.S. cities, and the Kaiser sample derived from blue collar union members in the San Francisco area. The reported admission rates were as follows: Kaiser - 79; Commercial - 71; BC-BS - 76; all unadjusted. 36 One fact i s immediately obvious. If we allow ourselves, for a moment only, to foray into an inter-study comparison,, we note the remarkably low Kaiser rate of 79, as compared to ear l i e r figures of 98 and 104. A l l standardization qualifications aside, this i s s t i l l a dramatic difference. Furthermore, the commercial and'BOBS rates are markedly lower than most of the other reported rates for non-PGP settings. We would venture to guess that this evidence should be c l a s s i f i e d as 'soft', insofar as no geographic standardization i s used and as i t appears that we may be witnessing downward biased rates due to the p o s s i b i l i t y of inaccurate survey responses. m particular, a l l three rates are lower than one might have anticipated, irrespective of their ordering. Finally, sample sizes were so small as to v i r t u a l l y eliminate any chance of finding 20 significant rate differences. (ix) Dozier et a l . (1964): California State Employees Retirement  System. This is another in the growing series of studies comparing Kaiser groups with other insurance and provision schemes. In this case, comparison was with BC-BS and a commercial plan but, unlike the previous study, the subscribers were a l l from a common area, being California state employees 21 and their dependents, or retired employees. The data are for the period 1962-63. The unadjusted admission rates were 62 for Kaiser, 104 for the commercial plan and 96 for BC-BS, and an ordinal ranking of t o t a l days stay rather than admission rates maintained the position of the Kaiser plans. 22 (x) Federal Employees Health. Benefits Program (FEHBP) . (I960's) The FEHBP has published u t i l i z a t i o n data since the early 1960's and these data, although often not geographically standardized, provide a nationwide picture of u t i l i z a t i o n rate differences. Prior to a recent publication by the FEHBP (jUedel et al;, 1975), the most widely cited reference on this program (Perrott, 1966)'. compared, among other things, non-maternity surgical procedure rates of employees covered by either BC-BS or group practice prepayment plans. The rates were, respectively, 70 and 39 (per thousand persons per year), unadjusted for age and sex, indicating close to'80% greater frequency of surgical procedures for those employees covered by BC-BS, and seeing fee-for-service physicians. When this 80% differential is analyzed, it turns out that approximately 1/3 of it is accounted for by higher rates for tonsillectomies and adenoidectomie (10.6 vs 4.0), appendectomies (.2.6 vs 1.4) and female surgery (hysterectomy etc: 8.2 vs 5.4). The most alarming single figure was the rate for tonsillectomies: two and one-half times as high for BC-BS subscribers. Perrott does not report general admission rates oir ALS, but rather total non-maternity days per 1000 persons per year. For the 1961-1962 period, the rates reported were 454 for those subscribers enrolled in prepaid group practice plans, 826 for BC-BS, and anywhere from 538 to 729 for various other plans. Similar spans were reported for 1960-1961 and 1962-1963. For later comparison purposes, we note that one particular group, GHA, had a rate of 459, approximately the average for the group practice 23 plans. In 1968, reporting on the 6th term of coverage and utilization for the FEHBP, Perrott and Chase found the fee-for-service plans incurring 135% more surgical procedures than the group plans (Williams, 1971, 83). For non-maternity admission rates, group plans reported 47 per 1000 subscribers while the BC-BS rate was 101. Other plans ranged from 72 to 90 (Foulkes, 1973a,24). Perrott's 7th term report C1970) confirmed the previously mentioned vast differences in several surgical rates: tonsillectomies 200% higher 3 8 in fee-for-service plans, appendectomies 5Q% higher, etc, CWilliams, 1971,93). Cxi) Roemer et al. (1972); PGP vs Provider vs Commercial In a study employing a somewhat different methodology, the authors found that commercial plan subscribers experienced the lowest admission rates, a result that was counteracted by the fact that group practice plans reported an ALS approximately 45% lower than the commercial plans. Whereas a number of the previously reviewed studies involved the analysis of admission experiences for a particular occupational group with a choice of medical plans, this particular study first isolated the plans to be considered and then chose random samples from within each plan. All subscribers were from a common geographic area and the samples did not differ significantly with respect to socio-economic composition. A serious problem. with comparability arises, however, in that the extent of benefit coverage varied among the plans chosen (see Roemer et al., 1972, 11-12). In particular, the prepaid group plans provided more extensive benefits than either the commercial (BC-BS) or provider (hospital or physician-sponsored) plans. Furthermore, the authors present evidence indicating that the commercial plans succeeded in enrolling a lower percentage of high risk persons than the other two plans. These factors should be kept in mind when considering the following admission and ALS figures from this study: Admissions ALS Commercial Plans 102 8.5 Provider Plans 150 7,4 Group Practice Plans 107 4.9 Whereas the majority of other studies indicated a lower admission rate for group practice, this report produced the most marked difference in 3 9 ALS rates. The result is that total days stay is considerably lower for group plan Cone of which was-KaiserI subscribers. As mentioned above the group plans appeared to contain a greater proportion of high-risk families, and therefore if populations were standardized for such an effect, we would expect a considerably lower relative admission rate for prepaid group practices. (.xii) Riedel et al. (1975): FEHBP Utilization Study A recent comprehensive investigation of the differences in hospital utilization patterns amongst FEHBP members has extended the earlier analyses of this particular group. The authors focus on subscribers to two plans: GHA and BC-BS. Not only do they report admission and ALS statistics, but they provide a detailed disaggregation of these figures, by diagnostic category. This data source is employed later in our project. Not surprisingly, in light of the earlier FEHBP reports, the reported admission rates of the group practice plan members were significantly lower than the corresponding BC-BS rates. The project's population samples derived from the Washington, D.C. area, for the years 1967-70. Coverage was similar, but not identical, under the two plans, but the extent of coverage inequality would [suggest that the benefit structure accounted 24 for no more than a minimal share of the following differences: Total Admissions Non-obstetrical Admissions GHA 69.6 51.3 BC-BS 121.8 99.8 Major diagnostic admission differentials (among those not explained by differences in coverage) occurred for Disorders of Menstruation, Respiratory Conditions and Diseases of Gallbladder, Admissions for -Tonsillectomies and Adenoidectomies were, as usual, markedly lower for the prepaid group practice, the GHA age-sex adjusted rate of 1,5 admissions per 1000 member years being significantly lower than the rate of 5.9 for BC-BS subscribers. (x i i i ) Health Maintenance Organizations (HMO's). - recent evidence There i s an extensive, and rapidly expanding, body of literature 25 devoted to the description arid evaluation of American HMO's. In particular, we have already reviewed some of the evidence pertaining to these institutions, as Kaiser, HIP and other PGP's f a l l within i t s definitional boundaries. These prepaid group practices, however constitute only one side of the HMO domain. The other ' h a l f i s comprised of, for example, the San Joaquin County Medical Society, a medical care foundation. The former sub-group of HMO's i s similar, in organization and ideology, to the Canadian C.H.C.'s. To repeat, perhaps the major difference i s the fact that patients prepay the H.M.O. i t s e l f for care. However, the medical care foundation (MCF), although classed as an H.M.O., diff e r s markedly from the C.H.C. ideology. While in a PGP "there i s only one insuring agency, the physicians are either salaried or share the income of the groups partnership, and the hospitals are ... (at times)... owned and managed by the plan", the medical care foundation "approach i s more varied, typically involving many insurance companies, physicians compensated by fee-for-service, and independent hospitals. The foundation i s considered an HMO, however, for i t undertakes to monitor the u t i l i z a t i o n and charges of the individual physicians and guarantees to third-party payers that annual per capita costs w i l l not exceed a specified amount" (Fuchs, 1974,138). As noted above, there i s no shortage of literature pertaining to HMO performance. Thus, we w i l l not further burden this section with a kl review of additional evidence deriving from studies of these organizations. Instead, we consider one extremely recent study in some detail, and refer the still interested reader to Roemer and Shonick (1973) for a comprehensive review of HMO performance primarily over the 1969-73 period. In a study which effectively standardizes for hospital bed availability (to be discussed in Chapter 3 as a potential cause of the utilization rate differentials), Wersinger et al. (1976) compare the hospital utilization experiences of three HMO-type settings. All three settings are in the Rochester area "with essentially the same access to the community's supply of hospital beds",26 and cover the spectrum of organizational entities which fall within the HMO definition. In particular, the authors compare the experiences of (i) a medical care foundation (MCF) (ii) a PGP located in a single health centre (iii) "a decentralized network of health centers" (Wersinger et al., 1976, 722). Details on each organization will not be replicated here, but it is worth noting that peer review in (i) occurred only for ambulatory services, and not for inpatient services, during the study period. The insurance burden was carried by BC-BS, and physicians were reimbursed by fee-for-service. We might also expand briefly on the health care network involved in (iii), as such an organizational entity has not, to this point, been discussed. Termed the Rochester Health Network (RHN), this system contains seven distinct group practices varying in staff composition and location (one is hospital-based), and in method of remuneration (a mix of prepayment and fee-for-service). Blue Cross carries the hospital insurance responsib-ility for the RHN, and ambulatory care (other than outpatient hospital services) financial risk is shared by the RHN and Blue Shield. <*2 In addition to inter<-plan comparisons, the authors also strive to provide comparable BC-BS area population utilization figures. However, although benefit structure was similar amongst the three plans, it was more extensive than that available through BC-BS. The age-standardized 27 admission rates were reported as follows: Admissions per 1000 persons per year Difference Blue Cross f roir Rate Blue Cross, 1972 74.4 MCF, 1974 85 +14. 2% PGP, 1974 54 -27. 4% RHN, 1974 70 - 5. 9% MCF, 1973-4 fiscal year 79 + 6. 2% PGP, 1973-4 fiscal year 48 -35. 5% RHN, 1973-4 fiscal year 63 -15. 3% The fiscal year/calendar year distinction is made by the authors since the HMO plans commenced operation in July of 1973. Thus, we may expect patterns peculiar to the start-up period which might be partially eliminated through observation of a slightly later period. In particular, "the calendar year was added because of a larger enrollment base and because it avoided the initial "warm-up" period when patients were taken in for first evaluations with possible delays in scheduling admissions" (Wersinger et al., 1976, 725). It is of primary interest to note that the PGP plan's age-adjusted admission rates were 36%-39% lower than the comparable MCF rates and 23%-24% lower than the RHN rates. As the authors correctly emphasize, and as we have already mentioned, the combination of no financial risk to organization or member physicians (in the MCF case), and the lack of i*3 hospital procedures peer review are likely to be jointly responsible for the former differentials. The rates included in the Summary Table (Table 2 .1 ) are only those of the BC-BS and PGP schemes, so as to ensure some degree of comparability, with earlier studies. Finally, no diagnostic disaggregat-ion was included in the study. This concludes our look at U.S. based experiences over the past quarter-century. Despite the difference in health care financing, Canadian experience, such as it is, has been generally similar to that below the border. However, before considering the evidence, it may be useful to emphasize certain factors related to U.S./Canada data comparability. First, we recall that the panel membership issue may cause health clinic data to be downward biased (at least when compared with a plan where financial ties to a particular institution do exist, as in the U.S.). Second, except where otherwise stated, Canadian admission or separation rates refer to those for adults and children and are thus comparable with American rates which also exclude newborns. Finally, there is some question as to the comparability of the chronic/acute composition of beds in the hospitals supplying the data on the respective sides of the border. Canadian hospital data are commonly disaggregated by hospital type, pertaining to General and Allied Special, Mental, Tuberculosis, and Government of Canada hospitals. The former group of hospitals supply the Canadian data relevant to this thesis. The most closely corresponding group of hospitals across the border is referred to as Non-federal Short-term General and other Special. The degree of comparability of bed make-up in these two groups is, unfortunately, unknown. Another category of hospital in the U.S. is labelled Non-federal Long-term General and other Special. It is possible I l l * that some patients admitted to such a hospital, and thus not appearing in our data, would (given the same disease condition in Canada! have been admitted to a hospital in the General and Allied Special category. However, as mentioned earlier, our primary consideration has been, and continues to be below, intra-study comparisons. The above comments do bear on comparability of rates reported in study C x i v l . (xiv) Quebec Commission on Health and Social Welfare (1970). This commission reported comparative admission and ALS figures as an attempt to emphasize the relatively high rates experienced in Quebec. In 1966, the reported admission rate for all of Quebec was 138.4, close to the 1964 average figure of 135.2 for the U.S. In sharp contrast to these figures are the 1964 figures for Kaiser and HIP, 87.7 and 84.0 respectively. Whereas Kaiser patients remained in hospital for an average 6.2 days in 1964, the corresponding Quebec figure for 1966 was 10.3. (xv) Anderson and Crichton (1973): Saskatchewan Community Health  Association Clinics. The authors conducted an investigation into the effects upon hospital utilization of three large comprehensive care community clinics, in Prince Albert, Saskatoon and Regina. They considered five regions in the province, three of which contained one of the above community clinics. In region 1, a major urban centre, the comprehensive community clinic separation rate was 144.5 per 1000 beneficiaries for 1967, while the corresponding general practice figure was 227.5 (Anderson & Crichton, 1973, 241). . Two physician-sponsored comprehensive clinics in this urban centre were reported to have rates of 218.4 and 207.1. Region 2, a major urban centre which contained a medical school showed rates of 157,8 and 164,9 respectively for a comprehensive community clinic and the general practitioner population. <• 5 Region three contained the third community clinic, as well as two physician-sponsored clinics. There were insufficient solo general practitioners in this region to include them; the separation rates were 235.9 for the community clinic, compared to 280.2 and 289.2 for the other clinics. It is evident that intra-regionally, the community clinics showed lower separation rates. However, the inter-regional disparity in community clinic rates themselves is striking. The third community clinic was in a rural location, where it is common for hospitalization rates to be higher. This is the likely explanation for a good deal of the disparity. The study also found lower rates of elective-type surgery in the comprehensive clinics, although the clinics also undertook more investigative procedures and referrals. (xvi) Hastings et al. (1973a); Sault Ste. Marie CHC vs commercial. This is the fourth of the five studies which provide utilization statistics by diagnosis, suitable for application to our case cost figures. The study population, from 1967, is, like those of the Densen studies, derived from a union local (this one being in Sault Ste. Marie, Ontario, in the Algoma Territorial District) in which members were offered a dual choice of medical insurance coverage: Sault Ste. Marie and District GHA or a plan administered by the Prudential Insurance Company of America. The former offered care through a community health clinic, while the latter reimbursed private practice physicians on a fee-for-service basis. All hospital care costs were borne by the Ontario Hospital Services Commission. In this study, the geographic location and extent of coverage were virtually identical, The only drawback, from this thesis' point of view, was the small sample size (approximately 33QQ persons) which precluded a fine 29 diagnostic breakdown being reported. However, the utilization disaggreg-if 6 ation by diagnosis corresponds to the broad ICDA categories, and an attempt i s made to aggregate our cost data into these categories so as to estimate expenditure impact of the u t i l i z a t i o n d i f f e r e n t i a l s . Discharge rates were reported as follows CHastings et a l . , 1973a, 941: Rate per 1000 persons per year GHA 109.4 Prudential 136.4 The ALS rates were 8.95 for GHA, 9.32 for the Prudential subscribers. The major difference in discharges derived from respiratory conditions. GHA subscribers also experienced significantly fewer surgical procedures involving Pharynx, Tonsils and Adenoids, as witness (Ibid., 95): T & A's per 1000 children  aged 10-14, per year GHA 8.8 Prudential 26.7 Algoma D i s t r i c t , 1964-69 27.3 The GHA subscribers underwent these surgical procedures much less frequently than either their Prudential counterparts, or the general Algoma d i s t r i c t population. (xvii) McPhee (1973):' Saskatchewan Community Health Association Clinics, An investigation by J.L. McPhee into the hospital u t i l i z a t i o n experience of the three Saskatchewan CHAC's investigated by Anderson and Crichton, produced f a i r l y similar results. Although positive c l i n i c , identification was not included in the lat t e r study, one can at least identify the Prince Albert c l i n i c through a comparison with this present study. In any case, the hospital discharge rates ("including only beneficiaries who contacted physicians at least twice during the study period), adjusted for age and sex, were as follows: h7 CHA Non-rGHA Prince Albert 235 303 Saskatoon 173 226 Regina 186 229 Although no diagnostic breakdown of separations or days stay is included in the study, such figures were obtained for use in a later chapter. (Analytic difficulties, arising from small sample size and the large number of diagnostic categories by which cases were recorded, are discussed in detail in Chapter 8).. The preceding review is not an exhaustive survey. However, it presents the majority of the studies which have appeared in the past twenty five years. Other data are provided in Donabedian (1969), Klarman (1963), MacColl (1966) and Roemer and Shonick (1973). The Kaiser Foundation frequently publishes statistics similar to those reported here, and the references contained at the conclusion of any of the above studies provide additional data sources. As mentioned earlier, we have attempted to collate and summarize certain of the statistics mentioned in this section. They appear in Table 2.1. A recurring pattern has suggested itself in most of the data reviewed above. In fact, the incidence of utilization differentials 'favouring' the PGP/CHC settings suggests that there are forces of a non-random nature at work here. The data are, at the very least, consistent with the hypoth-esis that PGP's and CHC's generate lower rates of hospital utilization than comparable alternative plans employing private practitioners. A number of the authors of the above studies have suggested various plausible explanations for the observed differentials. The intent of the TABLE 2,1; Summary of Hospital Utilization Data Study # and date Admission* Rates of 1000 patients of: Average Lenth of Stay for patients of: U.S. PGP or CHC private practice/ private insurance % difference PGP or CHC private practice/ private insurance Comments (i) 1952 70 - 104 122 17.3 to 42.6 6.2 - 7.0 7.4 populations not matched; benefits not the same. (ii) 1957 74 67 -10.4 10.6 11.6 populations not matched; benefits not the same; household survey/ . 81 74 - 8.6 adjusted for deaths not recorded by survey . (iii) 1958 77.4 95.8 23.8 7.6 7.2 benefits not same; crude rates . 81.1 93.9 13.6 age-sex adjusted rates . (iv) 1959 . 63 110 42.7 6.5 8.0 dual choice; fairly com-parable benefits; household survey; age-sex adjusted rates 43 76 43.4 surgical admissions only . ^  0  TABLE 2.1 (Cont'd) Study # and date Admission* Rates per 1000 patients of: Average Length of Stay for patients of: U.S. PGP or CHC private practice/ private insurance % difference PGP or CHC private practice/ private insurance Comments (v) 1960 98 . 135 - 140 27.4 to 53.1 6.4 7.6 - 7.8 common employment group but no geographic standar-dization; unadjusted rates. (vi) 1960 70.2 88.3 20.5 10.4 . 10.8 adjusted for age, sex and union local composition• (vii) 1962 64.3 63.9 - 0.6 8.3 8.4 adjusted for age-sex and union local composition. (viii) 1962 79 71 - 76 -11.3 to - 3.9 7.7 7.6 - 8.6 populations not matched; household survey. (ix) 1964 62 96 - 104 35.4 to 40.4 - - geographic standardization, unadjusted otherwise. (xi) 1972 107 102 - 150 - 4.9 to 28.7' 4.9 7.4 - 8.5 unstandardized subscriber groups, particularly with regard to risk classes. to Table 2.1 (Cont'd) Study # and date * Admission Rates \ 1000 patients o per f: Average Length of Stay for patients of: U.S PGP or CHC private practice/ private insurance % difference PGP or CHC private practice/ private insurance Comments (xii) 1975 69.6 121.8 42.9 6.6 6.5 standardized for age and sex. Benefit structures similar. Geographic standardization. (xiii) 1976 48 - 54 74.4 27.4 to 35.5 limited procedures (medical/ surgical only); age stan-dardized; geographic standardization; benefit structures somewhat different. CANADA-U.S. (xiv) 1970 84 - 87.7 138.4 36.6 to 39.3 6.2 10.3 gross rates, no standardi-zation. (xv) 1973 144.5 157.8 235.9 227.5 164.9 280 - 290 36.5 4.3 15.8 - 18.7 9.48 10.73 9.25 9.43 10.73 10.2 - 13.4 age-sex adjusted, geogra-phic, benefit coverage standardization. S TABLE 2.1 (Cont'd) Study # and date * Admission 1 Rates per 1000 patients of: Average Length of Stay for patients of: U.S. PGP or CHC private practice/ private insurance % difference PGP or CHC private practice/ private insurance Comments (xvi) 1973 109.4 136.4 19.8 8.95 9.32 age-sex, geographic, benefit coverage, socio-demographic standardiza-tion. (xvii) 1973 235 303 22.4 9.1 9.7 age-sex, geographic, 173 226 23.5 7.9 8.6 benefit coverage standardi-186 229 18.8 9.1 9.4 zation. * Admission or Discharge 5 2 f o l l o w i n g chapter i s t o c o n s i d e r r i n a more r i g o r o u s f a s h i o n , numerous p o t e n t i a l c a u s a l f o r c e s . The evidence o u t l i n e d i n t h i s . c h a p t e r w i l l f a c i l i t a t e the e l i m i n a t i o n o f many o f these p o t e n t i a l e x p l a n a t o r y v a r i a b l e s . Chapter 2_ - Footnotes 1. The format of this section i s similar to that of Roemer (1965) who examined the primary care f a c i l i t y choices available to the American patient, 2. In Ontario, for example, recent Ministry of Health data indicate that, of 15000 physicians, 7780 are catalogued as solo practitioners. This figure undoubtedly underestimates the number actually practicing i n this manner, as the 7220 other physicians include those with any type of group or c l i n i c a f f i l i a t i o n . (Source: personal correspondence with Mr. B. Leach, Ontario Ministry of Health). : 3. The distinction between the labourer-entrepreneur role of the physician i s crucial throughout the discussion of this chapter. Evans (1975b) elaborates on the dental analogy. 4. This i s not s t r i c t l y true, insofar as the CHC ideology often includes an integated role for non-medical services, such as social assistance. 5. This refers to the payment of a fixed pre-arranged sum, by the patient, in return for which he/she i s 'covered' for a l l care provided by the group. 6. The community health centre i s ideally visualized as "a f a c i l i t y , or intimately linked group of f a c i l i t i e s , enabling individuals and families to obtain i n i t i a l and continuing health care of high quality. Such care must be provided i n an acceptable manner through a team of health professionals and other personnel working in an accessible and well-managed setting..." (Hastings et a l . , 1973c, 1). Physicians are reimbursed in a variety of methods. For a more detailed discussion of the ideology, consult Hastings et a l . (1973c, 1-11). 7. The following discussion i s by no means the f i r s t literature review of i t s kind. In fact, i t draws extensively from Donabedian C1965, 1969) and KLarman (19631, a l l of which are reviews of a similar nature. However, this review extends these three American studies to incorporate more recent evidence and, in addition, provides a review of 'comparative Canadian experiences. These figures are all borrowed from Klarman (.1963, 956 - Table 2). The PGP's considered were Kaiser, Group Health Cooperative CSeattle), and Labour Health Institute (St, Louis). HIP was designed to provide the subscriber with comprehensive medical care at any location (physician's office, hospital, or home), provided by any one of approximately thirty medical groups in the New York city area. The groups were reimbursed on a capitation basis (an agreed-upon remuneration per patient-year, regardless of incidence of consultation), and individual physicians were not paid on a fee-for-service basis. The interested reader is referred to Densen et al., (1958a) for further details, and to Donabedian (1965, 69) for a brief summary of this particular study. Donabedian (.1969) apparently forgot to remind the reader that this adjustment was undertaken for the figures which he reports, so that his two studies report identical figures but one set is stated to be standardized; the other set contains no explanatory note. Blue Cross (BC) is the most common hospital insurance program in the U.S. Blue Shield (BS) was the medical care insurance program. However, in the majority of cases it was restricted to coverage of in-hospital surgical and physician care, thus excluding coverage for most ambulatory care. See Somers and Somers (1961) for a historical account of BC and BS development, scope of benefits etc. See MacColl (1966, 206). The GHI plan provided more extensive ambulatory medical coverage than Blue Shield in that subscribers were covered for general physician and specialist services in the home or office, as well as in the hospital. As was the case with Blue Shield, GHI reimbursed physicians by fee-for-service, and subscribers had free choice of any physician. We should qualify the final remark, howeyer, as consultation with a non-GHI-participating physician entailed considerable risk-^ bearing on the part of the consumer. In a situation similar to that for 'opted-out' physicians in Ontario, such non-GHI physicians could charge above and beyond the agreed upon GHI fee schedule, in which case the consumer was 5 5 responsible for the difference,. The GHI scheme is described at considerable length by Densen et a l , (i960), 14. The data and information on this study have been compiled from Klarman (.1963). and Donabedian (1965) . 15. For a comprehensive discussion of the Kaiser plan, the largest PGP in the United States, the reader might consult Williams (1971). Further information on Kaiser i s scattered throughout MacColl (1966). 16. See Donabedian (1965, 57) for a clear i l l u s t r a t i o n of the danger involved in drawing conclusions from inter-regional rate comparisons. Using data from this particular study, his breakdown indicates that BC-BS subscribers from the same union but from 21 different geographic regions, experienced average regional admission rates per 1000 subscrib-ers ranging relatively evenly over the range 120-189, for a common time period. 17. The rate of 98 admissions per 1000 population appears markedly higher than the rates reported for other PGP settings. This i s confirmed by the fact that the high end of the 70-104 range cited in study (i) was occupied by none other than Kaiser plans. No immediate explanation comes to mind and, in any case, we are not particularly interested in inter-study comparisons. 18. Donabedian (1965) thoroughly dissects, analyses and retabulates the diagnostic data from this a r t i c l e . See pp. 59-60 and pp. 22-25, in particular. 19. Again we employ second hand information, compliments of Donabedian (1965) and Klarman (1963). The former source provides the figures for our study (ix), below, as well. 20. Number of cases ranged from 168 to 184, magnitudes that "would preclude the finding of differences i n hospital use of a magnitude comparable to those found in the earlier HIP studies, even i f they existed" (Klarman (1963, 962).) . 21. Details on the Retirement System may be found in MacColl (1966, 203-7). 22. The Federal Employees Health Benefits Program is a voluntary, U.S. government sponsored health insurance program for its employees. Employees have the option of choosing membership in one of several different plans, among them BC-BS and group practice plans. At present, at least nine million persons fall under its coverage. See Riedel et al, (1975, xii-xiiil for further details. 23. The membership of GHA (Group Health Association, Inc., Washington, D.C.) is made up largely of federal employees falling under the FEHBP. It is consumer-owned and subscribers prepay for comprehensive care over a certain period. A brief discussion of this group plan is contained in Riedel et al. (1975, xiii). 24. Riedel et al. (1975, 19-21). Figures for total admissions are age-sex adjusted. 25. The literature is, in fact, so extensive as to merit its own bibliography. See U.S. Department of Health, Education and Welfare (1974), the most recent version of this bibliography. More recent evidence is provided by Wersinger et al. (1976), discussed below. 26. Wersinger et al. (1976, 722). 27. The 1972 Blue Cross under 65 years sample was used as the base for age standardization. The rates reported here are exclusive of the over 65 groups and obstetric, nursery and psychiatric admissions. The over-65 group was excluded due to the low enrollment from that population in the prepaid plans. 28. Commenting on the apparent lack of a consistent pattern amongst the various clinics studied, Foulkes (1973a) suggests that the probable explanation may be found in the failure, at that time, of the clinics to institute a prepayment system. The clinics were still operating on a fee-for-service basis; in other words, one of the major parts of the ideology of the CHC concept was still missing. The clinics had to generate operating income in the same manner as a solo fee-for-service physician, although the physicians themselves were not paid in this manner. 5 7 29. Further discussion of data limitations is delayed u n t i l we reach the point of applying cost figures to the u t i l i z a t i o n s t a t i s t i c s reported in this study. 5 8 Chapter 3: Hospital Ut i l i z a t i o n - Behavioural Considerations The admission of a person to hospital, as an in-patient, i s preceded by the interaction of numerous factors which leads to determination of the 'need' for hospitalization. This chapter i s devoted to an investiga-tion of many of the variables potentially involved i n this interaction. An attempt i s thus made to isolate the dominant behavioural factor (or factors) from within this process. This f a c i l i t a t i e s determination of the major variables underlying the apparently one-sided data reviewed in the preceding chapter. A distinction i s essential here between determinants of hospital expenditures once a patient has been admitted to hospital, and those responsible for the admission i t s e l f . In particular, the same factors w i l l l i k e l y affect both, but with different weights. Given a physician's admitting privileges and the a v a i l a b i l i t y of an appropriate bed, patient admission may largely be determined by medical assessment of the relevant condition, family influence and patient preferences. Eventual length of stay, and expenditures as a result thereof, w i l l be influenced, to a far greater degree, by the interaction of nursing staff, hospital policy as determined by the board of trustees and administrator, house medical staff, attending physician, and relevant non-medical staff personnel unions. We w i l l limit our attention to the process underlying inpatient admission,^" and w i l l u t i l i z e the framework established by Roemer and Shain (1959) in 2 the following discussion. 3.1 Patient, Physician or Hospital: Who 'Generates' the Data? We may usefully consider an admission to hospital as the f i n a l outcome of a process of demand and supply interaction, wherein the patient i s almost exclusively responsible for the i n i t i a t i o n of each medical care i l l n e s s episode. If we confine our attention for the moment to conditions brought to a physician's attention by the patient, rather than to those 'discovered' i n the course of a routine physical examination, we see that i t i s the patient*s perception of a 'need' for some sort of care which precedes contact with the health care delivery system."* Once the patient i s aware of an i l l n e s s or condition requiring professional care, he (she) commonly enters the medical care 1 system' by contacting a nurse of physician practising i n one of the organizations . on our previously delineated spectrum. At this point, the attending physician(s) commences an inter-action with the patient which w i l l determine the extent of future demands upon medical care resources. In fact, i t i s often contended that this 4 point marks the beginning of a physician-dominated demand process. The following discussion expands on these introductory remarks by considering the influence of each of the hospital, physician and patient 'sectors' in 'creating' the utilization., differentials reported i n the preceding chapter. We take each i n turn: 3.1.1 Patient Factors The immediately obvious, and perhaps dominant, variable amongst those categorized as patient factors, must be the incidence and prevalence of i l l n e s s . This refers to the natural occurrence and existence of the mix of illnesses within a given population group. Prevalence refers to the i l l n e s s present in the group at a given point in time, while incidence i s a rate of occurrence concept and i s thus dependent on a particular time period. Either measure w i l l clearly influence general hospital u t i l i z a t i o n . But the extent to which we might attribute the differences in u t i l i z a t i o n experiences, to i l l n e s s incidence i s less obvious, Inmost of the studies cited, there was no evidence to indicate that the incidence and prevalence of i l l n e s s amongst the matched populations was anything but random. This statement cannot be extended to studies which f a i l e d to.standardize for geographic influence (i.e. studies comparing subscriber groups from different regions!, but we are not particularly interested i n pursuing those studies for just that reason. To the extent that i n the cases of interest the matched subscriber groups were taken from common locales and were even, in some cases, from similar employment settings, i t appears unlikely that t h i s factor i s responsible for anything more than a random, and minor, proportion of the observed differences. This conclusion, i s reinforced by the repeated incidence of similar d i f f e r e n t i a l patterns. The same conclusion i s suggested for a second factor, that being a patient's attitude toward, and awareness of, i l l n e s s . There i s evidence to indicate that educational level i s positively (although not necessarily linearly) correlated with willingness to seek medical care for a given condition.^ However, to the extent possible most of the studies reviewed in Chapter 2 used matched populations, which would seem to preclude the p o s s i b i l i t y of any major influence from this factor. In addition, Densen et a l . (1960) reported that their study populations were questioned in an attempt to ascertain the likelihood of factors other than educational level influencing il l n e s s attitudes. "The results of the survey indicate that the two groups were very similar in how they rated their own health status, i n their general perceptions of health, their attitude towards the use and value of medical care" (Densen et a l . , 1960, 1722). We thus group this factor with the f i r s t , in a category of variables considered to contribute to the u t i l i z a t i o n differentials i n no more than 6 a small,, ramdom fashion. The direct medical care costs to the patient or, equivalently, the range of benefit coverage provided by the subscriber's insurance plan, may be thought of as having dual influence on hospital u t i l i z a t i o n . F i r s t , 6 1 the range of insured hospital services may, through, the. well-known moral hazard process, influence use. But in addition to this factor the extent of out-of-hospital insurance coverage may influence a patient's use of 7 in-hospital f a c i l i t i e s . Wherever possible, the previous chapter highlighted those times when i t appeared that there was unequal in-hospital procedure benefit coverage between study populations, but the second factor merits considerably more attention. Advocates of extended ambulatory coverage have argued that such extensions would remove the financial incentive to hospitalize. In particular, we r e c a l l the f i r s t HIP study reviewed in the last chapter wherein Blue Shield subscribers were covered only for in-hospital medical care, while HIP enrollees prepaid for a l l medical care i n the hospital, home or o f f i c e . The authors suggested that this coverage discrepancy provided a major explanation for the observed in-patient u t i l i z a t i o n differences. There i s other evidence, however, which indicates that this factor i s not a variable of significant influence. The second HIP study (Densen et al.,1960) considered populations with similar coverage, yet the u t i l i z a t i o n differences persisted. Lewis and Keairnes (1970) and H i l l and Veney (1970) report on an experiment i n which additional out-of-hospital service coverage was provided to a population of Blue Cross subscribers, with no concomitant change in hospital u t i l i z a t i o n patterns, and a surprising 38% increase in surgical admissions for single subscribers. Roemer (1958) undertook a study of four types of coverage in Saskatchewan, and found a positive correlation between the extent of ambulatory coverage and the rate of hospitalization. The latt e r two studies both suggested that increased physician contacts resulting from the extended benefit coverage was at least p a r t i a l l y responsible for the resultant hospital u t i l i z a t i o n s t a t i s t i c s . The inference was that increased v i s i t s to a physician as a result of coverage extension may, particularly in the short run, result in added detection of disease requiring hospitalization. Finally, Hastings et al. (1973a) provided evidence indicating that tonsillectomy rate differences could not be explained by the out-of-pocket expense to patients and, in general, the evidence from Canadian sources in which the utilization differentials persist under uniform coverage, provides further support for suggesting this to be a variable of minimal influence. It is also interesting to note that by the end of 1969 seven of the ten provinces were participating in the medical insurance programs. By 1972, all ten provinces plus the Yukon and Northwest Territories were participating. This extension of medical coverage appears to have influenced hospital utilization, as illustrated below: Table 3.1: Admissions per 1000 population to Canadian General and Allied Special Hospitals, 1967 - 1973 Year Number of Admissions Per 1000 Population % Increase from Previous Year 1967 151.5 -0.33 1968 155.1 2.38 1969 156.4 0.84 1970 161.1 3.01 1971 164.9 2.36 1972 164.8 -0.06 1973 165.6 0.49 SOURCE: Admissions statistics from Lefebvre (1976, 31) 6 3 This suggests that the introduction of medical insurance led to larger than average increases in admissions during 1970 and 1971, In the lat t e r year, admission rates per capita were running 5.4% higher than in 1969. There i s evidence that marital and family status, and other socio-economic factors, influence the rate of hospital u t i l i z a t i o n . For example, for given age levels and insurance coverage, single, widowed and divorced 8 persons tend to u t i l i z e hospitals more frequently than married couples. However, our review of the past chapter embodied no evidence indicating that the proportions of the study populations constituted by this segment of subscribers varied in any significant way. One e x p l i c i t breakdown (Riedel et a l . , 1975,33) showed a 1.5% difference in the proportion of BC-BS families of size one compared to the same proportion of GHA families, the former group having the higher figure. However, this small difference in unlikely to have influenced the u t i l i z a t i o n differentials i n a major way, especially insofar as the authors' Appendix Table 5, p.34, indicates that the differences in single contract non-obstetrical admission rates per 1000 member years were significant for a l l 5 year age categories (at the .05 level), the BC-BS rates being higher i n each case. The indication is that the greater proportion of single contracts in the BC-BS membership was not l i k e l y to account for much of the overall 'surplus' i n BC-BS admissions per 1000 member years, since a similar 'surplus' occurred within the single contract subset. There i s also no evidence indicating that any other socio-economic factors would have contributed more than minimally to the u t i l i z a t i o n d i f ferentials. Although certain studies have found evidence of an inverse relationship between socio-economic level and amount of hospital care received, the HIP studies arid the others from which we derive our data constructed generally matched populations from common areas and back-grounds. Again, any differential influence is likely to be minimal. While not a 'patient factor* in the strict sense of our discussion here, subscriber group composition in the studies reviewed in Chapter 2 may be held responsible for hospital utilization patterns. Densen et al. (I960) considered the composition factor in their quest for the explanatory variable responsible for their.reported statistics. They raised the "possibility that some type of selection process took place when the members of the union made their choice of medical care plan" (Densen et al., 1960,1712). As noted earlier, they provided evidence suggesting that there was little support for this notion. Roemer and Shonick (1973) review further evidence, indicating again that this potential influence has apparently not been operational in studies cited. In particular, it has been argued that PGP's and CHC's show lower hospital utilization rates because they select low-risk patients. However, Roemer and Shonick (1973) review a study undertaken in southern California in 1968 in which the authors found that "significantly higher proportions of persons with generally greater risk of sickness were members of PGP organizations than were in commercial insurance or provider-sponsored (BC-BC) plans. This was reflected by slightly higher proportions of plan members aged 41 years and over, substantially higher proportions of families with a history of one or more chronic illnesses ... and somewhat greater proportions of persons scoring high on a 'symptom sensitivity test'" (Roemer and Shonick, 1973,277). While admittedly not sound empirical evidence, these examples tend to suggest that this factor, too, has had minimal influence on the utilization patterns. If there is any consensus deriving from the above discussion of patient influence on the hospital utilization differentials, it must be that such influence is either non-existent or minimal. We now turn to look at the providers of care. 3.1.2 Physician Factors It has been argued at various times that PGP physicians i n the U.S. and CHC member physicians in Canada are denied equal access to hospital beds, through restrictions on admitting privileges as a result of peer pressure. It would then follow that this i s the behavioural factor responsible for lower rates of hospital u t i l i z a t i o n amongst such subscribers Two particular examples come to mind. F i r s t , the available bed/population ratio for the Kaiser Permanente plan (which owns i t s hospitals) enrollees, i s considerably lower than the U.S. average (approximately two beds per 1000 population vs. upwards of four for the U.S.). Second, c r i t i c s of the HIP studies have suggested that HIP-affiliated physicians were discriminated against when i t came to receiving admitting privileges i n the New York area hospitals. Densen et a l . (1960) delved further into this question, finding that amongst HIP general practitioners, 80% were a f f i l i a t e d with at least one municipal hospital, considerably higher than the 44% rate for a l l family physicians in the New York c i t y area. However, Klarman (1963) points out that the more illuminating s t a t i s t i c s would have been those for specialists (as they do the majority of admitting) and, at any rate, i t does not follow that a f f i l i a t i o n can be equated with access. 10 . . This i s a debate which s t i l l persists, and i s largely an i d e n t i f i c a -tion problem - do we include access to hospital beds as a 'physician factor' or number of hospital beds as a.'hospital factor'? Each has i t s own unique considerations, but the two are also closely related and, as in.the Kaiser case, i t i s d i f f i c u l t to ascertain direction of causality. Further discussion of the hospital bed issue i s l e f t for consideration with the hospital factors. For the time being, we retain bed access as a potential major explanatory variable. Unfortunately, the lack of further evidence precludes assigning any relative weight or importance to it. 6 1 It is widely acknowledged(and intuitively appealing) that the number of physicians in an area is positively related to the number of hospital admissions. It has also been shown that the population/physician ratio 11 may bear a negative relationship to hospital admissions. However, our concern is not with such absolute relationships but, rather, with the differential impact of this effect across population groups. The evidence reviewed in the previous chapter did not suggest that access to physicians was unequal or that the numbers of physicians serving each of two (or more) f subscriber groups in a given study were significantly different. Therefore, while we acknowledge the importance of this factor as a determinant of hospital utilization we suggest it be added to the growing list of 'minimal influence' factors. While physician access may not have differentially influenced the matched population groups, in most cases the physicians in question were reimbursed in a number of ways. Recall that in our earlier (Chapter 2) discussion of study (iii), two of the three major differences between the two population groups being studied were the mode of practice organization and the method of payment to the physicians who supplied care to the groups. The third major variable isolated was the marked difference in the extent of benefit coverage, a factor which was subsequently eliminated, primarily due to evidence from the second HIP study (vi). According to Densen et al. (1958), this leaves only two possible explanations for the utilization statistics. Our discussion to this point has failed to be quite that decisive, but it is agreed that the medical remuneration factor is a potentially major influence underlying the idata of the previous chapter. In particular, this is one factor for which the studies of the past chapter never standardized. Without becoming embroiled in the voluminous literature on methods 6 7 of physician remuneration, we consider this factor in somewhat greater 12 detail. The many discussions of this subject revolve almost exclusively around four alternative schemes: fee-for-service, capitation, salary and the.less common case payment. Not a l l of the related work makes the distinction between payment to the medical practice, and payment to the 13 physician as an input to that practice. Here we attempt to focus on both while maintaining the distinction. In that regard, the u t i l i z a t i o n studies reviewed in this thesis commonly involved a comparison of two or more modes of health care delivery which embodied the f i r s t of these methods, fee-for-service, and one or more of the remaining schemes. But in what form was this comparison manifested? If we think of a physician as the entrepreneur in a private practice, who concurrently pays himself an implicit wage in return for his time, then there i s no distinction, through  payment to the physician as factor input, between that mode of delivery and an organization i n which a doctor i s paid a salary, regardless of whether the organization i t s e l f i s reimbursed by fee-for-service, capitation, or case payment (a fixed amount for the care of an entire episode, or case, of i l l n e s s ) . Thus, the distinction i s not e x p l i c i t l y between methods of physician remuneration for practice time, but between methods of p r o f i t , or income, sharing. The private practitioner receives practice profits net of expenses, in addition to his shadow wage, i s this distinction which sets him apart from his counterpart who receives a salary, or even (to a lesser extent) receives a share of residual p r o f i t s . In effect, then, the comparisons, noted above were often between physicians who received only an e x p l i c i t wage (jLe, salary), and those who had at least a p a r t i a l l y vested interest i n practice pr o f i t s . The physicians in the PGP/CHG settings are commonly reimbursed by 6 8 14 salary, or some pre-arranged income sharing plan. The organizations themselves, in the U.S., are financed on a capitation basis. In Canada the CHC generally arranges a global budgeting agreement with the relevant government agency dies). In contrast, BC-BS and commercial plans, as well as the third party in Canada, reimburse private practices according to agreed-upon fee schedules, on a s t r i c t l y fee-for-service basis. Mode of practice reimbursement, and the physician's role within the practice organization, contain the potential for being significant factors in explaining the di f f e r e n t i a l use of hospitals. This i s due to the basic conflict of interest with which a physician/entrepreneur i s confronted. As an entrepreneur, his incentive i s l i k e l y to be the maximization of net receipts, (subject to other variables in his u t i l i t y function, to be discussed l a t e r ) . As a physician and provider of care to the often uninformed consumer, his incentive ought to be to undertake whatever the patients' interests and conditions warrant, and no more. The resultant joint incentive structure would appear to favour throughput maximization of those services which are both highly remunerative and of l i t t l e or no risk (or perhaps help) to the patient. Such services might include hospital admissions for elective surgery, since the hospital provides inexpensive resources (including own-time, as many patients can be vis i t e d i n one locale), while elective surgery, by i t s very name, suggests surgical procedures of minimal risk (and often minimal value) to health status. (The interested reader might find Williams 0.971) enjoyable). The.basic tenor of this discussion i s quite strikingly supported by the data reviewed in Chapter 2, In addition, Monsma's (1970) seminal a r t i c l e on the relationship between demand and marginal revenue for physicians' services i l l u s t r a t e d that empirical support exists for his 6 9 hypothesis that "the demand for physicians' services i s influenced by the marginal revenue physicians receive..." CMonsma, 1970, 145). Further affirmative evidence supporting the importance of this factor has appeared in two analyses of a natural experiment in Baltimore. Although not s t r i c t l y pertinent to hospital u t i l i z a t i o n , the evidence i s relevant to this remuneration discussion. In 1963 Baltimore's medicare program was experiencing d i f f i c u l t y with a capitation system, due to the inequitable distribution of older persons across physician workloads. Those physicians caring for a proportionately large number of these patients were being inadequately reimbursed for the additional services they were required to provide. In response, the program altered the remuneration system to fee-for-service early i n 1963. Rodman (1965) and Alexander (1965) analyzed the resulting physician u t i l i z a t i o n data for the remainder of 1963 and for 1964, concluding that there was a definite trend towards higher u t i l i z a t i o n of physician ' f a c i l i t i e s ' developing i n the data. Rodman suggested an increase i n the order of 10% for 1963, with an even higher average'increase indicated for 1964. The evidence would appear to suggest that methods of remuneration in a broad sense, encompassing the entrepreneur-worker dichotomy should join access to beds as a potentially crucial explanatory variable. We noted above that study ( i i i ) (Chapter 2) had delineated difference in mode of practice organization as one of the three potential explanations for the u t i l i z a t i o n data. No argument i s offered here. The predominance of solo practitioners i n a f i e l d which increasingly requires sophisticated technical support, applies considerable pressure to hospital f a c i l i t i e s . For these private practitioners, access to much of the diagnostic equipment necessary may be obtained through one of three channels: hospital-based f a c i l i t i e s , or ref e r r a l , either to a specialist or to a private diagnostic c l i n i c . Referral to a specialist requires a certain degree of risk-taking on the part of the general practitioner, insofar as the patient may exercise the option of retaining the specialist as a more permanent medical care contact. However, for patients requiring radiological or laboratory testing, but not specialist consultation, a general practitioner must choose between private laboratories and hospital f a c i l i t i e s . In some cases the hospital w i l l be a more convenient setting for a physician, causing a degree of unnecessary hospitalization. For example, a physician who suspects that .a patient w i l l require hospitalization, but who wishes to run a battery of tests to confirm the existence of a particular condition, might choose to hospitalize a patient, run the diagnostic work-up at the hospital and, i f the condition i s not, in fact, serious enough to warrant further hospitalization, release the patient. This i s a costless and time-saving method, from the physician's vantage point. Group practice and health c l i n i c settings, on the other hand, provide some combination of laboratory, radiology and therapeutic services.on an ambulatory basis without outside referral being necessary. This would appear to provide a means of alleviating a certain amount of pressure on hospital f a c i l i t i e s . Unfortunately we are not aware of any related data which might provide an indication of the magnitude of this form of 'abuse'. 1 5 For example, i t i s d i f f i c u l t to differentiate between those 'excess' upper respiratory hospital cases which are a result of premature admission for diagnostic tests, and those which are induced by other considerations. Suffice i t to say that this factor i s l i k e l y of some importance. The degree of importance i s dependent upon the incidence of the practice of hospitalizing patients so as to u t i l i z e hospital diagnostic f a c i l i t i e s , as opposed to referring diagnostic work to private laboratories. In the absence of relevant data, 7 1 there is l i t t l e that can be added. The influence of hospital medical policies on types of cases requiring admission, and length of stay after admission, w i l l be reflected primarily in ALS experiences and i s thus not of concern to us. In passing, however, i t i s worth b r i e f l y commenting on the ALS figures displayed in Table 2.1. A number of the studies reviewed reported comparable ALS s t a t i s t i c s between populations. A word of caution might inhibit incorrect interpretation of such evidence. Since we may r e a l i s t i c a l l y assume that the majority of the admissions 'saved' by the prepaid group practices are of a short-stay nature, the implication i s that, for a given hospital admission, the ALS w i l l be shorter for the group practice e n r o l l e e . 1 6 The alternative plan admissions include relatively more short stay patients of the types not admitted under the group plan. Before leaving this discussion of 'physician factors', we b r i e f l y turn to quality considerations. Quality of care provided could be regarded as a- factor influencing incidence of admissions only i f one could assume that early detection or a preventive care emphasis in one setting might lead to fewer hospital admissions. Counter-balancing this i s the fact that early detection, in and of i t s e l f , could induce additional admissions. Finally, there i s no evidence suggesting that such prevention and early detection i s synonymous with higher quality care. Ideally, one would like to measure the change in health status of a patient over the l i f e of an episode of ill n e s s and to compare this change with the change undergone through receiv-ing care at alternative settings. Such controlled experiments are rare and are often beset by disagreement regarding the measurement of health s t a t u s . 1 7 The rather limited application of conventional health status indices has provided no evidence to indicate that the PGP/CHC settings provide lower quality of care. In fact, i f anything, there are contra-indications. While 7; i t has been argued t h a t u n d e r - u t i l i z a t i o n o f h o s p i t a l f a c i l i t i e s by p a t i e n t s o f PGP/CHC s e t t i n g s may j e o p a r d i z e the h e a l t h o f such p a t i e n t s , the counter-argument i s t h a t p h y s i c i a n s expose p a t i e n t s to. a t l e a s t equal r i s k by p r e s c r i b i n g unnecessary, o r excess, c a r e . Monsma (1970) c i t e d evidence i n d i c a t i n g t h a t the l a t t e r phenomenon, amongst f e e - f o r - s e r v i c e 18 p h y s i c i a n s , i s the more l i k e l y r e l a t i o n s h i p . This d i s c u s s i o n o f p h y s i c i a n f a c t o r s has l e d t o the r e t e n t i o n o f two v a r i a b l e s f o r f u r t h e r c o n s i d e r a t i o n , w i t h an a d d i t i o n a l f a c t o r ( p r a c t i c e o r g a n i z a t i o n ) b e i n g c a t e g o r i z e d as of indeterminate i n f l u e n c e . Access t o h o s p i t a l beds and method o f remuneration appear t o c o n t a i n some explan a t o r y p o t e n t i a l . With t h i s i n mind, we co n s i d e r the h o s p i t a l e n t i t y i t s e l f . 3.1.3 H o s p i t a l F a c t o r s The impact o f h o s p i t a l s on o v e r a l l u t i l i z a t i o n , through such t h i n g s as supply o f beds and i n t e r n a l p o l i c y as determined by a d m i n i s t r a t o r s , medical s t a f f and boards o f t r u s t e e s cannot be d i s p u t e d . However, asi d e from the bed supply i s s u e d i s c u s s e d e a r l i e r i n a d i f f e r e n t guise (with regard t o p h y s i c i a n a c c e s s ) , there i s no i n d i c a t i o n t h a t these f a c t o r s would be d i s c r i m i n a t o r y i n t h e i r i n f l u e n c e . In-house decision-making w i t h r e s p e c t t o p a t i e n t care i s not, t o our knowledge, a f u n c t i o n o f the type o f o r g a n i z a t i o n from which the p a t i e n t has sought primary ca r e . To r e t u r n t o the bed supply i s s u e i t was suggested above t h a t access t o h o s p i t a l beds might be p a r t i a l l y r e s p o n s i b l e f o r the u t i l i z a t i o n d i f f e r e n t i a l s I t was f u r t h e r noted t h a t p e r t i n e n t evidence was scarce and t h a t such evidence as d i d e x i s t d i d not a l l o w i d e n t i f i c a t i o n o f c a u s a l i t y . Here we cons i d e r the case from the ot h e r s i d e o f t h a t c a u s a l l i n k : do h o s p i t a l beds i n f l u e n c e use and, i f so, might a v a i l a b i l i t y o f beds be r e s p o n s i b l e f o r p a r t o f the data r e g u l a r i t i e s ? 7 3 There i s some evidence i n support of the notion that per capita supply of beds tends to influence u t i l i z a t i o n rates. Feldstein (1967) found evidence of an apparently insatiable demand for beds. Occupancy rates tended not to be a function of beds per capita. Roemer (1961a), reporting on an American county in which approximately 200 additional beds were added in a community which had experienced a 78% occupancy rate, found a sharp rise in number of admissions and ALS for the next two years, a period of time i n which population rose marginally. In particular, while bed capacity increased by 42%, Blue Cross subscribers increased hospital days i n the f i r s t year by 38%. On the other hand, Stevens (1970) argues that physician-generated demand for beds, originating with open-staff hospital policies which set no l i m i t on number of physicians gaining admitting privileges, i s the prime factor. The result i s increased bed supply followed by a corresponding increase in admissions. In either case, supply of beds cannot be considered solely a 'hospital factor', as the physician i s , i n both arguments, an important part of the linkage; i t would appear that we are confronted with three inter-related processes: (i) access to hospital beds as a precursor to hospital admissions (ii) physician-generated demand for beds ( i i i ) the bed entity as a variable determining u t i l i z a t i o n . Without attempting to resolve this identification problem we w i l l , nevertheless, report one additional recent piece of evidence. It w i l l be recalled that Wersinger et a l . (1976) compared three HMO-type settings with equal access to hospital beds, and found significantly lower admission rates for the PGP than for the other HMO's or BC-BS. This suggests that access to hospital beds may be of l i t t l e importance, since the differentials persist even in the face of equal access. If, as has been argued by those doubting 7i» HIP physicians' access or c i t i n g the limited bed supply faced by Kaiser physicians, such, bed considerations are responsible for decreased admissions, one would surely expect u t i l i z a t i o n differentials to disappear in a setting such as that described in this particular study. The geographic standardization in many of the studies reviewed also eliminates bed supply as a means of generating the data of the past chapter. Thus, i t would appear that neither access to hospital beds, nor bed supply i t s e l f i s responsible in any significant way for the u t i l i z a t i o n differentials, The same conclusion i s indicated for other 'hospital factors'. Direct hospital policy as to when patients may be admitted and discharged, the influence of the medical staff i n determining operating policies within i the hospital and the method in which a hospital i s reimbursed w i l l a l l be 19 crucial to i t s occupancy rate. (For example, reimbursement on a per diem basis i s l i k e l y to encourage a high occupancy rate). The a v a i l a b i l i t y of alternate chronic care f a c i l i t i e s in the surrounding neighbourhood w i l l determine the extent to which acute care beds must be f i l l e d by extended care patients. Similarly, the a v a i l a b i l i t y and accessibility of alternative sources of ambulatory care w i l l influence hospital use. B e l l i n et a l . (1969) report that adjacent hospital u t i l i z a t i o n declined markedly in the two years subsequent to the opening of a Boston neighbourhood health centre. Finally, one cannot neglect ownership of the hospital as a contributing factor, in that the concomitant financial responsibility for f a c i l i t i e s may be an important means of controlling u t i l i z a t i o n . Insofar as the majority of Canadian hospitals are i n the public, non-profit, domain, the means of payment to hospitals generally overshadows this factor. Reimbursement schemes such as global budgeting appear to have minimal effect on hospital u t i l i z a t i o n and, at any rate, they are not important to theipresent discussion. 7 5 The above hospital factors do share a common characteristic - they a l l affect the magnitude of hospital u t i l i z a t i o n . They are also similar in that none of them i s l i k e l y to influence one population sub-group more or less than another. 3.1.4 Summary We have considered in some detail a wide spectrum of factors potentially capable of some input into the hospital u t i l i z a t i o n process. Yet we appear to be inexorably drawn to one factor which embodies the potential to explain the u t i l i z a t i o n differentials reviewed i n the previous chapter - method of remuneration and entrepreneurial responsibility. We emphasize again that although this variable may not be the most important in determining absolute volume of admissions, i t does appear to be atypical i n that i t seems to have had a d i f f e r e n t i a l impact on the various study groups reviewed in the literature of Chapter 2. At the very least, the basic economic theory surrounding methods of remuneration i s consistent with, as well as supported by, this data. In a discussion devoted to a similar investigation, Evans (1975b, 21) provides an apt conclusion: "Klarman (1970)... points out ... that the differences between fee for service and capitation or administered budget practices are much more complex than simply the difference in mode of practice or physician reimbursement. Organization and philosophy d i f f e r dramatically across modes, as presumably does the psychology of the participating physician. It i s not rigorously proven, therefore, that the remarkably consistent reduction of hospital use of about 20%-25% which i s associated with shifts away from fee-for-service i s i n fact a result of the removal of economic incentives to excess use. Nevertheless, on the basis of the existing evidence, i t i s clearly much more plausible than the n u l l hypothesis". This discussion raises a related question. Given that the data appear to be consistent with what theory predicts regarding alternative forms of remuneration, are they also consistent with, or do they lend credence to, one or more theories of physician behaviour? Does there exist a model of the physician which predicts such behaviour, while concurrently explaining 7 6 other empirical regularities? The following section addresses i t s e l f to these questions. 3.2 Economic Modelling of Physician Objectives Despite an abundance of attempts at modelling the economic behaviour of physicians, there i s a dearth of reviews or comparative, c r i t i c a l evaluations. Space considerations limit the extent to which we w i l l review particular theories. Rather, we attempt to establish a framework for review, and place a number of existing models within this framework, so as to ascertain the advantages and weaknesses of each 'set' of models. The 'market' for physician services i s characterized by a combination of factors, any one of which may, in isolation, be associated with various other markets but which, in combination, tend to distinguish the patient-21 physician relationship. The demand side of this market i s characterized by one particularly distinguishing feature - consumer ignorance. When coupled with the uncertainty surrounding incidence of i l l n e s s , the resulting consumer influence i s suggested to be of minimal impact. In particular, the average patient i s inadequately equipped to judge the quality of the product whatever i t may be; unable even to determine the extent of a change in his/her own health status. It goes without saying that such a consumer would also have considerable d i f f i c u l t y evaluating a physician as to the quality of his 'production process' (other than clear cases of negligence, of course). The problem i s augmented by absence of any learning opportunity -the majority of serious illnesses (.and many of a less life^threatening nature) occur so seldom as to preclude patient accumulation of the information necessary for any such evaluations. Thus, the market i s characterized by an almost total dependence by the consumer, on the provider of care. The provider i s expected to have his (the consumer's) best 7 7 interests i n mind while, at the same time, acting as a market supplier. The resulting consumer agent/supplier interaction eliminates any neat dichotomy 22 between supply and demand. The market i s also characterized by a distin c t lack of advertising and 1 shopping around', although patient abuse of publicly funded medical care, through numerous consultations, i s not 23 unheard of. We proceed now to consider a physician's objectives within this market. The majority of the literature devoted to this area has appeared in the last decade. It has been primarily concerned with attempts at modelling the market structure and the factors underlying price setting for physicians' services. Inherent i n each theory, however, i s an implicit ( i f not explicit) model of the behaviour of the physician-supplier as an economic entity. In addition, there have been a number of studies devoted solely to this latter objective. The models reviewed below appear to f a l l within one of three broad categories: (i) income/profit maximization (ii) u t i l i t y maximization ( i i i ) non-maximization models For each of these sets of models we consider their general distinguishing characteristics and follow this with a brief review of the literature. 3.2.1 Income/Profit Maximization Income and pr o f i t maximizing theories are grouped together for two reasons: Ci) they effectively collapse to the same thing ( i i ) they emphasize the entrepreneur/provider c o n f l i c t which often receives l i t t l e or no acknowledgement in this literature. 7 8 What do we mean by income maximization? If we adhere to s t r i c t l i t e r a l usage, we are s t i l l faced with determining whether i t i s gross, or net, income to which we refer. And, since maximization, of gross income (or revenue) makes l i t t l e economic sense, as i t entirely ignores factor costs, we may confine our attention to the l a t t e r . But i s net income distinct from p r o f i t : total revenue minus total costs? It i s here that we are forced to define our terms of reference with more c l a r i t y . A medical practice which employs a physician (who may be both supplier and entrepreneur) as a labour input might be hypothesized to maximize p r o f i t : TT = total revenue - (implicit physician wage) • (physician hours) -total other factor costs If such a theory i s suggested, total 'firm* costs must include an imputed physician wage x physician work-hours. Thus, there i s necessarily a distinction to be made between the physician-entrepreneur maximizing p r o f i t , and the physician-labourer, who i s paid (albeit by his own practice) a 'shadow-wage'. The distinction between income maximization and p r o f i t maximization i s primarily one of physician function. The l a t t e r model requires that we provide the cost of physician time in calculating total practice costs. This becomes d i f f i c u l t , since we have no reason for believing such a shadow wage w i l l be constant - clearly the implicit cost to a physician of making a house c a l l at 2:00 a.m. w i l l exceed the per unit 24 time cost of a routine office v i s i t in regular working hours. If, instead, we believe the entrepreneur/physician maximizes net income (the sum of implicit wage income and practice profits with no distinction necessary), we require some supply side restrictions to eliminate the 168 hour work week. This problem effectively does not occur in the p r o f i t maximizing formulation, i f we assume that the marginal-own-time^-cost for the physician-supplier increases at an increasing rate over time worked - a f a i r l y r e a l i s t i c 79 assumption. Thus, the entrepreneur's objective may be practice p r o f i t maximization, in which case the physician's own^time. wage costs are an expense to the practice which is d i f f i c u l t to determine and the p r o f i t motive must be the dominant feature of the practice. If, instead, i t i s assumed that the physician/entrepreneur maximizes net income irrespective of i t s source (although he/she must e x p l i c i t l y determine own-time allocation which i s , in a sense, a question of deciding upon an optimal wage/profit mix), we must introduce an additional variable into the model 25 to eliminate unrealistic work-hours. We have no a p r i o r i j u s t i f i c a t i o n for choosing one physician function over the other as the dominant force within a practice. Without regard to other weaknesses within the theories, at the outset we are beset with indecision regarding their relative merits. The dilemma was captured by Evans' (1976) statement that "there i s no automatic presumption that the physician wearing his owner's hat w i l l always impose his objectives over himself wearing his manager's or worker's hat; yet owner-domination i s required by the profit-maximizing model" (pp. 5-6). What do such theories suggest with regard to alternative methods of remuneration? A practice being reimbursed on a capitation basis, and concurrently maximizing p r o f i t , would be expected to advertise and actively recruit patients. Such proceedings are rare i f not banned by Medical Associations. If an individual physician i s paid by capitation, income maximization would require both active patient recruiting and an inhuman a b i l i t y to carry on without sleep, so as to maximize number of patients treated. Similar observations would be appropriate for an income-maximizing physician who was reimbursed on a per case basis. In both instances one would l i k e l y find a distinct reticence on the part of the physician to recall patients, except where absolutely necessary, although the lat t e r 8 0 (case payment) physician would tend to encourage episodes such as semi-annual check-ups which could be reported each time as a new case. We have a particularly d i f f i c u l t time f i t t i n g salaried physicians into an income-maximizing framework, insofar as their net income i s effectively fixed in the short run. It would appear then, that the p r o f i t - or income-maximizing models pose more questions than they are able to answer. One might thus expect a dearth of such models in the literature. On the contrary, however, numerous well-intentioned attempts dating as far back as 1958 are noted below. Rimlinger and Steele (1963J, i n proposing a theory which purports to explain the geographic distribution of physicians i n the U.S., implicitly assume that a l l physicians maximize incomes, without regard to the physician/ 2 6 practice dichotomy. Prior to this research, Kessel (1958) and Garbarino (1959) indirectly implied a p r o f i t maximizing role for physicians. These forerunners have been followed in recent years by a relative abundance of advocates. Newhouse (1970), Freeh and Ginsburg (1972) . and Newhouse and Sloan (1972) have devoted considerable space to arguing the merits and demerits of a p r o f i t maximizing model proposed by the f i r s t author to explain price determination in the market for physicians' services. The debate was apparently concluded with Newhouse and Sloan favouring a target income type model origi n a l l y suggested by the former. Masson (1972) assumes p r o f i t maximization (or rather expected p r o f i t maximization) en route to a further theoretical exposition of price formation in a modified competitive marketplace (i.e. one characterized by imperfect information which leads to consumer 'price shopping'). In a novel approach to hospital objective modelling, Pauly and Redisch (1973) assume that physicians within the hospital setting act as "traditional income maximizing economic agent(s) ... in a decision-making role within ... 8 1 not-for-profit enterprise." 2 7 In an extension of this idea, Pauly (1974) employs similar assumptions. Finally, Sloan et a l . (1973) assume physicians maximize profits as we have defined them here: net income less imputed wage x time input, while considering the relative effects of price and non-price rationing in response to exogenous demand for their services. It i s interesting to note, however, that the authors' imputed physician own-time cost equation takes the form, C = a + a AGE + a HEALTH + (a + a AGE + a HEALTH)-Q 0 X 2 3 k 5 so that the physician's imputed time value i s comprised of a fixed and marginal component, the latter depending upon Q (quantity of services provided). In this form, the cost of physician time i s independent of physician income and of amount of time devoted to the practice. In effect, given the physician's age and health status, cost of own time i s a function only of his practice's throughput, to the exclusion of physician income and magnitude of own time devoted to the practice per time period. This discussion i s admittedly brief. However, the intent i s not, as noted above, to provide a comprehensive literature review, but rather to indicate the sources of this particular type of application, in lig h t of the apparent ambiguities or inconsistencies in the theories. In reviewing this literature, we were unable to find any acknowledgement of the fact that not a l l practices charge on a fee-for-service basis. Finally, within the context of the data from Chapter 2, both p r o f i t -and income-maximizing models p a r t i a l l y explain the empirical regularities ill u s t r a t e d in that chapter. We would expect comparison of a fee-for-service practice with a practice remunerated by any other of the discussed methods, to produce results of this nature. Yet such models have been shown to incorporate other problems described below and they do not attempt rationalization of the hospital vs. ambulatory treatment choice. We have.seen that net income-maximization breaks down in the absence of supply side constraints, and that profit-maximization requires entreprenuer domination of the physician-supplier of care and i s , in any event, a model of the medical firm rather than of the physician per se. We can circumvent the open-ended supply problem through the introduction of an income-leisure tradeoff, but this inauspicious addition of a leisure proxy to the physician objective function i s a fore-runner to the expansion of the u t i l i t y function variable l i s t ; an expansion which often incorporates nebulous, or d i f f i c u l t to quantify variables. Thus, we consider what are broadly termed the u t i l i t y maximization models. 3.2.2 U t i l i t y Maximization The modelling which f a l l s within the bounds of this category involves variations on a basic theme, that being that the physician maximizes an objective (utility) function defined over any number of variables, two of which are net income and leisure. Thus, the basic model i s one employing only these two variables. Does this solve our dilemma? The answer i s , unfortunately, yes and no. A function of the form U = U(Y,L) Y = net income U > Q L = labour hours U < 0 L when maximized does allow circumvention of the open-ended work week which characterizes straight income maximization. However, other empirical observations and regularities cast serious doubt on the r e l i a b i l i t y of this type of model, as well as further undermining the c r e d i b i l i t y of the income/profit maximizing models. 8 3 Evans (1976) discusses a number of such observations, and we use that source as a framework. (References related to the empirical evidence cited below may be found in that source as well). The empirical regularities to which we refer are: (i) evidence of low (close to zero) market price e l a s t i c i t i e s of demand (where direct charges to the consumer exist -reference to U.S.) i s inconsistent with income, p r o f i t and income-leisure maximization unless, despite the inelastic market demand curve, each supplier faces an elastic (greater than 1.) demand curve. This can be shown simply by considering the implications of p r o f i t maximization. At the pr o f i t maximizing level of output, marginal revenue (MR) must be greater than zero. If we assume the market demand curve i s linear, and denote price e l a s t i c i t y by e, we have the familiar relationship, MR = p ( l - 1) where p = market price e But MR > 0 + p (e - l) > 0 - > - e - l > 0 e + e > l Given the evidence that £ < 1 for this market, we are l e f t with the alternative choice - ela s t i c individual demand curves as would be expected in competitive markets. The suggestion that physicians are price competitive i s d i f f i c u l t to support. Thus, i t would appear that the i n e l a s t i c i t y of both individual and market demand curves undermines the income-leisure-profit maximizing theories. However, the r e l i a b i l i t y of the data relating to this point i s suspect i f one considers the measures used as proxies for demand (Stoddart (1975)). The evidence associated with this empirical observation i s , in isolation, therefore unlikely to provide sufficient grounds for refuting the income-leisure related models. (ii) there is a tendency, i n inter-provincial comparisons, for those provinces replete with a relative abundance of physicians to exhibit the relatively higher 'prices', a contradiction of basic economic theory i f we assume the market to be in equilibrium. In particular, i f this market was in equilibrium we would expect to observe similar price levels, or at least physician real income levels, across provinces, ceteris paribus. If at the time of data compilation, the market was in a disequilibrium state, we might instead expect to observe a migration of physicians from low to high income level regions, after which a f a l l in price levels and in incomes in the latt e r areas might result. We have compiled i n Tables 3.2 and 3.3, data for the period 1966-71 which i l l u s t r a t e percentage changes in average net physician income and in number of physicians. The lat t e r i s used rather than population/physician ratios since we can assume that physicians w i l l migrate to high income areas irrespective of population level or growth, although the high incomes may p a r t i a l l y be a result of a swiftly growing population and thus low physician density. A number of interesting trends are evident i n these two tables. - Newfoundland experienced successive years of +15% increases i n average net income from 1967-69. This was apparently followed by a rapid influx/graduation of physicians i n 1968-69 and in 1970-71 and i t appears that the supply progressed past some equilibrium point in the process, as net incomes f e l l i n the 1970-71 period. In 1966 Newfoundland ranked f i f t h amongst the provinces i n average net income. By 1969 i t boasted the highest average net income, a position i t maintained in 1970. It i s hardly surprising, then, that Newfoundland's physician stock experienced the most rapid increase over the 1966-71 period. Yet that increase appeared to be taking i t s t o l l at the end of the period, as the average provincial net income f e l l to fourth place i n 1971. Another revealing provincial pattern i s that of Alberta. In 1965 and 1966 Alberta was ranked sixth by average net income, but moved rapidly to second place with 12.4% and 16.3% increases in the sub-sequent two years. The period 1966-68 saw a corresponding steady, much higher than average but unspectacular, growth in physician stock. When Alberta's relative position slipped (to third) i n 1969 with only a 1.8% increase in net incomes, perhaps as a result of this increased number of physicians, the physician growth vi r t u a l l y stopped. The stock of physicians increased by only 1.7% from 1969 to 1970. From 1966 to 1967 Saskatchewan f e l l from second ranked (by average net income) province to f i f t h ranked, and dropped further to eighth place i n 1968. The physician stock adjustment appears to have been dramatic. Growth dropped off to 1.1% from 1967-68 and from 1968-69, and the number of physicians f e l l from 1969-70 (in 1969 Saskatchewan occupied the 9th ranked spot in the provincial l i s t of average net incomes). Over the five year period Saskatchewan's growth in average net income was lowest amongst the Canadian provinces and not surprisingly the growth in number of physicians followed suit. One puzzle is posed by B r i t i s h Columbia, which experienced the second lowest growth in net incomes over the 1966-71 period and, by 1971, ranked lowest in average net provincial physician incomes. Yet that same province experienced the third largest growth rate in physician stock. Apparently there are non-income related, perhaps geographic, tastes which tend to overwhelm income aspirations. 8 5 TABLE 3.2: Percentage Changes in Average Net Fee-Practice Physician Incomes 1966-1971 % Change Province Average Net Income 1966 1966-1967 1967-1968 1968-1969 1969-1970 1970-1971 1966-1971 Newfoundland 27906 6.9 15.4 20.8 6.8 -4.6 51.9 Prince Edward Island 23226 3.9 5.1 7.9 5.7 43.1 78.2 Nova Scotia 27079 1.7 11.9 15.4 12.3 0.3 48.0 New Brunswick 28383 6.5 7.9 4.9 7.1 18.9 53.6 Quebec 28150 4.6 6.3 5.6 1.3 35.7 61.4 Ontario 30788 10.9 8.5 4.8 12.7 0.7 43.1 Manitoba 28058 3.9 8.6 16.4 16.5 -1.9 50.1 Saskatchewan 29690 -0.2 2.4 7.6 10.0 3.2 24.7 Alberta 27777 12.4 16.3 1.8 12.6 6.4 59.4 B.C. 26426 8.2 3.1 11.5 4.0 -1.6 27.4 CANADA 28985 8.0 7.9 6.5 8.0 9.8 47.1 SOURCE: Average Net Incomes from Table A19, Earnings of Physicians in  Canada, 1961-1971; Health and Welfare Canada TABLE 3.3: Percentage Changes in Estimated Number of Active Fee- Practice Physicians, 1966-1971 86 % Change Province Estimated # of Physicians 1966 1966-1967 1967-1968 1968-1960 1969-1970 1970-1971 1966-1971 Newfoundland 157 2.5 6.8 15.1 5.6 10.5 47.1 Prince Edward Island 74 1.4 2.7 5.2 -3.7 11.5 17.6 Nova Scotia 579 3.8 2.8 4.0 6.1 7.6 26.8 New Brunswick 377 1.9 1.6 3.1 -0.7 7.0 13.3 Quebec 4728 2.3 2.0 3.0 4.6 8.2 21.7 Ontario 6469 3.4 4.2 6.0 3.8 6.8 26.6 Manitoba 803 0.1 1.4 2.2 -0.4 6.7 10.3 Saskatchewan 719 4.6 1.1 1.1 -4.2 . 5.6 8.1 Alberta 1130 7.3 8.5 8.0 1.7 10.6 41.3 B.C. 1984 3.1 6.2 11.3 3.9 7.5 36.2 CANADA 17040 3.2 3.7 5.6 3.4 7.6 25.7 SOURCE: Estimated Number of Active Fee-Practice Physicians from Table A l , Earnings of Physicians in Canada, 1961-1971; Health and Welfare Canada. 8 7 The above figures and discussion seem to suggest that the physician market i s in an almost constant dis-equilibrium state, with some tendency for physicians to migrate towards relatively high and relatively swiftly growing net income areas. But we suggested that the peculiar empirical observation concerned prices. We might expect regions which experience rapid growth i n physician stocks to display subsequent drops in prices. We have not assembled data on fee schedule changes for the period 1966-71, as Evans (1973) provides some figures for a l l but the latter two years (as well as a much more complete discussion of migratory patterns in response to incomes) and, as he suggests, the price data "are so poor that we have been ashamed to drag them in before now" (Evans, 1973,73). Evans found that B.C. had both the highest prices and highest physician density from 1963-68, and we note that from 1968 to 1971 the B.C. physician stock increased by an 'additional 24.4%. In addition most other provinces displayed a positive correlation between relative price levels and relative density. Although i t was reported that B.C. did have a relatively low increase in price levels from 1963-68, Alberta "had both above-average income and very rapid price increases" (Ibid., p.79). Although the data are admittedly soft, there i s at least p a r t i a l evidence suggesting that increased physician density does not give rise to f a l l i n g , or less rapidly rising, prices.28 Thus, although the data suggest a fluctuating, disequilibrium, physician stock market, price data do not seem to respond as a simple supply/ demand market model would predict. ( i i i ) the evidence pertaining to physicians' use of paramedical support staff i s inconsistent with an income/leisure u t i l i t y maximizing hypothesis; For whatever reason, and one p o s s i b i l i t y i s uncertainty associated with the practice (i.e. i f physician gets sick he s t i l l has to pay staff; fluctuation i n work load; i n a b i l i t y to exercise a sufficient level of scheduling freedom, etc.), another being the d i s u t i l i t y associated with the supervisory function, i t has been shown that physicians could increase net incomes, while possibly concurrently increasing leisure time, by taking on considerably more paramedics than appears to be the rule (Reinhardt (1972,1973)). Of course the licensure requirements bearing on both medical schools and medical practices ensure that the free entry condition of perfect competition i s not met. This has obvious price implications and also implies that one of the conditions for a perfectly competitive market, cost minimization by participating firms, need not be met for the purposes of survival. There i s therefore no overwhelming reason for believing that p r o f i t maximization should be the sole or even dominant objective in this market and the underutilization of paramedical personnel may be partly a result of that phenomenon. Any of these possible explanations implies that the (Y,L) l i s t of objective function parameters is insufficient. They might imply, for example, that some variable representing number of aides should be included in the u t i l i t y function, with the marginal u t i l i t y associated with the addition of aides being negative, for reasons noted above. (iv) Physician throughput i s insensitive, or at most minimally responsive, to patient a v a i l a b i l i t y as measured by physician/population ratios. For example, Evans (1974a) has shown that, at best, a weak negative relationship exists between these ratios and physician workload (as measured by standardized gross r e c e i p t s ) . 2 9 This may be the result of physicians' a b i l i t y , as a group, to modify service mix i n response to actual patient demand, without the need for shifts in prices. A well-known example has been the almost complete elimination, in the past decade, of house c a l l s . These points, taken as a group, suggest that we should incorporate variables which represent the physicians' 'production process preferences', in addition to the income/leisure tradeoff. In particular, nebulous characteristics such as 'professional freedom', the need to provide 'own-time' to each patient in order to maintain some sort of physician-patient relationship, and other equally un-quantifiable factors might have a role to play in taking account of ( i i i ) above. Such a variable l i s t extension i s not only cumbersome and l i k e l y non-operational, but i t cannot cope with (iv), which suggests a considerable supplier influence on 'demand' levels for his/her services. A model in which the physician maximizes u t i l i t y defined over income, leisure and characteristics such as those described above does not provide any apparent explanation for the observed unwillingness of physicians to exploit this demand-generating capability f u l l y , to the point where the marginal effect on u t i l i t y of additional such a c t i v i t i e s i s zero- i . e . "Given only these objectives, the physician should always (in a private market) push demand out as far as he can and then set price to maximize a function of income leisure and the other variables suggested above (Evans (1976,39)). 89 As always, there are a number of ways in which the theory might be modified to account for such observations. Inclusion of a demand generation variable, DG, with U = U(Y,L,DG...) and Y = f(DG ) might incorporate that empirical observation. In particular, i f we assume that 3Y/3DG > 0, so that demand generation i s undertaken up to the point where 3U/3DG becomes large enough negative to y i e l d dU/dDG = 0, then we are able to incorporate 30 a taste constraint on demand generation. We return to item ( i i i ) . Given that some means such as the above is found to account for unexploited demand side influence, we may now reconsider explaining the underutilization of support staff. It was noted above that one p o s s i b i l i t y entailed the inclusion of number of aides in the objective function, with the assumption that after some c r i t i c a l number the d i s u t i l i t y associated with task delegation, responsibility for the work of others, and uncertainty, reaches a level sufficient to outweigh the positive u t i l i t y derived indirectly through the practice income effect of additional aides. Although our above-discussed assumption of 3U/3DG < 0 imp l i c i t l y introduces a degree of interdependence into the objective function, i t i s also possible to take more e x p l i c i t account of the belief that physicians do care about their patients' health. As patients entrust physicians with an 'agent-type' function, as well as expecting them to undertake the supply role, we might expect a physician's u t i l i t y function to contain some proxy for the patient's u t i l i t y , or at least the marginal effect on that u t i l i t y of physician-motivated procedures. It would appear, then, that the introduction of a sufficient number of behavioural and practice organizational characteristics into the physician's objective function allows us to build a plausible model which i s also consistent with the empirical evidence presently available. The major objection to the more sophisticated models of this type i s that they are, i n general, non-operational to the extent that they are effectively empirically untestable. Our extensive literature search indicates that the majority of attempts at modelling physician behaviour f a l l within this u t i l i t y maximization cla s s i f i c a t i o n . In addition, the literature i s of a f a i r l y recent vintage. In fact, one of the early applications was that of M. Feldstein (1970). 3 1 In his market disequilibrium model (wherein i t i s argued that physicians maintain a state of excess demand to f a c i l i t a t e their choosing cases of particular interest), he implicitly assumes that physicians maximize u t i l i t y defined over income, leisure, 'case-interest', and medical ethics. Reinhardt's (1972) and (1973) research into the form of a medical practice production function i s b u i l t (again implicitly) around a behavioural model i n which the physician entrepreneur seeks to maximize a u t i l i t y function comprised of income and leisure variables, subject to various time and technical (production function) constraints. As mentioned earl i e r , i t i s primarily his evidence on the underutiiization of task delegation which casts serious doubt on the c r e d i b i l i t y and be l i e v a b i l i t y of income maximizing models. A similar model underlies Sloan's (1973a) work on investigating the causal factors which determine physicians' own-time input into their medical practices. Building on the earlier work of Masson (1972), Masson and Wu (1974) appear to s h i f t ground from p r o f i t maximization to income-leisure maximization almost at w i l l , without considering the connotations of doing so. Their formal model employs the maximization of expected u t i l i t y , which i s a function of income, leisure and eventually some sort of charity variables incorporated as a 'psychic income' component of income. However, the prior and posterior discussions e x p l i c i t l y refer to the implications of their model for the pricing practices of p r o f i t maximizing physicians. If e x p l i c i t cognizance i s taken of the entrepreneur/physician distinction, as noted above, net income maximization and practice p r o f i t maximization effectively collapse to one model. It i s not clear here that the authors are aware of any distinction, as they e x p l i c i t l y suggest that physicians maximize profi t s , whereas the correct usage would imply that the practice maximizes pr o f i t s . Prior to the work undertaken by Masson and Wu, Ruffin and Leigh (1973) also investigated the apparent price discrimination evident in the physician services market. Underlying their empirical testing i s a model of u t i l i t y maximization based on income, leisure and patient characteristics (ethics) variables. Evans (1974a) e x p l i c i t l y introduces a demand generation variable into the u t i l i t y function, along with income and work load variables, while Murphy and Satterthwaite (1973), i n an investigation of physician time allocation decision-making (between office and hospital), e x p l i c i t l y employ physician u t i l i t y defined over income, hours worked per week and "a variable which represents his professional standards concerning how he thinks he should practice medicine" (p.4). In particular, i t i s postulated that the latter variable i s , in turn, a function of auxiliary office inputs per week as a proportion of own-office-hours per week, auxiliary hospital inputs assiting him per week as a proportion of own-hospital-hours, and the relative amount of care he 'produces' in the office and at the hospital. None of these models e x p l i c i t l y considers the implications of alternative means of remuneration or allows predictions regarding their effects on hospital use. We complete our spectrum of physician models by looking at non-maximizing models. 3.2.3 Non-Maximizing Models 9 2 In most of the literature which we have b r i e f l y reviewed in the above two sub-sections of this chapter, the authors appear to have im p l i c i t l y , i f not always e x p l i c i t l y , assumed that the physician does, indeed, maximize some objective function. This i s not surprising, insofar as most micro-economic theory i s based on similar assumptions for a l l consumers and producers. However, alternative hypotheses do exist, and despite their scarcity i n the literature, we include a brief discussion of the concept so as to provide a complete treatment of the available alternatives. Why might one believe that the 'correct' formulation of physician behaviour can be embodied in a non-maximizing model? It would appear that such a route creates an alternative means of explaining away, or providing consistency with, two empirical observations - low price e l a s t i c i t i e s , and a significant correlation between market price and number of suppliers - both of which were discussed e a r l i e r . While we have seen that additions to the l i s t of objective function parameters provide the capacity for dealing with these observations, we have also suggested that such additions are, in general, d i f f i c u l t to quantify and thus to employ i n any empirical work. In our above discussion of profit/income maximizing models, we mentioned that Newhouse (1970) had alluded to the p o s s i b i l i t y of non-maximization in the short run. The f i r s t reference to this concept arose from Newhouse's discontent with certain of his empirical results relating to variables thought to affect demand for medical services (Newhouse, 1970, 181-182). Thus, "...physicians do not f u l l y maximize profit s , but do charge higher prices when income raises demand. Physicians may fear the p o l i t i c a l consequences of maximizing profits i n the short run, so that the observed prices are long-run p r o f i t maximizing prices. Alternatively, they may be satisficers rather than maximizers. Satisficing 9 3 behaviour may explain the high positive correlation of the number of practitioners with price. Suppose physicians have a certain income target. As the number of physicians in an area increases, v i s i t s per physician w i l l tend to f a l l . To achieve any given target income, each physician w i l l then have to charge higher fees" (Newhouse, 1970,181 including footnote 30). Evans (1973) was the f i r s t (and the only, to date) to formulate e x p l i c i t l y a model around the s a t i s f i c i n g , target income concept. In particular, he added one dimension of choice to Newhouse's statement by assuming that, i n addition to physicians being able to charge higher fees, they could also vary their degree of demand generation in order to maintain income at some pre-ordained satisfactory, or sufficient, l e v e l . "The physician does not act as a price taker and determine what volume of services he w i l l offer at each of a set of possible prices; rather he responds to price and income as well as to professional considerations in advising the consumer as to how much care should be consumed. The he meets the resulting demand" (Evans, 1973,21). Thus, i n reacting to decreased 'true demand' as measured by patient-initiated contacts, due perhaps to an influx of physicians into an area with stable population, the physician who faces an expected negative change in income has two potential adjustment mechanisms: price and demand influence. It i s interesting to note, before proceeding, that this type of model may be formulated i n a maximizing framework, by assuming that i t i s (Y-Y^) which appears as a variable i n the u t i l i t y function, rather than simply Y; (Y, - desired, or target, income). Thus, i f we postulate that d a physician maximizes U = U(AY, L, D...) where L = labour hours D = demand generation as above AY = Y - Y, d and, furthermore suggest as a specific example that U 'AY > 0 for every Y U A Y A Y > 0 for every Y < Y , where Y i s some Y < Y d = 0 for Y = Y we effectively capture the s p i r i t , i f not the specification elegancies, of Evans' model. In particular, the income u t i l i t y function takes a form such as that i n Figure 3.1: Figure 3.1: U t i l i t y As A Function of Income in a Target Income Model No useful purpose would be served by setting out Evans' entire model. Rather, a brief description follows. Physicians are assumed to desire some optimal workload, W^ , which i s a function of prices and net income, and i t i s the difference between actual (W) and optimal work load which effectively drives the 'system'. A surfeit of physicians, or alternatively, a negative S = W-W^ , w i l l lead (in the short run) to an increase i n q, per capita demand for services, through the demand generation effect. This w i l l , in turn, increase Q, quantity of services supplied and W, d u n t i l S -> 0. W i s a function of net income (N) and prices (P) "in the customary way predicted by the work-leisure trade-off, i.e., a rise in U Y Y N for P constant leads to a reduced ... and a rise in P for N constant d leads to an increase in W ..." (Evans, 1973,22). Thus the individual physician can affect N through both P and q effects. If S > 0, implying an excess workload, the physician may be inclined to do away with marginally needed work. If S < 0, the physician might raise prices (to the extent possible) so as to increase net income and reduce W^ , or he/she might increase q and thus W, or a combination of both variables may be employed to the point where S = 0. Like the other models b r i e f l y reviewed e a r l i e r . i n this chapter, this model does not e x p l i c i t l y consider the effects of changes i n payment mechanism for hospital u t i l i z a t i o n , or any other u t i l i z a t i o n for that matter. In particular, no distinction i s made between 'hospital-generated' and 'office-generated' income, the related factor costs, and the effect on each component of a change in method of remuneration. 3.3 Summary of Physician Modelling The physician modelling framework and review of the literature which have comprised this past section serve to i l l u s t r a t e two alternatives: (i) attempts i n this direction, to date, are p a r t i a l l y and i n t u i t i v e l y (but not explicitly) consistent with the data of Chapter 2, but are not supported by one or more other empirical regularities outlined above; or (ii) models such as the non-maximizing model just cited appear to be consistent with a number of these empirical 'anomalies' (i.e. Evans' (1973) model might explain under-utilization of paramedical personnel by suggesting that, so long as P and q d t provide sufficient f l e x i b i l i t y to attain W and N (target net income), there i s no need to use additional staff to generate income) but f a i l to 96 consider the hospital/office allocation choice (except for Murphy and Satterthwaite (1973)) or at least the l i k e l y effect on this choice of changes in remuneration. The increasing pressure for changes in methods of remunerating physicians suggests that there is considerable scope for analysis in this area, prior to policy implementation, and particularly in ligh t of the fact that no presently formulated model appears to have captured sufficient consistency with empirical observation and physician choice, to merit applied use. 3.4 Conclusion This chapter has covered a rather vast and varied collection of materials. We commenced with an in-depth consideration of the factors which underly hospital u t i l i z a t i o n , and eventually determined that one explanatory factor appeared to stand out, that being method of physician/ practice remuneration. This finding prompted a review and analysis of attempts at physician modelling, the aim being to ascertain the capability of the frameworks and models considered to y i e l d predictions with which such a conclusion would be consistent. It was mentioned earlier that the scope of the thesis entailed three interdependent focal areas. We have now completed our treatment of one segment of the analysis, that being the behavioural considerations associated with hospital expenditures. In addition, the previous chapter's description of the hospital u t i l i z a t i o n data provides the groundwork for our analysis of the expenditure implications of PGP's and CHC's. Such an analysis i s dependent upon the derivation of case-specific expenditure figures which may be matched with these u t i l i z a t i o n data. In the following chapter we turn our attention to that derivation. Chapter 3 - Footnotes 9 7 Thus, we w i l l not be particularly interested in the determination of the length of stay, not because i t i s unimportant, but due to our focus on admission/separation data in the previous chapter. In addition, our entire cost analysis of later chapters i s b u i l t around estimating costs per admission or discharge, rather than per day. The interested reader might have a look at Rosenthal (1970) for American evidence on the pr i c e - e l a s t i c i t y of hospital length of stay. For a discussion of ALS i n relation to the HIP studies cited i n the previous chapter, see Klarman (1963,961) who contends that ALS rates adjusted for HIP's elimination of many potential short-stay patients would l i k e l y indicate shorter average hospital v i s i t s for HIP subscribers. In particular, a more comprehensive, and at the same time general, discussion of many of the individual variables considered in this chapter, may be found i n that source. Our attention w i l l largely be limited to considering the scope each variable might have for influencing differences i n hospital u t i l i z a t i o n patterns. Note that i t i s the perception which i n i t i a t e s the process. There are, undoubtedly, numerous cases of need which go unattended due to the patients' ignorance of the existence of a condition requiring medical attention. For a more complete discussion of the related connotations, and the implications of this dichotomy for the modelling of the .demand for health care, see Stoddart (1975) on the 'Health Belief Model'. There are abundant data to support this claim. Lewis and Keairnes (1970), for example, found that for a population of 5000 Blue Cross subscribers, physicians i n i t i a t e d approximately 70% of a l l patient-physician contacts. See, in addition, Evans (1973a) and Stoddart (1975). See, for example, study (ii) of the previous chapter, Manga (1977), and Stoddart (1975). Roemer and Shonick (1973, 304-306), look at a peripherally related segment of patient attitudes involving satisfaction (or lack thereof) with care received through PGP's. In general, their review of the evidence indicates that such subscribers are no more, nor less, happy with the care received than persons receiving care from other sources. The discussion i s , of course, concerned with the American setting and the studies i n the previous chapter deriving from that source. See Roemer and Shain (1959,9-11) for a review of this evidence. Roemer and Shain (1959,9-10) in particular, discuss the evidence pertaining to the influence of housing, rural-urban differences etc. Those interested i n following the progress of the debate might have a look at Klarman (1969) and Shapiro (1970). See Roemer and Shain (1959,25-26). In a later study, Roemer (1961b) observed that, for areas i n which the population/physician ratio was above 910:1, the rate of hospital admissions bore a negative relationship to the supply of physicians. This i s consistent with a target income type of physician behaviour model, as suggested by Evans (1973) Our deliberate avoidance of a ful l - s c a l e discussion of methods of remuneration arises from the fact that such 'analyses' are already numerous. In addition to this subject being b r i e f l y considered i n many volumes and a r t i c l e s , such as Fraser (1975), Evans (1975b), Crichton (1972) , Pauly (1970) , Home (date unknown) , Ontario Economic Council (1976), Migue and Belanger (1974), Shortell (1972), Foulkes (1973), Roemer and Shain (1959), Somers and Somers (1961), and Pickering (1973) to mention but a handful, i t i s also the sole topic of i t s f a i r share of research: Glaser (1970,1976), Boudreau and Rivard (1976), Roemer (1962), and Hogarth (1963) made this subject the foundation and major content of their work. For a delineation of the consequences, see Evans (1975a) and Evans (1976a). See Weil (1976, 345-6), who states that "Physicians in ... prepaid groups are usually salaried ... A l l of the plans pay salaries to their full-time physicians. Salaries are often determined by the number of persons for which the particular group of physicians i s responsible (capitation), but in the case of full-time staff, the income from prepayment i s pooled and redistributed in a previously agreed-on manner". Personal communication with Mr. Jock Ferguson of CBC Television News, Toronto, regarding the Ontario situation has suggested that the greater form of abuse i s manifested through 'conflict of interest' private practice laboratories, wherein informal referral patterns are established, or physicians are part-owners of laboratory c l i n i c s etc. Support for the hypothesis that the majority of 'saved' cases occur i n conditions otherwise requiring short hospital stays, i s provided in Riedel et a l . (1975, 21T23). The four conditions showing the greatest adjusted differences i n admission rates a l l had lengths of stay averaging four days or less, as compared to the overall average of 6.5 days. Culyer (1977) describes the numerous analytic, measurement and value judgement problems associated with deriving health status measures. One set of studies indicates that quality of care, as measured by prematurity and perinatal mortality s t a t i s t i c s , i s superior for enrollees of a group practice plan (HIP). See Shapiro et a l . (1958) and Shapiro et a l . (1960, 1312-1313). The reader is also referred to M i l l e r et a l . (1967, Appendix IV: 203-206), which highly commended the quality of care found i n Kaiser Plan groups. Finally, the lack of contrary evidence i t s e l f suggests support for the contention that quality of care in prepaid group practices and community health centres i s at least as good as that i n alternative settings. 1 0 0 19. Dr. D.O. Anderson has suggested in personal communication that ease of access to operating f a c i l i t i e s , privileges to use diagnostic equipment without peer consent, setting up and scheduling times for f a c i l i t i e s etc., were largely a function of a physician's position i n the hospital pecking order, and that such a hierarchy w i l l have considerable influence on f a c i l i t y u t i l i z a t i o n . 20. The reader interested in the recent evolution of hospital reimbursement in Ontario might find Milne (1977) useful. He considers the effect of a number of Ontario Ministry of Health budgetary changes on such goals as efficiency improvement and cost containment. Shifts from l i n e , to global, budgeting and from no incentive to positive incentive reimbursement are argued to have had l i t t l e , i f any, effect on these goals. 21. The seminal a r t i c l e regarding medical care i n general, i s that by Arrow (1963). 22. This theme i s far from new, and can be found i n any number of references. Yet there s t i l l remain those with eternal faith in the market place (i.e. Helms (1976), paper presented to the 18th Canadian-American seminar, University of Windsor, November 1976). See also Evans' review of Perlman (1974), in C.J.E., August 1976. 23. Wolfson and Solari (1976) consider the extent of such abuse using an Ontario survey sample and find . that to the minimal extent that abuse exists, i t derives primarily from the supply side. 24. Evans (1976a) elaborates on the implications for the im p l i c i t wage of an exogenous price change. 25. That optimal wage/profit mix i s l i k e l y to be p a r t i a l l y influenced by the existing d i f f e r e n t i a l tax treatment of profits and employees' income 26. See Evans (1973) for an elaboration of the breakdown of the Rimlinger and Steele (1963) model when subjected to analytic scrutiny. 1 0 1 27. More sp e c i f i c a l l y , Pauly and Redisch propose that hospital medical staff act jointly to ensure the 'production' of hospital services i n a manner consistent with the maximization of joint net incomes.: 28. In addition to Evans (1973) and Evans (1975a), further support for this relationship i s offered by Baltzan (1973), M. Feldstein (1970) and Newhouse (1970). 29. See Lewis and Keairness (1970) and the Task Force Reports (1970) for further support of the general 'demand generation' hypothesis. 30. Thus 3U/3DG i s assumed to be negative and also to be a decreasing function of the extent of the demand generation. This distasteful demand generation assumption follows from the observation that i t s powers are not f u l l y exploited. 31. For comments on that piece, a rebuttal and a reconciliation, the reader i s referred to Brown and Lapan (1972), M. Feldstein (1972) and Brown et a l . (1974). 1 0 2 Chapter 4: A Hospital Average Cost Equation - Theoretical Specification The thesis has, to this point, considered the evidence pertaining to 'excess hospital u t i l i z a t i o n ' , and has undertaken a discussion of the behavioural considerations potentially responsible for the apparent trend. The remaining chapters concern themselves with quantification, in expenditure terms, of the u t i l i z a t i o n patterns reported in Chapter 2. The modus operandi,as b r i e f l y outlined e a r l i e r , i s to develop a set of marginal cost per hospital discharge figures. In conjunction with the u t i l i z a t i o n d i f f e r e n t i a l vectors developed above, these figures w i l l provide estimates of expenditure on excess hospital u t i l i z a t i o n , disaggregated by case type. The methodology involves application of a behavioural hospital cost equation, to be developed and estimated in this and the following chapter, which includes a measure of hospital case-mix complexity as an explanatory variable. This variable i s a function of hospital case-load and diagnosis-specific complexity values, so that the more complex i s a given hospital's 'average* case, the higher w i l l be i t s hospital complexity value. The derivation of both case complexities and, from them, hospital complexities i s contained in the following chapter. Suffice i t to say, at this juncture, that the composition of the hospital complexity variable f a c i l i t a t e s consideration of minute changes in a hospital's throughput, so that the comparative static implications of a change in hospital case mix for hospital cost per case may be deduced. Furthermore, such an analysis may be performed at a disaggregated level which considers the effect on cost per case of a change in the case load of only one diagnostic category. Extending this analysis to each category provides a basis for deriving our marginal case costs. A departure from common format i s employed here, in that no extensive review of the hospital cost equation estimation literature i s included. 10 3 This derives from the fact that a number of such reviews already exist, and repetition here w i l l add l i t t l e to the ultimate analysis. 1 However, familiarity with some of the major problems encountered i n previous exercises of this nature w i l l f a c i l i t a t e understanding of the measures taken to circumvent such problems in the present analysis. Perhaps the most widely recognized d i f f i c u l t y in estimating cost equations for the hospital care 'industry' i s that of defining output, due 2 to the multi-product nature of the firm. As suggested e a r l i e r , the ideal measure might be change in patient health status between admission and discharge. Digressing from that, however, the definitional problem i s s t i l l comprised of two levels. F i r s t , the hospital embodies numerous functions, among them inpatient medical care and a l l i t entails, outpatient care, emergency care, administrative services, and hotel-type services. Each of these hospital services may be the object of a specific output measure, or attempts may be made to aggregate them into one measure of output (unlikely to be homogeneous). Ultimately the measure employed i s l i k e l y determined by the question being addressed. At the second level, we find that within each of these broad categories, many conflicting proxy measures exist. Thus, for example, i f one wished to compare costs of hotel services across hospitals, necessitating the development of a unit of measurement, the problems entailed i n aggregating food services, laundry etc., would severely hamper any such efforts. In a similar vein, our emphasis on comparing unit costs for inpatient care requires the definition of a unit of inpatient a c t i v i t y . Such measures as patient days, episodes of i l l n e s s and admissions have been, or might be, employed. Yet each of these i s of a heterogeneous nature and, i n addition, use of any two alternative measures from this group may yi e l d conflicting ordinal and cardinal hospital rankings - i.e. one hospital which reports twice as many days stay as a second hospital and ranks f i r s t amongst a l l hospitals by that measure, may find i t s e l f far down the l i s t when admissions or discharges are employed, and may even rank lower than the second hospital. While this i s a simplistic example, i t does i l l u s t r a t e the conceptual d i f f i c u l t i e s inherent i n the output measure choice. In what sense, then, i s i t legitimate to estimate short- or long-run average cost curves which relate capacity to average cost per unit? Costs w i l l vary dramatically according to type of case, severity of case and quality of care. Furthermore, attempts at time series analysis encounter the additional problem of product change over time due to fluctuations (or trends) in quality. Thus any meaningful, and potentially useful, analysis of the variance i n average costs across production units i s dependent upon the establishment of a homogeneous output measure which standardizes for variation (across hospitals and over time) i n the product. Commonly used measures of output for hospitals (with and without adequate standardization for case mix) have been discharges, separations 3 or admissions, and days stay. Failure to standardize the former measures results in the implicit assumption (in the extreme case) that the discharge of a tonsillectomy patient and the three month stay of a patient suffering from a malignant carcinoma are equivalent output units. Even i f one could assume that treatment costs are roughly equal (and there i s no evidence to indicate that this i s a correct assumption), the di f f e r e n t i a l in 'hotel-type' costs as a direct result of variation i n length of stay makes use of unadjusted cases an analytically vacuous procedure. Use of un-standardized patient days as a measure of hospital output hinges on equally tenuous assumptions. In this case, the supposition that 'hotel-type' costs (food, laundry and linen etc.) are f a i r l y uniform across days of stay may not be unrealistic. Extending this to treatment costs, however, presupposes 1 0 5 homogeneity of (.for example) the treatment associated with a recuperation day subsequent to the tonsillectomy, and a day spent in the operating room undergoing major surgery, a clearly unrealistic supposition. The measure of hospital output employed in this project, hospital discharges and deaths of adults, children and newborns, employs one of a number of possible methods of standardization. In general, the problem of standardization for variance in case mix i s one of reducing a C - element vector (C = total of discharges and deaths) for each hospital to a manageable level, through some use of weights or proportions. A number of approaches have appeared i n the literature. One basic methodology involves the aggregation of cases into a specific grouping of diagnostic categories, computing the proportion of t o t a l cases f a l l i n g within each category, and using the resulting proportions as independent variables i n an average cost per case equation. Feldstein (1967) u t i l i z e d this method of analysis to develop an alternative means of standardization which w i l l be discussed below. However, i t has two major shortcomings. The model can be extremely burdensome, especially i f one wishes to capture a significant level of distinction between case types. Recourse to use of 188 variables corresponding to the 188 category Canadian l i s t , for example, i s clearly intractable. Secondly, one may encounter serious 4 collinearity problems amongst the proportions. Reduction in the number of independent variables may, in i t s e l f , take many forms. The most simplistic, and least satisfactory, i s to increase the level of aggregation so as to decrease the number of diagnostic categories. However, anything gained through aggregation w i l l be lost through the re-introduction of heterogeneity within categories. A second approach employs principal components or factor analysis, whereby the number of variables i s reduced while the major portion of the variance in the original maintained. This method was employed by Evans (.1971) , who reduced forty-one diagnostic proportions to ten principal components (linear combinations of the original vectors, after standardization to zero mean, unit variance) which accounted for 70% of the variance i n the case mix proportions. Further reduction of the number of independent variables required to capture the variance i n case mix i s possible through the use of information theory, and i t i s that route which we follow below. This method i s employed to derive a measure of the complexity of case mix, as well as a 'specialization 1 measure, for each hospital. Development of each i s described i n detail i n Chapter 5. The principal advantage of this methodology, as i l l u s t r a t e d by Evans and Walker (1972), i s that a small number of variables appears to more than adequately standardize cost per case for variations in case mix. Use of some variant of the 'case proportions as independent variables' route does not, however, exhaust the p o s s i b i l i t i e s for standardization. Attempts at s t r a t i f y i n g hospitals according to their service mix (range of available services and f a c i l i t i e s ) and at estimating separate equations for each hospital grouping involve the implicit assumption that hospitals offering similar services and f a c i l i t i e s produce relatively homogeneous output. While this may be one step better than no standardization, i t also requires that we believe s e r v i c e / f a c i l i t y mix to be a vali d proxy for case mix. This neglects not only the p o s s i b i l i t y that similar capacity may be d i f f e r e n t i a l l y deployed in different settings, but also the fact that some hospitals may embody varying degrees of excess, 6 underutilized, capacity. Feldstein (1967) made use of case mix proportions in i l l u s t r a t i n g another potential standardization technique. By regressing ward cost per case for each hospital on twenty-eight case mix proportions (actually 1 0 7 twenty-seven plus a constant), he was able to derive case-specific average costs. By adding the parameter estimate on a given case proportion to the estimated constant term, he computed relative case costliness figures which could then be employed as weights in the derivation of a composite output measure for each hospital. In theory this i s an admirable method and, indeed, the case costs we derive in this project could be used for just such a weighting exercise. Feldstein's analysis ran up against two major roadblocks, however: (i) use of the twenty-eight case proportions yielded three negative average cost per case values (1967,34); (ii) reduction of the twenty-eight categories to nine eliminated the problem described in ( i ) , but substituted an equally serious problem which was noted above: his nine categories, such as "general medicine", "general surgery" and "ear, nose and throat", embodied a level of disaggregation which we suspect solves l i t t l e of the heterogeneity problem. As noted above, the output standardization approach u t i l i z e d in this project derives from information theory, and was pioneered by Evans and Walker (1972). This method successfully circumvents the problem of overburdened equations, while concurrently retaining the a b i l i t y to incorporate the information inherent i n any level of diagnostic dis-aggregation (subject to the absence of extremely small samples). This i s achieved through weighting and aggregating a l l elements in the case mix vector. Derivation of the weights, or case complexity values employs the information theory, but we leave that discussion to the following chapter. We turn now to consideration of other problems encountered in this type of analysis. If standardized cases are employed as the output measure, and assuming the data are available, i t i s relatively straightfor-ward to compute average cost per case as total hospital expenditure divided by t o t a l cases (discharges, admissions or cases at a point i n time, depending on the particular requirements of the analysis). However, r e c a l l that we are interested only i n inpatient a c t i v i t i e s , so that the resulting figure tends to be misleading (upward biased) for a hospital i n which a c t i v i t i e s other than inpatient care take place. Particularly susceptible w i l l be teaching hospitals, hospitals with emergency and/or outpatient departments, and hosp-i t a l s in which any significant amount of research i s undertaken. Variation across hospitals in depreciation, interest payments and related non-depart-mental expenses further complicates the issue. In particular, depending upon the vintage of the hospital capital stock (physical structure), depreciation and interest are l i k e l y to vary. Construction costs themselves pose no problem, since they are not recorded as part of operating (or total hospital) expenditures in our data and we do not wish to include them, as there i s no overwhelming reason for supposing that they w i l l affect inpatient cost per case. The lat t e r consideration arises due to the fact that the hospitals being considered are not-for-profit enterprises, receive funds for replacement of equipment, construction and renovation from a third party, and thus feel no obligation (i.e. to shareholders) to attempt to recapture capital costs through increasing prices. For that reason we can r e a l i s t i c a l l y assume that capital expenditures w i l l have no effect on operating expenditures and that they w i l l therefore not influence unit inpatient costs. The development of the dependent variable, cost per case, described i n Chapter 5, includes a detailed guide to our entire 7 process of non-inpatient activity deletion. Bri e f l y , an attempt (admittedly not 100% successful) i s made to extract a l l non-inpatient related expenses from total hospital expenditures, prior to division by total separations. 1 0 9 The issue of quality of care i s s t i l l largely unresolved, and no new methodology i s introduced here. Thus, the implicit assumption in our analysis i s that a l l hospitals provide care of equal quality. Note that this i s a separate issue from that of sophistication of care. If we assume that general practitioners and specialists, for example, produce different products, rather than similar products of different quality, then i t may not be unrealistic to assume that hospitals do, i n general, 8 provide equally competent care, but at varying levels of sophistication. Remaining considerations include the appropriate measure of scale (or size, or capacity) of hospital operation and the interpretation of, or underlying micro-foundations for, cost curves as developed in the ensuing discussion. Turning f i r s t to the former problem, an excellent discussion of the relative merits and demerits (more of the l a t t e r than of the former) of measures such as beds, bed days, bed complements and patient days, appears in Berki (1972, 100-104). The thrust of the issue, however, i s that capacity i s meaningful only i f stated in terms of the relevant output and the associated binding production constraints and, i n the case of a multiproduct 'firm' such as the hospital, no one measure captures a l l constraints. As noted ear l i e r , subsets of bed capacity are often not inter-changeable across service areas (and thus across case types). The measure used here, rated bed capacity, thus embodies the unrealistic assumption of perfect substitutability between beds set aside for various diagnostic conditions. It i s superior, however, to the other measure prevalent in research in.this area, patient days, use of which involves the problem of regression fallacy and i s , at any rate, more a 9 measure of throughput than of capacity. Finally, we noted in the introduction to this chapter that we would be employing a behavioural average cost equation. To elaborate on that, 110 a true cost curve " i s l o g i c a l l y predicated upon the existence of a production function which specifies, for any level of output, the e f f i c i e n t com-binations of relevant inputs". (Berki, 1972,85) We can propose no convincing argument to support a suggestion that hospitals operate as cost minimizers, combining inputs in an e f f i c i e n t manner for any level of output. The' absence of p r o f i t maximization, and the presence of a t r i p a r t i t e power structure overseeing the operation of the average hospital (administrator, board of trustees and medical staff) while concurrently maximizing individual u t i l i t y functions (which we assume include various hospital characteristics), provides no rationale for assuming a hospital to be operating on an economically e f f i c i e n t production frontier. Thus, economically e f f i c i e n t production functions cannot be identified and we must satisfy ourselves with the estimation of cost equations characterized by "parameters (which) contain a mixture of behavioural and technical effects" (Evans and Walker, 1972, 398). The .equations are thus referred to as behavioural i n the sense that they describe the actual behaviour of the hospitals during the relevant period of time. This discussion has provided a brief description of some of the more prevalent obstacles encountered in hospital cost equation estimation. In addition, i t has delineated those problems with which we are prepared to l i v e , and has concisely outlined our approaches to circumventing the others. The following development of a hospital cost equation draws heavily on the work of Evans and Walker (1972) and i s , i n fact, an extension and modification of that analysis. We proceed from an i n i t i a l assumption - that hospital in-patient costs are comprised of a fixed (per bed) and a variable (per case) 10 component. In addition, we allow for possible non-linearity in the capacity variable by entering beds in quadratic form.^ Specifically, 1 1 1 we are assuming that TC = PjB + p 2B 2 + p 3C where TC = total inpatient cost B = rated bed capacity C = cases (separations i n year) P i = cost per bed 2 P 2 = cost per bed P 3 = cost per separation. In the formulation below, p 1 and p 2 are assumed to be constant functions. One could argue that, for the sake of consistency, a C 2 term should also be included, to incorporate possible non-linearity of case load influence. However, the convention has been to include a quadratic form of the capacity variable to test for economies of scale. There i s no compelling intuitive argument for including C 2, other than int e l l e c t u a l curiosity. Such a hypothesis was tested empirically, with the resulting parameter estimate on C 2 proving to be s t a t i s t i c a l l y insignificant (not significantly different from zero) at a 99% confidence le v e l . Let us now consider the form of p 3, the cost of a particular case. It i s plausible to presume that the cost of a standardized 1 2 inpatient case w i l l be a function of the length of hospital stay (L) for that case. The specific formulation of that function was the subject of a considerable amount of attention. Three p o s s i b i l i t i e s are discussed here: (i) Let d x, d 2 d^ represent costs in each successive 'day of stay' within a case of length of stay L. Then, L TCC = I d . i»l 1 where TCC i s the t o t a l case cost for a specified case. 112 The simplest form for p derives from assuming d. to be a linear 3 1 function of time elapsed in hospital: d. = d + X(i-l) where d., d T > 0. 1 l Xi This yields TCC = S d. = Ld + A(L 2 - L) = Ld i=l 1 2 where d, average cost per day = Ed : = d x + d L = ^ 1 + A(L-l)) Clearly, the case of constant cost per day i s an element in this set of functions, that being where A = 0, implying TCC = Ld (ii) At a slig h t l y more sophisticated level, one might hypothesize that cost per day declines in such a way as to asymptotically approach a-a minimum cost per day, d, which may be thought of as the 'hotel' costs embodied i n an inpatient day i n hospital. As a particular case, we postulate that (d^ — d) declines geometrically, so that (d^ - d) = A(d^ - d), where A i s a scalar. This i s i l l u s t r a t e d below: Figure 4.1: Geometrically Declining Treatment Costs Per Day cost per day d • '—< « * — i — i — * — * • — i — « — t — > 1 2 3 1 * 5 6 7 8 9 10 11 12 13 L day 1 1 3 Thus, lim d. = d or, as the average case nears discharge date, the i-*L 1 major portion of cost per day i s comprised of non-varying hotel-type costs. In this particular example, 5'1 * L * TCC = E d . = Ld + I (d. - d) 1=1 1=1 ^ !^ ^ , i - l = Ld + Z (d - d)X i=l The second term on the right hand side of the f i n a l equation above i s a geometric series whose sum i s : (1 - X )•(d x - d) 1 - X so that ^ ,L *Vi TCC = Ld + (1 - X )•(d 1 - d) (1 - X ) for a particular case, ( i i i ) There i s clearly no l i m i t to the number of configurations one could dream up and attempt to j u s t i f y as being reasonably representative of the pattern of hospital cost per day as the 'average case' progresses. So far, we have considered the family of linear relationships between cost per day and time, and the case in which cost per day i s at a maximum on day 1 and declines geometrically toward a long run cost per day, d, thereafter. Intuitively, a more satisfactory formulation would incorporate what casual observation suggests - that costs per day commonly peak early on in a case, but subsequent to the f i r s t day, and then decline u n t i l date of discharge. The gamma distribution, with an appropriate selection of parameter 1 3 values, provides us with a method of capturing such a cost pattern. This distribution, f (x) = ( 1 ) • (x e H) i s i l l u s t r a t e d below f o r $ = 1, and v a r i o u s v a l u e s o f a. F i g u r e 4.2: Gamma D i s t r i b u t i o n l.o 4 f (x) .75 .5 0 + I f , as i n t h e p r e v i o u s c a s e , we assume t h a t (d^ - d) appr o a c h e s 0 as i + L, t h e n t h e a r e a under t h e gamma d i s t r i b u t i o n , from some i n i t i a l p o i n t A, t o A + L, may be h y p o t h e s i z e d t o be d i r e c t l y p r o p o r t i o n a l t o t h e ' n o n - h o t e l ' component o f c o s t p e r c a s e . To c l a r i f y , A+L f f (x;(X , 3)dx = (TCC - Ld ) / 6 A where 6 = c o n s t a n t o f p r o p o r t i o n a l i t y . F i g u r e 4.2 i l l u s t r a t e s a case o f s i x days d u r a t i o n , assuming A i s e q u a l t o h. The i n t e g r a l i s t h e n t h e shaded a r e a o f t h e f i g u r e . F o r o u r p u r p o s e s a v a l u e o f a = 1 was cho s e n , as f ( x ; l , 3 ) most c l o s e l y a p p r o x i m a t e d t h e p a t t e r n we b e l i e v e d t o be r e p r e s e n t a t i v e o f t h e c o s t / d a y t r e n d . Three f r e e p a r a m e t e r s , 5 , A and 0 r e m a i n e d . To s i m p l i f y , we p r o c e e d as f o l l o w s -x /B . A+L A+L / f ( x ; l , 3 ) d x = / 1 xe dx 6 ' A+L r i 2 -kx, = J k xe dx A ( s e t t i n g k=l) 8 L e t t i n g F ( x ) r e p r e s e n t t h e c u m u l a t i v e d i s t r i b u t i o n , X 1 5 x . -x/8 FCx) = / — i - • X 6 d x  0 cv.3 a + 1 we have, for a a positive integer, F(x) = 1 - ( 1 + x + x 2 + x 3 + ... + x a ) - e ~ x / &  3 2 1 6 2 3 ! B 3 a'.if (Mood & Graybill, 1 9 6 3 , 1 2 8 ) . In this particular example, a = 1 and k = 1^, yielding, B -kx But, F(x) = 1 - ( 1 + kx) -e A+L / fdx = F(A+L) - F(A) A = - ( 1 + k(A+L))-e" k ( A + L ) + ( 1 + kA ) - e _ k A —kA — V T . = e (i + kA - e • ( 1 + kA + kL)) = SUMD (for convenience of notation) Thus, TCC = Ld + 6SUMD We now consider development of the complete average cost equation, given each of these cases. Recall that the equation is based on the assumption that total inpatient hospital cost takes the form TC = p xB + p zB 2 + p 3C As noted above, pl and p 2 are assumed constant functions, while p g, cost per case, was hypothesized to be a function of average length of stay (L), after appropriate standardization. We have delineated three distinct possible formulations for the effect of length of stay, those being: (i) p 3 = Ld - a. , L % (ii) p 3 = Ld + 1-X • (d1 - d) 1 -X a, ( i i i ) p 3 = Ld + SUMD 1 1 6 where p 3 i s the standardized cost per case. The task remaining i s the formulation of this standardization. Recall that the earli e r discussion in this chapter dealt with two main themes, those being standardization for case mix variation, and elimination of non-inpatient components of total expenditure. Thus, we can postulate that p = f(p„, CMPXC1, SPCLC1, ) 3 d where CMPXC1 and SPCLC1, to be defined below, are the case mix and specialization standardization variables respectively. In addition, to adjust for the possible unequal influence of age-sex patient distribution, we wish to standardize for this through inclusion of a set of variables representing the actual age-sex patient distribution within each hospital. Finally, the cost of a specific case may be a function both of wage levels within a hospital, and of the s k i l l mix of non-medical staff personnel attending to the patients. A variable i s included to standardize for each of these potential variants across hospitals. Costs of similar cases in. different hospitals may vary to the- extent that the effects of non-inpatient a c t i v i t i e s in some hospitals influence a l l hospital functions. A good example might be education, where elimination of s t r i c t l y educational expenses (see next chapter for l i s t of items which require deletion) does not detract from the fact that the educational function, and the expertise and capital attached to i t , i s undoubtedly shared by a l l inpatients. To this end, we include three variables, for education, outpatient and non-departmental expenditures, which play a dual role: (i) they attempt to standardize for any influence of these a c t i v i t i e s which spreads beyond those items which can be spe c i f i c a l l y delineated as being comprised of expenditures only for those functions, and, 1 1 7 (ii) they provide a check on the success of our non-inpatient expenditure elimination. The resultant standardization yields a p, function of the form: p„ = an + a,CMPXCl + a SPCLC1 + a EDRAT + a DEPRAT + r 3 0 1 2 3 i+ a,Fl + acF2 + a,F3 + a F4 + a F5 + a, F6 + 3 o 7 8 9 10 a,,OUTXPR + a,„WAGEl + a, WAGE2 + p 11 12 13 f 3 The variables are only briefly explained here, as their development is the subject of Chapter 5: CMPXC1 - As mentioned earlier, this variable is intended to capture differences across hospitals in case-mix proportions and is a measure of the complexity of hospital case load; SPCLC1 - a measure of hospital specialization; i.e. an indication of the degree to which a hospital is limited in its capacity to handle a wide range of case types. "... in general we expect small hospitals to be more specialized as they are geared up to handle only a smaller range of cases." (Evans and Walker, 1972, 402) ; EDRAT - indicates the magnitude of the effect of educational activities on inpatient costs; DEPRAT - as in EDRAT, for non-departmental (i.e. interest and depreciation) expenditures; OUTXPR - as in the above two, for out-patient expenditures; FI - F6 - the factor scores from a factor analysis of the inpatient age-sex distribution of cases across hospitals. WAGE1 WAGE 2 a relative measure of the degree to which a hospital utilizes a skill-intensive non-medical staff labour force. a relative measure of the wage level of non-medical staff personnel. Then, for each of the three formulations of p3, we have a distinct p3 function. It should be noted, before we proceed, that whereas the p3 function suggests that the cost of a specific case is a function of various hospital variables, it is also a function of the length of stay, L, for that case. When attempting to extend this over all hospital cases, we 1 1 8 are forced into the aggregative analogy,.that the average cost of hospital cases i s a function (and in particular the identical functional form) of average length of stay for a l l hospital cases. This act of faith i s the result of the fact that we believe i t imposes no unrealistic assumptions and that there i s , as usual, l i t t l e else one can do. We now return to our three p 3 specifications, and b r i e f l y set out the average cost per case equation for each: (i) CASEX = average inpatient cost per case = TC/C TC = total inpatient expenditure C = number of inpatient discharges and deaths; = PjB + p 2B + a + ajCMPXCl + a 2SPCLCl + C G a3EDRAT + a^DEPRAT + a 5 F l + ... + a 1 QF6 + a,,OUTXPR + a,,WAGEl + a, WAGE2 + Ld 11 12 13 ( i i ) In this case, the f i n a l term i n the CASEX equation i s replaced by Ld + (1 - A ) . (d x - d) 1 - A so that, since we know L and can set A , the parameter on the second term w i l l be an estimate of ( d 1 - d). In general, we would expect A to take on a value such that .5 < A <_ .9, since i t i s unlikely that costs of successive days stay w i l l decline in a more rapid manner, for the 'average case*, ( i i i ) . Here, Ld i s replaced by Ld + 6SUMD and i t i s necessary to estimate jointly the 'best' values for k and A. The value of 6 then provides an estimate of the magnitude of the 'multiplicative factor' which must be applied 1 1 9 to the cumulative distribution in order to arrive at the estimate of the variable cost per case. One other formulation of the TC equation was considered and i s br i e f l y discussed here before we proceed to determine the relative merits of the above three equation specifications. It seems plausible to suggest that hospital planning and budgeting take into account, among other considerations, the expected case load in determining estimated expenditures for a future time period. To the extent that this i s the case, one might believe TC to be a function not of actual cases, but of expected case load, so that average case cost would be a function of the ratio of expected, to actual case load. More e x p l i c i t l y , TC = PjB + P 2B + p 3C* * where C i s the expected case load, determined prior to the period being considered, so that, 7 * CASEX = p B + P 2B + (a Q + ajCMPXCl + ... + Ld)C C C C for the (i) formulation of the average length of stay term. The theoretic appeal of this formulation tends to diminish as one * attempts to determine a method of calculating C . The route followed * * * here was to assume that C_ may be approximated by OCC , where OCC = C OCC expected occupancy rate. Two methods of calculating expected occupancy rate were then u t i l i z e d . Briefly, one expected occupancy value was constructed on the premise that the hospital planners expect occupancy to grow at a constant rate (assuming no change in capacity). The second * value was simply OCCfc = OCCt_^; expected occupancy i s equal to last time period's actual occupancy rate. The development of these variables appears in Appendix 4A, along with a brief discussion of empirical results from the equations which employed them. Both of these alternative specifications were rejected for econometric reasons, leaving a number of alternative hypotheses as potential explanations for the lack of explanatory power exhibited by these options: (i) this was not, in fact, as good a representation of the relationship between TC and C as the e a r l i e r formulation employing C rather than C ; * * (ii) OCC i s not a good proxy for C ; OCC C ( i i i ) capacity changes, which were not taken into account, occurred to such an extent that no accurate trend i n occupancy rates could be established. The lat t e r hypothesis may be eliminated immediately, as such changes were scarce in relation to the number of hospitals under consideration. 1 There i s also no immediately apparent j u s t i f i c a t i o n for accepting ( i i ) , as we would expect these terms to move together, again assuming no anticipated changes in bed capacity. We are l e f t with ( i ) , i n the absence of al t e r -native hypotheses, and therefore we confine our subsequent attention to the original TC equation specification. We now return to consideration of the three alternative average cost equations based on using C rather than C* i n the underlying TC equation. Specification ( i i i ) has the greatest intuitive appeal, being based on an hypothesized increasing and then decreasing cost per day pattern. A p r i o r i expectations would dictate a positive parameter on the SUMD term, a result not supported by actual estimation of the equation. A regression routine labelled GRIDMAX (U.B.C. Computing Centre) was employed to scan parameter estimates and error sums of squares over various ranges of k and A. This program carries out parameter estimation for user-specified pairs of (k,A) values. In the majority of cases, the optimal value of k (that value for which the error sums of squares was a minimum, for given A) f e l l in the range 0.6 to 1.1; the optimal value of A f e l l between 0.01 and 0.5. However, in a l l optimally f i t t i n g equations for various years, the estimate of 6 proved to be negative, hardly coinciding with the theoretical interpretation of that parameter. Further reflection suggests that this should not have been a tot a l l y unexpected result and, in fact, l i t t l e gain should have been expected from increasing the sophistication of the length of stay term. The d i f f i c u l t y stems from the fact that, with this formulation, the majority of the variance i n the variable portion of case cost (SUMD) would occur for observations i n the lower range of length of stay. As the bulk of our observations for hospitals f a l l in the range of 6 to 10 days for L, there i s very l i t t l e variation across hospitals i n the value of SUMD. A similar problem appears to plague the results using specification ( i i ) . Again, negative parameter estimates, this time corresponding to (d^ - d), resulted from the estimation. The additional sophistication of formulations (ii) and ( i i i ) i s not supported by their explanatory power. For the observed range of average lengths of stay, one can find an appropriate d (average cost per day) such that variation i n Ld across hospitals closely approximates the variation a. in Ld + either the sum of the geometrically declining difference or the integral of the gamma distribution, appropriately weighted. Thus, inclusion of a linear specification for average length of stay not only f a c i l i t a t e s the mechanics of estimation, but suffices in capturing the effect of L on CASEX. This chapter has devoted i t s attention to development of an i n i t i a l average cost equation which, i t i s f e l t , captures a major portion of the behavioural characteristics of the acute care hospital. The equation undergoes further minor surgery as a result of econometric diagnoses in Chapter 6. Prior to that, however, a chapter must be devoted to operation a l i z i n g the variables described above. Chapter 4 - Footnotes 1. See, for example, Lave (1966), Jenkins (1974), Mann & Yett (1968), and Chapter 2 of Migue and Belanger (1974). 2. For a thorough treatment of the entire hospital output issue, the reader i s referred to Berki (1972), Chapter 3. 3. Feldstein (1967) discusses the advantages of using cases as opposed to days (or weeks) stay, prior to case-mix adjustment. The primary consideration i s the fact that using days as an output measure tends to penalize hospitals which attempt to concentrate nursing or medical costs into a shorter time frame, i n order to reduce length of stay, and thus case costs (pp. 24-5). The major d i f f i c u l t y i n using cases as a measure of output, even with case-mix standardization, derives from duplicate admissions (the same patient being re-admitted for the same episode of illness) or transfers between hospitals. This may bias downward the case costs and, more important, the bias may be confined to, or concentrated within, certain diagnostic categories, making relative comparisons across cases a somewhat suspect exercise. 4. This was, i n particular, the experience of Evans (1971) . See pp. 202-3. 5. A detailed look at principal components analysis appears in the following chapter, where age-sex factor scores are derived from the age-sex distribution of hospital discharges. 6. For a description of other similar approaches the reader i s referred to Berki (1972, 87-97). 7. Also, see Evans (1971, 199). 8. The SPCLC1, or specialization, variable described i n the following chapter may be thought of as a reasonable proxy for average level of sophistication of care. 9. The regression fallacy may be simply i l l u s t r a t e d by considering two hospitals, each reporting 10000 patient days per year. Assume 1 2k hospital A also reports an occupancy rate (defined as total patient days divided by rated bed days - 365 x no. of beds) of 80%. Hospital B on the other hand i s underutilized a l l year and compiles an average occupancy rate of only 25%. Use of hospital days as a scale measure describes these two hospitals as having equal capacity (or being of equal 'size'). Yet i t i s quite l i k e l y that hospital B w i l l report a much higher average cost per case than hospital A, due to the large fixed cost proportion of this figure. While a large portion of the variation i n case costs might be the result of differences i n rated bed capacity i n that particular year, use of patient days w i l l almost certainly lead to erroneous conclusions regarding scale effects. See also Feldstein (1967, 79-80). 10. It i s important to note our use of the fixed cost terminology here, as i t differs from standard economic usage. Normally, fixed costs would refer to the value of capital stock and equipment, and associated costs. But i n this analysis, such costs have been deleted from total operating expenditures, as we are considering only inpatient costs. Within those operating expenses (inpatient), i t i s then assumed that a l l expenses associated with a staffed bed are 'fixed', while the remaining expenses which are a function of the occupancy of that bed are termed variable expenses. The premise i s , of course, that the costs of the capacity (both staff and equipment) necessary to support a potentially f i l l e d bed are fixed i n the short run, whereas the actual treatment, diagnostic, food and laundry costs, for example, are encountered only upon the admission of a patient to f i l l that bed. 11. The inclusion of bed size in quadratic form allows subsequent testing for evidence of economies of scale. See Chapter 6 for details, and Berki (1972) for problems associated with such an analysis. 12. By standardized i s meant the adjustment for variation over hospitals in case mix which may include adjustment also for variation in the age-sex composition of hospital case load. 125 13. See Whitmore (1975) for a similar formulation, using an inverse Gaussian distribution. Unfortunately Whitmore does not test i t s applicability for this type of analysis. 14. See the B.C. Department of Health's Report on Hospital Statistics which, for each year, contains a section entitled "Hospital Construc-tion and Changes i n Hospitals". In 1973, for example, the entire province of B.C. experienced a net addition of 112 inpatient acute care beds in the 87 hospitals being considered in this analysis. Furthermore the number of hospitals involved i n these capacity changes was small. 126 Appendix 4A: Expected Occupancy Rate Options The original motivation for considering plausible methods of calculating an expected occupancy rate was, as earlier discussed, i t s use as a proxy for expected case load. More correctly, the ratio of expected to actual occupancy was to be used to approximate the corresponding case load ratio. This derived, i n turn, from the feeling that total hospital expenditure did not depend so much on actual case load, as on anticipated case load. Such a hypothesis holds particular appeal in a setting in which hospitals are funded on a global budgeting basis. If expected expenditures are linked to expected case load, and the hospital i s bound to i t s expectations in that reimbursement i s a function of a prospective global budget, one might indeed find total cost and expected cases being closely related, even in the presence of a deviation from the case load target; i . e . corners may be cut elsewhere in the presence of case overload. The prime concern of this appendix i s , then, to consider b r i e f l y the development of proxies for the C term which appears i n the TC equation C based on the above hypothesis. In particular, i t was suggested i n the text of this chapter that OCC* provides a reasonable approximation, OCC leaving us the task of computing reasonable estimates for expected occupancy rate. The following notation i s employed: 0* = expected occupancy rate, year t 0 = actual occupancy rate, over year t = actual total patient days, over year t B = rated bed capacity, as of December 31, year t. Assuming that hospital planning and budgeting are based upon an estimated patient load, one possible configuration results from the simple presumption that the occupancy rate expected in year t w i l l be much the same as that of the most recently concluded year, or 0* = 0 , t t-1 Then, °V ° t = °t-i / 0t . A second method hinges on an assumed constant growth of days stay (assuming no capacity (B) changes). This may be i l l u s t r a t e d as: ln DFC = B + <$T so that D - * D An equation of this form was estimated, using ordinary least squares on eight observations (1966-73) for each hospital, yielding hospital specific th parameter estimates b. and c. (i hospital) for B. and 5.. Since 1 1 i i °t = V3-65-Bt i t follows that 0*t = (exp(bi+cit))/C3.65-B ) One could hypothesize increasingly sophisticated trends for occupancy rate. However, the personnel responsible for planning or budgeting are unlikely to hypothesize any pattern of a more complex nature than those described here when estimating budgetary requirements, as they would be primarily interested in a close approximation, based on relatively recent past performance and any other relevant information peculiar to the upcoming year. Results from estimations u t i l i z i n g 0* in the CASEX equations were 0 unimpressive. In a l l cases, the 0* variable (irrespective of which of 0 the two formulations was included) added considerably less explanatory power to the equation than straight inclusion of unweighted p.. 128 Chapter 5: From Theory to Practice - Data Compilation and Variable Creation In the previous chapter we outlined the development of an average cost equation which took the form: CASEX = a + PjB + p2B_2+ ajCMPXCl + a 2SPCLCl + a 3 EDRAT ° C C + a^DEPRAT + a5OUTXPR + a g F l + + a u F 6 + a12WAGEl + a13WAGE2 + dL This chapter w i l l be devoted to a discussion of the sources of data harnessed to create these variables and to the development of the variable values themselves. The relevant hospital data are comprised of three components: f a c i l i t i e s and services, expenditures, and u t i l i z a t i o n . A l l public hospitals are required to f i l e completed HS-1 and HS-2 forms with Statistics Canada, Health Division, on an annual basis. The HS-1 return records f a c i l i t i e s and services, while the HS-2 form contains the expenditure and income information. The data supplied on these forms are coded and stored on magnetic tape. In B r i t i s h Columbia, the Research Division of the B.C. Hospital Programs, within the Department of Health i s responsible for a l l admission/separation records, and stores these on magnetic tape. These tapes provide age, sex, length of stay and diagnosis data for a l l patients who were released from the hospitals under consideration. The data u t i l i z e d i n this study are from 87 public general B.C. hospitals, for the years 1966-73. No rehabilitation or extended care hospitals are included in the analysis, although acute care hospitals do treat some extended care patients. In addition, any hospital which did not operate for the f u l l eight years (1966-73) was excluded, except for the purposes of creating the case-mix and specialization variables which are dependent upon total provincial case load. A list of the relevant hospitals, their locations and their code numbers (both provincial and federal) is included as Appendix 5A. At this point it may be useful to note that the equations reported by Evans and Walker (1972) explicitly included OCC - occupancy rate, ALS - average length of stay (our L here), and CFR -case flow rate, in a linear form. Case flow rate was defined as cases per bed year or, in terms of the earlier notation, CFR .= C/B The alternative equation formulation suggested in Chapter 4 yields, as short run variables, the reciprocal of case flow rate, average length of stay as in the Evans/Walker equation, and does not include occupancy rate at all.'*" Thus we can reformulate our equation as follows: CASEX = aQ + PjINVCFR + p2BDCFR + a^ MPXCl + a2SPCLCl + a 3EDRAT + a,DEPRAT + acOUTXPR + a Fl + + a,,F6 k 5 6 11 + a12WAGEl + a13WAGE2 + dL where INVCFR = B/C BDCFR = B2/C . The construction of each of the variables from the data sources noted above is described in the following sections of this chapter. CASEX, CASEXD CASEX is formally defined as in-patient cost per hospital separation. Thus it is total expenditure on inpatient care divided by number of separations. From total hospital expenditure (TOTEX) as reported in the HS-2 form, the following items were subtracted to arrive at an estimate of inpatient expenditure (IPEXP): 13 0 (i) expenditure on nursing and medical education; (ii) non-departmental expenses, which include interest on loans, depreciation on land improvement, depreciation on buildings and service equipment, depreciation on major equipment and rental expenses;2 (iii) expenditure on special research projects; (iv) share of administration expenses allocatable to non-inpatient care (see below); (v) estimated direct outpatient expenses which include expenditure on the organized outpatient department, outpatient portion of radiology and laboratory department expenses'*, outpatient share of emergency department expenses, all ambulance service expenses, outpatient share of operating room expenditure, and outpatient physiotherapy expenses.4 With regard to item (iv), total administrative expenses were initially subtracted, after which the following adjustment was undertaken to add back the inpatient share of administration services: Let IP = TOTEX - (items (i), (ii), (iii) & (v) above, plus total administration expenses (ADMIN)). Thus, the initial deletion of non-inpatient expenses includes the entire administrative expenditure component. Now, if we denote the inpatient share of administration by IPADMIN, and items (i), (ii), (iii) and (v) together, by NONIP, it follows that ADMIN = TOTEX - IP - NONIP If we then presume that administrative activity is allocated according to relative shares of total non-administrative (IP + NONIP) expenses, then it follows that IPADMIN = ADMIN • IP IP+NONIP = ADMIN * IP TOTEX-ADMIN Adding this back to IP, we arrive at IPEXP = IP + IPADMIN = total inpatient expenditure. 1 3 1 Thus, the inpatient share of total non-administrative expenses was used as the inpatient weight on administration expenses. Then, CASEX = IPEXP/SEPNS (SEPNS = no. of separations). For the purposes of time-series analysis, either a time variable should be included amongst the independent variables, or the dependent variable should be computed in constant dollars (any independent variables susceptible to price changes over time would be treated i n a similar manner, although no such variable was included i n this particular analysis). The latter route was chosen in this analysis, with 1970 being a r b i t r a r i l y assigned as the base year, and CASEX values for a l l other years being deflated. A detailed description of the creation of an appropriate deflator i s contained in Appendix 5B. B r i e f l y , the deflator was the reciprocal of a Paasche Index constructed using price indices for four components of hospital expenditure: gross salaries and wages, medical and surgical supplies and other expenses, drugs and food, each weighted by i t s relative share of total hospital expenditures.. The resulting variable value, referred to as CASEXD in subsequent discussion, i s then inpatient cost per case expressed in $1970. CASEXD i s the dependent variable employed in the econometric analysis discussed i n the following chapter, and a l l case cost estimates emerging in later chapters are similarly expressed in $1970. INVCFR It was noted above that CFR = C/B = (3.65 • 0CC)/L. Thus, this variable was straightforward. The number of beds (B) was taken from the HS-1 tapes, as rated bed capacity on December 31 of the particular year in question. The 'movement of inpatients' section of the HS-1 form provided data on separations for adults, children and newborns, the 132 total of which formed C. Then, INVCFR = l./CFR BDCFR Corresponding to the B 2 term i n the TC equation, this variable i s simply, BDCFR = B • INVCFR CMPXC1, CMPADJ The development of CMPXC1, described below, i s based upon Theil (1967, 1971) and Evans and Walker (1972). A detailed discussion of the conversion from CMPXC1 to CMPADJ, an adjusted complexity measure, follows the deri-vation of the former variable. Recall, f i r s t , that this independent variable i s to be employed as an alternative to inclusion of either a l l the case load proportions, or principal components derived from these proportions. Basically, hospital complexity (CMPXC1) i s a weighted sum of the (standardized) complexities of cases treated in the hospital, the weights being the proportion of total case load f a l l i n g within each case category. Thus, the principal innovation in the Evans/Walker analysis was the development of a suitable methodology for deriving case complexities. The methodology adopted was an application of information theory. Let us consider an event, say the admission of a particular patient to a hospital, for which we have an a p r i o r i expectation or probability. For example, given that a patient requires hospitalization, and given no further information other than the number of hospitals, N, i n the province, our best ex ante guess might be that that patient has a 1/N chance of entering hospital i . For notational purposes, the probability that a particular patient w i l l enter (or be discharged from) a particular hospital, i , i s denoted 13 3 by p. We wish to consider the information gain arising from a message indicating the exact location of admission or separation for a particular patient. Intuitively, i f p is close to 1 for that patient and a given hospital, and the patient ultimately enters that hospital, we have gained l i t t l e information. On the other hand, i f we have no information other than the number of hospitals, and N i s large, then the information gain from a message conveying the hospital chosen w i l l be higher. Thus, " i f we want to measure the information received from a message in terms of the probability p..." of an event occurring, we would need a decreasing function of p (Theil, 1971, 637). The logarithm of the reciprocal of the probability i s commonly used, due to i t s additivity for independent events (Theil, 1967, 4). Letting h represent the 'information gain' function, we postulate, h(p) = ln(l/p) . 5 Given that we know the probability of an event occurring, we can derive the expected information gain from a message indicating whether or not the event occurred from EG = p-h(p) + (l-p)-h(l-p) = p-ln(l/p) + (l - p ) - l n ( l / ( l - p ) ) where (1-p) refers, of course, to the probability of occurrence of the complementary event. If we extend this to a situation i n which there are N mutually exclusive events, one of which must occur, then N S p. =1 In this case the expected information content of the message indicating occurrence of one event, or alternatively "the entropy of the distribution whose probabilities are p ,...,p^" (Theil, 1971, 640), i s given by 1 Zk N N EG = 2 p.h(p.) = I p.ln(l/p.) . , 1 l . , l l 1=1 1=1 To this point the discussion has dealt exclusively with prior probabilities of an event occurring, and with messages conveying information related to the actual incidence of events. We consider, now, messages of a different nature, which transmit information on posterior (or altered) probabilities. Returning to the case of one event with prior probability p, l e t us assume we receive a message indicating that the probability of that event occurring has now changed to q. (Clearly the earl i e r example, wherein the event did occur, i s but one p o s s i b i l i t y , with q=l). What information gain i s embodied in such a message? If the event which we are considering ultimately occurs, and we have prior information only on the original probability, p, of such an occurrence, i t was posited that the information gain from a message indicating occurrence was l n ( l / p ) . We have now received an updated probability, q, of that event occurring. If the event subsequently occurs, the information gain from the actual occurrence message w i l l be l n ( l / q ) . Therefore, the information gained by receiving the message conveying the altered probabilities w i l l be repre-sented by the difference in these two values, h(p) - h(q) = ln(l/p) - ln(l/q) = ln(q/p). Note, of course, that there i s an actual information gain deriving from knowledge of the revised probability only i f a subsequent message conveys further information regarding occurrence of an event. The expected information content of the message conveying the new probability, q, i s now straightforward, being, EG = q-ln(q/p) , i.e. the new (posterior) probability of the event occurring times the 13 5 information gain i f the event does occur. Extending this to N mutually exclusive events, for which we receive posterior probabilities q^ in a message, the expected information gain w i l l be EG = E q.•ln(q./p.) 1 1 1 Now, i n the context of hospital case load distribution we introduce the following notation: 7 p. . - c. ./C. ID ID i where c.. = no. of cases of type j i i i n hospital i ; = total cases i n hospital i . Then the p^^ are the above-noted weights to be used i n computing hospital complexity by aggregating across case categories. In addition, l e t q. . = c. ./C. where C. = total cases of type j i i i i i i i n the province Q. = C./C where C = to t a l provincial hospital ^ separations. If there are N hospitals i n the B.C. 'choice set', i t i s clear that one of these institutions must discharge each case. Then the N hospitals comprise the sample space, and the N mutually exclusive events are simply the p o s s i b i l i t i e s of a particular case being a separation from each of the N hospitals. If the prior probability of a case of type j being a separation from the i ^ 1 hospital i s assumed to be 1/N, i.e. i f there i s no reason for favouring one hospital over another (the only information being available i s the number of hospitals), and i f the posterior probability i s based on the ^ j ' * 3 ' the actual distribution of case type j discharges across B.C. hospitals, then the expected information gain from calculating the ^ j ' 5 1 S EG. = I q.. • ln(Nq..) . D j ID ID But how does a l l this relate to case complexity? The linkage i s 1 3 6 based on the assumed correlation between the magnitude of an information gain, and the complexity of a particular type of case. F i r s t "we hypothesize that complex cases tend to be handled i n a few hospitals with more extensive f a c i l i t i e s and more specialized staff, while relatively straightforward cases tend to be distributed more evenly over the hospital g system". It i s evident from the discussion regarding information theory that the magnitude of any information gained from new feedback i s dependent upon the magnitude of the deviation from the expected message content. As an extreme example, i f we expect 1/N eases of type j to be treated i n each hospital, but find that only one hospital i n the province treats this case type (q^_. = 0 V hospital except one), we experience a large infor-mation gain when a subsequent case of that type i s discharged from any hospital. Similarly, the value of EG_. for that case type w i l l be relatively high, which i s synonymous with what we may reasonably regard as an extremely complex case type. Thus we have a direct relationship between the hypothesized complexity concept, and the entropies of the distributions with probabilities of q^^ and 1/N. The larger the expected information gain, (or equivalently the more concentrated the case distribution) the more complex we believe the case type to be. The M vectors (for the M diagnostic categories) representing the distribution of each case category across provincial hospitals are reduced, using the information theory method described above, to a scalar denoted by EG_. , for the j*"* 1 diagnostic category and prior probabilities 1/N. Other hypothetical prior probabil-i t i e s w i l l lead to alternative measures of EG (see Evans and Walker (1972) , for examples). Derivation of CMPXC1 from the N-element vectors requires two further procedures. So as to have average case complexity equal to 1.0, we 1 37 standardize the EG.'s by setting . = EG./I EG.Q. 3 3 j J 3 It follows from the previous discussion that CMPXC1 for the i th hospital is then CMPXC1 We now leave the methodology and turn to the analytics. The case complexity was based upon data for 90.hospitals for the time period 1966-71, while an additional hospital was included in 1972. Three additions and one closure yielded a total of 93 hospitals for 1973. This entire data base was employed to compute case complexities, after which hospital complexities were derived only for the 87 hospitals appearing in Appendix A major obstacle in the computation of CMPXC1 was the fact that primary diagnoses were coded according to the 7th revision of the ICDA (International Classification of Diseases Adapted for use in the U."S.) for the years 1966-68, and according to the 8th revision for subsequent years. During the former time period, the Canadian Hospital Morbidity List consisted of 98 major diagnostic groups, each comprised of various ranges of ICDA categories. This list is contained in Appendix 5C, Table 5C.1. Table 5C.2 of the same appendix contains the corresponding Canadian List for 1969 and subsequent years. Note that this list is comprised of 188 categories. At the outset a C matrix, consisting of the was compiled for each year from the tapes described at the beginning of this chapter. This C matrix was constructed according to the Canadian List of diagnostic categories. Thus, for 1966-68, its dimension was 90 x 98, for 1969-71 5A. 1 3 8 i t was 90 x 188, and 1972 and 1973 contained 91 and 93 rows respectively. For comparability of CMPXC1 values across years, i t was necessary to aggregate the 1969-73 C matrices into N x 98 matrices. The aggregation 9 formulae contained m Table 5C.3 were adopted for this meshing exercise. The result was comparable C matrices for each year, with only the number of hospitals varying s l i g h t l y . Through operationalizing the information theory methodology we derived an N-element CMPXCT vector from the C matrix for each year. The case complexities, H_., are l i s t e d for each diagnostic category in Tables 5C.1 and 5C.2. Time series analysis necessitates further adjustment to the case-mix variable. I t i s not suff i c i e n t to use CMPXC1 since there may be a s h i f t over time i n the provincial case mix proportions. Such a trend would induce a similar s h i f t i n hospital case complexities which would not be captured by a yearly CMPXC1 construction. The hospital complexity measures should thus capture not only case mix dispersion within a given year, but also shifts over time in provincial case mix. To incorporate this temporal effect, an adjusted case complexity variable, CMPADJ, was used, constructed from a base year vector of H 's. The choice of a base year from which to take the case complexities proved to be inconsequential due to the time-invariant nature of these measures. The s t a b i l i t y of the figures i s il l u s t r a t e d i n Table 5.1 below, which reports the correlations of the case complexity vectors over time. i t i s clear that the relative complexity of diagnostic categories was v i r t u a l l y unchanged over the eight year period. In addition, the standard deviations in Table 5B.1 indicate that, i n the majority of cases, individual complexities remained f a i r l y stable. It i s particularly crucial to note that there i s no apparent discontinuity in the pattern Table 5.1: Correlation of Case Complexity Vectors 1966 1967 1968 1969 1970 1971 1972 1973 1966 1.000 0.975 0.946 0.919 0.895 0.894 0.904 0.903 1967 1.000 0.976 0.958 0.940 0.939 0.953 0.945 1968 1.000 0.964 0.951 0.949 0.954 0.953 1969 1.000 0.986 0.979 0.975 0.972 1970 1.000 0.990 0.978 0.976 1971 1.000 0.984 0.983 1972 1.000 0.991 1973 1.000 of correlations between 1968 and 1969, indicating that the aggregation algorithms of Table 5B.3 introduced no undue distortions. Further checks could have been undertaken using principal components analysis, but the above figures leave l i t t l e reason to doubt the s t a b i l i t y of these case complexity measures. An aggregated yearly complexity, defined as S C.H./C was calculated j 3 using various base years. Not surprisingly, the s t a b i l i t y of the H\ over time ensured that the choice of a base year was not c r i t i c a l , as ill u s t r a t e d i n Table 5.2. The hospital complexity measure for a given year i s directly dependent upon the dispersion of cases (and thus on case complexities) i n that year. Thus, i f we compare CMPXC1 values over time, for a given hospital, we w i l l have understated that hospital's s h i f t i n complexity by an amount indicated by the figures i n Table 5.2. For example, a hospital having a CMPXC1 value of .96 in 1966 and the same value i n 1967 would appear to be unaltered in i t s case mix complexity. These figures, however, are dependent on the 1966 and 1967 H j ' s respectively and thus ignore the fact that constant H_.'s would have l i k e l y yielded figures in the order of .96 and .978 (using 1973 H_.). The 1967 H_.'s, 1 if 0 Table 5.2: Aggregated Yearly Case Complexities Z C . H . /C v Z C . H /C j Dt Dt t J73 j t ' 73 1966 1967 1968 1969 1970 1971 1972 1973 Using 1966 H. ] 0.92602 0.94028 0.95558 0.97063 0.97700 0.98543 0.99192 1.00000 Using 1973 H_, 0.92306 0.94019 0.95546 0.96760 0.97619 0.98644 0.99382 1.00000 being based on that year's experience, do not incorporate the s h i f t over time i n the provincial case mix. In each year the case complexities are standardized, so that no intertemporal trends are captured. Thus, for 1967, even though the province as a whole tended toward a more complex mix of cases, as indicated through using base year case complexities, the fact of standardization around a mean of 1.0 eliminates the opportunity for that trend to be incorporated i n any hospital's CMPXC1 value. Only a hospital's s h i f t in case mix vis a vis the provincial mix for that year (1967) i s captured, to the exclusion of changes in the relationship between i t s proportions and provincial 1966 proportions. In the example chosen here, the fact that the provincial case mix trend was toward more complex cases could eliminate evidence of a similar trend in any specific hospital. The variable u t i l i z e d i n the econometric analysis of the following chapter i s constructed by weighting each hospital CMPXC1 value by the appropriate figure from the above table. Thus CMPADJ. = CMPXC1. • 0.92306 166 166 . th for the i hospital. Table 5D.1 (Appendix 5D) reports 1970 CMPXC1 and l < r l CMPADJ measures for each hospital. SPCLC1 It i s also possible to use the expected information concept to develop a measure of the specialization of a hospital. If we assume that small hospitals are generally prepared to handle a smaller segment of the spectrum of cases than large hospitals, we can hypothesize that smaller hospitals w i l l , i n general, be more specialized than their larger counter-parts. Thus, we would expect a hospital of over 400 beds to admit patients for every broad diagnosis i n our Canadian L i s t , whereas a community hospital of under twenty beds i s l i k e l y to admit only a 'handful' of case types over a year's time. By this format, the l a t t e r hospital would have a high specialization measure, while we would expect the former to have a 10 considerably lower measure. If we use the provincial case proportions, Q^ , as the prior probabilities, then the expected information gain from learning the new probabilities, the p^^, or equivalently from learning the deviation of each hospital from the provincial case distribution i s represented by G. = E p..-In(p../Q.) 1 j 1 3 *i} *p Thus, the greater the deviation of a hospital's case mix proportions from the provincial proportions, the larger the expected information gain from a message conveying that information and the greater the value of the hospital's SPCLC1 measure. For i l l u s t r a t i v e purposes, each hospital's SPCLC1 value for 1970 i s contained in Table 5D.1 (Appendix 5D) along with the respective rated bed capacities. EDRAT, DEPRAT, OUTXPR These variables are grouped together due to the similarity i n their construction and purpose. Each i s a measure of the proportion of TOTEX 1 if 2 (total operating expenditures) allocated to i t s particular function. Here the reader i s referred back to the discussion of the CASEX variable development, where the items included in direct educational expense (for EDRAT), non-departmental expenses (for DEPRAT), and direct out-patient expenses (for GUTXPR) are described i n d e t a i l . Each category was divided by TOTEX to arrive at the.values of these variables for each hospital. Recall that these three variables are included i n our regressions primarily to test the degree of success attained in attempting to eliminate the non-direct-in-patient expenditures from total hospital expenditures. Our a p r i o r i expectation, which was later confirmed, was that the effects of an education program in a hospital are widespread and not limited to the accounting items in the HS-2 form. FI, F2, F3, F4, F5,; F6 It i s clearly conceivable that differences, across hospitals, in the age and sex composition of inpatients could influence variation in cost per case. What i s i n i t i a l l y less clear i s the extent to which this effect w i l l be captured by case complexity and average length of stay variables, and to what extent there i s a direct linkage. It i s to this question that we address ourselves through inclusion of age-sex factor scores. The f i r s t stage in constructing age/sex standardization variables involved disaggregating the inpatient separations into an age-sex grid based on age at date of admission. This matrix contained 40 columns (one row per hospital) as follows: Column 1: male newborn (mature) Column 2: female newborn (mature) Column 3: male newborn (immature) Column 4: female newborn (immature) .,, ... cont'd Column 5: 0 - 4 years male Column 6: 0 - 4 years female Column 7: 5 - 9 years male Column 8: 5 - 9 years female Column 9: 10 - 14 years male etc. in 5 year groupings with alternating sex Column 37 80 - 84 years male Column 38 80 - 84 years female Column 39 85+ years male Column 40 85+ years female The resulting age-sex matrices (one per year) were standardized, by row, through conversion of the raw entries into case load proportions. Thus, i f the old (i,j) entry i s termed A^ _. (i=l,...,87 hospitals, j=l,...,40 age-sex categories), then the resulting new entry, _. , i s defined as 40 N.. = A../ I A. . I D I D J = 1 1 3 This naturally implies 40 Z N.. = 1 , for every i . j - l 1 3 A factor analysis of the 40 standardized case proportion vectors was then employed to derive age-sex factor scores. In particular, factors were derived as described below, by the principal component method, the factors were then rotated using the varimax procedure, and the factor scores were computed through regression a n a l y s i s . 1 1 It i s these factor scores which were then employed as independent variables i n our analysis. The principal component method i s often used in situations such as that described above, wherein i t is desirable to reduce a large number of potential variables into a less cumbersome set, with minimum concurrent loss of the variance of the original variable values. More s p e c i f i c a l l y , the aim i s to determine a minimum number of orthogonal vectors which embody a maximum (or pre-determined) amount of the original variance in the raw data set. Clearly, the more highly correlated are our original 40 columns, the fewer factors w i l l be required to capture any given precentage of the total variance, across hospitals, i n the 40 proportion vectors. The e x p l i c i t methodology (which i s considered here only in sufficient detail to allow subsequent discussion to be meaningful) derives i n i t i a l l y from the fact that each hospital may be represented by a point in a space of dimension forty, but more importantly from the fact that the points i n this 40-dimensional space may be grouped, according to uniform frequency density, into ellipsoids in 40-space. The principal components are then simply the orthogonal axes of these ellipsoids (Harman, 1975, 136). It follows that the 40 principal components may be described as linear combinations of the 40 original variables. Thus, "the f i r s t principal component i s that linear combination of the original variables which contributes a maximum to their total variance; the second principal component, uncorrelated with the f i r s t , contributes a maximum to the residual variance, and so on u n t i l the tot a l variance i s analyzed. The sum of the variances of a l l N principal components i s equal to the sum of the variances of the original variables" (Harman, 1975, 136). In effect, then, the co-ordinate axes are rotated to a new co-ordinate system characterized by the fact that the resultant components are the normalized linear combinations of the original variables with maximum variance. It turns out that these principal components are also the eigen-1 4 5 vectors of the standardized original data's covariance matrix. Furthermore, the corresponding eigenvalues represent the variance of each component, the eigenvalues decreasing in value with each successive component (Anderson, 1958, 272-9). Thus, the result of this analysis on the standardized matrix, Z (where Z.. = (A.. - A.)/s.; s. is the sample standard deviation ID ID D D D of the A^/s), is a set of principal components P1,...,P(t() wherein Pj is the best linear combination of Z l , . . . . , Z ^ in that that particular linear combination of the standardized vectors accounts for more of their variance than any other linear combination. P2 is the second best linear combination by the same definition, subject to the additional constraint that it be orthogonal to So each Z^  is a linear combination of the P vectors (j=l,...,40) and vice versa. The remaining steps, leading to our calculation of factor scores, will not be documented here since they are adequately described elsewhere. In particular, Harman (1975) covers factor matrix rotation in some detail, 1 2 as do Nie et al, (1970). The latter source also contains an adequate description of the process involved in obtaining factor scores which were used as our. six independent variables in the hospital cost analysis. Very briefly, after the factors have been rotated, factor scores for each hospital may be computed from the factor score coefficient matrix, derived by regressing the rotated factors on the standardized variable matrix. th Applying the standardized variables for the i hospital to the coefficient from the j t b " factor equation will yield the j t b " factor score for the i t b * hospital. Thus, the factor scores are derived as f = FZ where F is the factor estimate (factor score coefficient) matrix, computed as 1 1*6 T -1 F = S R T -1 where S i s the rotated factor loadings matrix and R i s the inverse of the correlation matrix. In our particular application i t was found that six factors comprised approximately 80% of the total accumulated eigenvalues, for a l l years. Thus, the decision to u t i l i z e six factor scores was implemented. As an i l l u s t r a t i o n the following data for 1972 are provided: Table 5.3: Distribution of Principal Components Variance Eigenvalue Proportion of sum Cumulative Proportion of eigenvalues of eigenvalues 13.4782 0.33696 0.33696 7.4323 0.18581 0.52277 4.6159 0.11540 0.63817 3.0122 0.07530 0.71347 2.7912 0.06978 0.78325 1.2479 0.03120 0.81445 0.9263 0.02316 0.83761. 0.7395 0.01849 0.85610 0.6648 0.01662 0.87272 0.5793 0.01448 0.88720 Six eigenvectors captured 81.4% of the total variance while an additional three eigenvectors would have added less than 6% of the variance to this sum. The calculation of the factor scores was f a c i l i t a t e d by a U.B.C. Computing Centre supported program, UBC Facto (1973). WAGE1, WAGE2 In addition to the independent variables (and mutations of them) contained in the Evans/Walker analysis, variables capturing variations in service mix costliness and hospital wage levels were thought to be potentially significant i n explaining variations in cost per case. To that end, two such variables were derived. Hospital support (non-medical staff) personnel were partitioned into eight sectors: (1) nursing administration (2) short-term and long-term units for adults & children (3) other nursing care C4) library administration (5) general administration (6) laboratory (7) diagnostic and therapeutic radiology (8) other special services Data pertaining to total hours of work for each sector, and total wage b i l l allocated to each sector were obtained from the HS-1 and HS-2 tapes. 1 3 The following notation i s used in the construction of these two variables: W.. = average wage in sector i (i = 1,...,8 above) 1 3 and hospital j (j = 1,...,87) H. . = number of labour hours i n sector i , hospital j . 1 1 * ID This basic notation gives rise to the following derivative variables: B. = Ew. .H. . = hospital j wage b i l l D L ID ID B. = Ew..H.. = total provincial sector i wage b i l l i j ID ID H. = EH.. = total hospital j hours 3 i ^ H. = EH.. = total provincial sector i hours 1 D 1 3 H = EEH. . = tot a l provincial hours i j 1 3 = B^/H^ = provincial average sector i wage rate W_. = B j / H j = average wage rate, hospital j H. = H./H = sector i proportion of tot a l provincial hours H_. = H_./H = hospital j proportion of total provincial D D hours PTP I . = ^ J / ^ = hospital j proportion of total provincial sector i hours 1 1 , 8 PTH . = H../H. = sector i proportion of total hospital j 1 3 1 3 3 hours. Clearly, one could use W_. as a wage level indicator for each hospital, and include this as an independent variable in the average cost equation. Ideally, however, we would like to squeeze additional information from the available data. In particular, i t would be useful to differentiate wage level and service mix effects which jointly determine hospital variation in W.. This was achieved through construction of two variables: 3 (i) WAGE1 - an indicator of the extent to which a hospital has a relatively costly service, or s k i l l , mix. A value greater than 1 would indicate that the hospital in question employs personnel in a more costly combination than the provincial average. (ii) WAGE2 - an indicator of the extent to which hospital j i s a relatively high wage hospital. The construction of each i s detailed below. If hospital j has a relatively costly s k i l l mix as defined above, we would anticipate a wage b i l l , for that hospital, greater than a wage b i l l constructed by using hospital j wage rates, but provincial s k i l l mix proportions. Thus, WAGE1. = B./H.-ZW..3. = W./ZW..3. 3 3 ] i i ] i ] i i ] i This measure w i l l be upward biased for any hospital having one or more sectors i n which i t employs no one, as the denominator i s constructed from provincial s k i l l proportions, but individual hospital sector wage rates. By computing H^ , for each hospital, as 3. = H. where IND. = (1 i f W.. / 0 i _ i • a. i t i ] EH.-IND. C„ .^ . i i (0 i f W.. = 0 we circumvented introduction of this bias. Thus i f W.. = 0 , the i ID sector hours were excluded in computing 'provincial proportions. If hospital j has a relatively high wage level, this would become apparent through a measure constructed from a numerator of hospital j's wage b i l l , and a denominator of provincial sector wage levels weighted by hospital j's s k i l l mix. Thus WAGE2 . = B./EW.H. .. = W./Sw.-PTH. . 3 3 i x 1 3 In this case, there are no zero-value d i f f i c u l t i e s , as provincial wage levels are employed i n the denominator. Table 5D.3, Appendix 5D, provides values of these variables for a l l hospitals and selected years. L The f i n a l variable to be considered i s L, the average length of stay, and i t requires l i t t l e explanation. From the HS-1 returns, the data on tota l hospital days of a l l cases (adults, children and newborn) discharged from the hospital in a given year were aggregated to form a total separated days stay figure. This was divided by total inpatient separations (again for adults, children and newborns) to arrive at an average length of stay figure for each hospital. This completes the theoretical specification and construction of an i n i t i a l average cost equation. The next logical step i s to subject the hypotheses and constructs of this and the immediately preceding chapter to rigorous econometric scrutiny, a task described in the following chapter. 1 5 0 Chapter 5 - Footnotes 1. This i s not s t r i c t l y correct, insofar as CFR may be equivalently defined as CFR = (3.65•OCC)/ALS, and i s thus i t s e l f a function of OCC and ALS. Note that a DAYEX (cost per day) equation formulated along the lines of the one employed by Evans and Walker (1972), but following the methodology of Chapter 7, would include the reciprocal of occupancy rate (weighted by 1./3.65), no CFR term, and would have a l l the terms contained in our expansion of the p 3 parameter weighted by the inverse of average length of stay (C/D = l . / L , where D = number of days stay). 2. See the 1968 HS-2 form, Sta t i s t i c s Canada, p. 8. 3. Unfortunately, the HS-1 and HS-2 reporting system did not directly provide figures for radiology, laboratory, emergency, operating room, etc. expenditures disaggregated into i n - and out-patient shares. For the exact methodology employed to calculate these shares, the interested reader may contact the author. 4. In 1969 there was a format change in the HS-1 and HS-2 returns. This allowed a more detailed, but not exactly compatible (with pre-1969 data) breakdown of expenditures. For years subsequent to 1968, therefore, more individual items were deducted from total expenditures, although comparability was f e l t to have been maintained. In particular, for item (v), rather than a straight deduction of laboratory and radiology outpatient expense being employed, i t was necessary to compute the outpatient share of components of these departments: standard laboratory units (i.e. hematology, urinalysis, biochemistry) done 'in-house', standard laboratory units referred outside the hospital, ECG, EEG, nuclear diagnostic and therapeutic medicine, diagnostic radiology, therapeutic radiology performed 'in-house', therapeutic radiology done elsewhere for patients of the hospital. In addition a category for outpatient share of medical and surgical supplies was deleted, as was a similar outpatient component of drug expenses. As before, items (i) to (iv) were also subtracted, although (i) now included other education-related items. 1 5 1 As was mentioned above, this function i s chosen from a multitude of decreasing functions due to i t s property of additivity. For two independent events with probabilities p 1 and p 2 the information content of a message indicating that both events have occurred would be h(p 1,p 2) = ln< 1 ) = -ln(p xP 2) = -ClnCp^ + ln(p 2)) = l n 1 + l n 1 Pi P 2 The entropy of a distribution i s actually a measure of the "disorder" inherent in the distribution. Thus, as a l l N events approach probabilities of 1_, we would say that the distribution's disorder i s N increasing, or that the entropy i s also increasing as N increases. The closer the N probabilities are to 1/N, and the larger i s N, the less order there i s in the system (Theil, 1967, 26). 7. Note the distinction between the and the recently employed p^, the probability of occurrence of event i . 8. Evans and Walker (1972, 399). See, also, footnote 4 on that page for an alternative hypothesis which suggests that the process of admission may be likened to a queuing process wherein cases are admitted i n order of severity and place in the queue. Under that formulation, hospitals with fewer beds would be expected to handle the most complex diagnoses f i r s t , with less complex cases remaining backlogged. The result would be a more even provincial distribution of complex cases which would yield, by our methodology, low case complexities. Evans and Walker's empirical results tend to refute this alternative hypothesis, as do our case complexities, since those cases which one might expect to have relatively high complexity ratings do, i n fact, bear out those expectations in most instances (see Appendix 5C, Tables 5C.1 and 5C.2). 9. This aggregation i s applied again later, as the u t i l i z a t i o n data obtained from the McPhee (1973) study are disaggregated according to the 188 item Canadian l i s t , while only 98 case costs are computed 152 in Chapter 7. Thus, the u t i l i z a t i o n s t a t i s t i c s from that study are aggregated according to the methodology in this table. Although i t i s clear, and unfortunate, that no precise comparability between ICD revisions i s possible, the aggregation formulae adopted here are apparently satisfactory to the extent that they create no immediately obvious discontinuities i n variable values. See, for example, Table 5D.2, Appendix 5D, where CMPXC1 measures for 1967-70 are l i s t e d , as an i l l u s t r a t i o n of the effect of bridging the years between which the revision was incorporated. Tables 5.1 - 5.2 provide further corroborative evidence. 10. As an i l l u s t r a t i v e example, consider the following 1969 measures for a hospital of under 20 beds and one of over 400 beds: less than 20 beds 3.6210 more than 400 beds 1.0540 11. An excellent source on factor analysis i s Harman (19 67). See, i n particular, pp. 136-7 on principal components analysis, pp. 304-13 on the varimax method of factor solution, and pp. 348-50 on the estimation method of computing factor scores. 12. Also, see Nie et a l . (1970, 482-5) for an interpretation of orthogonal factor rotation, and a discussion of the VARIMAX procedure. 13. Much of the i n i t i a l groundwork in this data manipulation was undertaken by Ulrich Kohli and Robert G. Evans. 14. No e x p l i c i t account i s taken of possible s k i l l - i n t e n s i t y differences across hours. Although the services data contained in the HS-1 returns provide, a breakdown, by department, of paid hours for various personnel classifications (graduate nurses, orderlies, etc.), the financial data from the HS-2 returns do not follow suit, thus precluding any finer disaggregation of sectors into personnel categories. 15 3 APPENDIX 5A: B.C..Acute Care Public General Hospitals* Federal B.C. Hospital Classification # Classification # 1. Alert Bay St. George's 1367 507 2. Armstrong and Spallumcheen . 1369 307 3. Ashcroft Lady Minto 1370 408 4. Bella Bella - R.W. Large Memorial 1373 904 5. Bella Coola General 1374 906 6. Burnaby General 1377 130 7. Burns Lake and D i s t r i c t 1381 707 8. Campbell River & D i s t r i c t General .". 1382 508 9. Castlegar & D i s t r i c t 1384 804 10. Chemainus General 1386 505 11. Chilliwack General 1387 601 12. Comox St. Joseph's General 1393 502 ** ** 13. Cranbrook & D i s t r i c t 1394 751 14. Creston Valley 1395 654 15. Cumberland General 1396 504 16. Dawson Creek St. Joseph General 1397 704 17. Duncan Cowichan D i s t r i c t 1398 203 18. Enderby & D i s t r i c t Memorial 1400 306 19. Fernie Memorial 1402 753 20. Fort Nelson General 1404 714 21. Fort St. John Providence 1405 701 22. Ganges & Gulf Islands 1407 206 23. Golden & D i s t r i c t General 1409 409 24. Grand Forks Boundary 1410 803 25. Haney Maple Ridge 1413 604 26. Hazelton Wrinch Memorial 1414 901 27. Hope Fraser Canyon 1415 606 28. Invermere Windermere D i s t r i c t 1418 755 29. Kamloops Royal Inland 1419 401 30. Kaslo Victorian 1420 • 653 APPENDIX 5A (Cont'd) 1 5 if Federal B.C. Hospital Classification # Classification # 31. Kelowna General 1421 302 32. Kimberley & D i s t r i c t 1422 752 33. Kitimat General 1423 917 34. Ladysmith & D i s t r i c t General 1425 506 35. Lillooet D i s t r i c t 1426 417 36. Lytton St. Bartholomew's 1428 405 37. Matsqui-Snmas-Abbotsford General 1366 603 38. McBride and D i s t r i c t 1430 713 39. Merritt Nicola Valley General 1431 403 40. Michel-Natal D i s t r i c t 1432 754 41. Mission Memorial 1433 602 42. Murrayville Langley Memorial 1434 115 43. Nakusp Arrow Lakes 1435 655 44. Nanaimo Regional General 1436 501 45. Nelson-Kootenay Lake General 1437 651 46. New Denver-Slocan Community 1440 652 47. New Westminster Royal Columbian 1444 109 48. New Westminster St. Mary's 1445 110 49. North Surrey Memorial 1446 116 50. North Vancouver Lions Gate 1450 112 51. Ocean Fa l l s General 1451 905 52. Oliver St. Martin's ** * ** * 1452 304 53. One Hundred Mile D i s t r i c t General 1403 708 54. Penticton 1453 303 55. Port Alberni West Coast General 1454 851 56. Powell River General 1458 111 57. Prince George Regional 1459 703 58. Prince Rupert General 1460 902 59. Princeton General 1461 305 60. Queen Charlotte Islands General 1462 907 APPENDIX 5A (Cont'd) 155 Hospital Federal Classification # B.C. Classification # 61. Quesnel G.R. Baker Memorial 1463 705 62. Revelstoke Queen Victoria 1464 402 63. Richmond General 1411 121 64. Rossland Mater Misericordiae 1465 802 65. Salmon Arm Shuswap Lake General 1469 404 66. Sechelt St. Mary's 1408 113 67. Sidney Rest Haven 1470 205 68. Smithers-Bulkley Valley D i s t r i c t 1471 903 69. Squamish General 1472 128 70. Stewart General 1473 910 71. Summerland General 1474 308 72. Terrace Mills Memorial 1476 912 73. Tofino General 1477 854 74. T r a i l Regional 1478 801 75. Vancouver Children's 1509 105 76. Vancouver General 1510 101 77. Vancouver Grace 1489 104 78. Vancouver Mt. St. Joseph 1499 106 79. Vancouver St. Paul's 1502 102 80. Vancouver St. Vincent 1s 1503 103 81. Vancouver University Health Service 1508 129 82. Vanderhoof St. John 1514 702 83. Vernon Jubilee 1515 301 84. Victoria General 1526 202 85. V i c t o r i a l Royal Jubilee 1525 201 86. White Rock Peace Arch D i s t r i c t 1532 131 87. Williams Lake Cariboo Memorial 1534 406 APPENDIX 5A (Cont'd) This i s not an exahustive l i s t , but rather contains only the 87 hospitals used in the major portion of this analysis. In 1968 and subsequent years, these codes changed to 1379 and 756 respectively. In 1973 these codes changed to 1480 and 309 respectively. 1 5 7 Appendix 5B: Deflation of Dependent Variable A time series analysis of CASEX requires the computation of this variable i n constant (base year) dollars. Rather than using a consumer price (or similar) index as a deflator, we constructed an index which attempted to incorporate only the components of the Consumer Price Index which are pertinent to the hospital. In that regard, hospital expenditures were partitioned into four categories: (i) gross salaries and wages (non-medical staff) (ii) medical and surgical supplies and other expenses ( i i i ) drugs (iv) food The proportion of total inpatient expenditure taken up by each was calculated. As in previous computations related to CASEX construction, some d i f f i c u l t y was encountered due to the changes in HS-1 and HS-2 format commencing with the 1969 returns. Again, only those expenditures directly related to inpatient care were considered. Accordingly, a description of the categories i s provided for each time period. 1966 - 1968 The procedure basically involved disaggregating TOTEX (total expenditures) into the four components l i s t e d above. This involved a basic extraction of tape data, and was followed by individual deletion of a l l non-inpatient expenditure from each category. For example, from total gross salaries and wages was deleted the wage and salary component of: nursing education, medical education, special research projects, ambulance, administration, outpatient portion of radiology, organized outpatient department, outpatient portion of laboratory, outpatient portion of operating room, outpatient portion of physiotherapy. A similar exercise was undertaken for categories (ii) and ( i i i ) . As in the development of the CASEX figures, the relevant administration expense components were added back before the proportions were calculated, so as to ensure that inpatient administrative expenses were not excluded. (Administration expense was disaggregated on the HS-2 form into gross salaries and wages, and other supplies and expenses). Total food expenditure was extracted directly from the tapes and was assumed to be used in i t s entirety for inpatient care. The following proportions of inpatient expenses were derived from a program constructed to carry out the above manipulation: Table 5B.1: Percentage Distribution of Inpatient Expenditures.- 1966-68 Gross Salaries & Wages (GSW) Medical, surgical supplies & other expenses (MSS) Drugs Food 1966 .711 .184 .041 .054 1967 .717 .184 .040 .049 1968 .733 .177 .036 .044 1969 - 1973 The methodology used for this time period was identical. The sole difference was in the degree of disaggregation provided in the HS-1 and HS-2 forms for these latt e r years. Thus, inpatient wage and salary expend iture was constructed by deleting wage and salary components of the following items from gross wages and salaries: education; emergency department; special research projects; ambulance; special c l i n i c s for psychiatry, T.B. and miscellaneous; administration; diagnostic radiology; organized outpatient department; electrocardiogram (EKG); electroencephal-ogram (EEG); radioisotope services; therapeutic radiology; and laboratory. As before, administrative (inpatient) expense was allocated back over categories (i) and (ii) according to the proportion of total inpatient expenditure claimed by each category, IPMS = IPMS + (IPMS/CMSSTOT - ADMMS))-ADMMS where IPMS i s the category (ii) inpatient expense, with the IPMS term to the right of the equality referring to this variable prior to addition of administrative expenses for inpatient care; MSSTOT i s the total category (ii) expenditure and ADMMS i s the category (ii) administrative expenditure. These computations yielded the following continuation of the previous table: Table 5B.2: Percentage Distribution of Inpatient Expenditures - 1969-73 GSW MSS DRUGS FOOD 1969 .755 .152 .037 .041 1970 .765 .148 .035 .038 1971 .768 .148 .034 .035 1972 .767 .149 .030 .035 1973 .768 .150 .028 .036 These expenditures were a l l i n current dollars, so that any apparent trends in the above figures could not be accepted at face value unless one assumed the i n f l a t i o n rate to have affected a l l sectors equally. Under that assumption, i t appears that salaries and wages were the only increasing relative component of hospital expenditures and, in particular, relative expenditures on drugs have decreased markedly during the eight year period. The price indices below confirm the suspicion that wage settlements during this time period far exceeded the inflationary price component of other sector expenditures. Therefore, the figures suggest that the relative increase in the share of wages and salaries i s , in large part, a result of price effects rather than input quantity influence. The above figures w i l l serve as quantity weights necessary for constructing a Paasche index. What remains to be assembled i s the colle tion of price levels for each of these categories over the eight years. The following price indices were compiled, or computed, as described below: Table 5B.3: Price Indices GSW MSS DRUGS FOOD 1966 63.12 114.5 100.1 113.8 1967 69.11 118.4 102.9 114.7 1968 80.79 122.6 104.1 116.1 1969 89.69 128.4 105.5 122.3 1970 100.00 133.6 106.5 125.5 1971 115.61 138.2 107.8 128.4 1972 123.73 144.7 110.1 138.9 1973 136.45 155.7 110.8 167.8 Of these four categories i t was, unfortunately, only possible to construct indices for GSW directly from the hospital data available. This followed from the fact that GSW was the only category from which there was a well-defined unit - the paid hour. The methodology w i l l be considered after discussion of the various sources from which the other price indices were taken. No specific indices could be found which were directly applicable to the MSS category. The source of the indices l i s t e d above i s the G.N.E. implicit price index, extracted from the Canadian S t a t i s t i c a l Review. The Industry Selling Price (I.S.P.) indices provided the figures for the drugs and food categories. For the latte r category, the I.S.P. indices were constructed on a food and liquor base. Since i t seemed plausible to assume that the liquor could be deleted from a hospital-specific index, that was in fact done. Thus, for 1972, the following I.S.P. figures were 1 6 1 converted into our index: Food D i s t i l l e r i e s Breweries Wines price index 137.2 113.4 122.0 115.5 weight 100,0% 3.1% 4.7% 0.4% P ? = 137.2- 0.13.4) • (0.031) - C122.01 • (0.047) - (115.5) • (0.004) ' 1.0 - 0.031 - 0.047 - 0.004 = 127.49 = 138.9 .918 (While the figures i n Table 5B.3 are formed around varying base years, the analysis i n the following pages effectively ensures that a common 1970 base year i s employed for a l l categories.) Turning now to creation of wage indices (the reader i s referred, for notation, back to the text of Chapter 5 where a description of the WAGE1 and WAGE2 variables i s contained), the data available allow creation of a Paasche index as follows: PIND = Z W.. H . / Z W..-H. _ • where t = 1970. t .. l i t i ] t .. l i t int 1 3 J J 1 3 J J Thus the index i s of the familiar P,Q,/P„Q, form. Given that we now have l x l ' 0 * 1 appropriate price indices and weights for each of our hospital expense categories, l e t us consider creation of a suitable deflator for CASEX. Let P = price level, category i , year t. X^t = quantity, category i , year t E^ t = p ^ t x ^ t = total expenditure, category i , year t. PI^ t = price index value, category i , year t. Then the weights l i s t e d in Tables 5B.1 and 5B.2 may be defined as h W.t - E.. / Z E.. i t i t . , i t 1=1 The problem i s now one of adjusting IPEXP, total inpatient expenditure, for inflationary effects by calculating IPEXP at base year (1970) price 1 6 2 levels. Thus, we wish.' to calculate E p . r x - ^ which, when divided by . - i t i t i=l number of cases, w i l l y i e l d CASEXD - constant dollar cost per case. We proceed as follows: i* k k k £ p.rX = (I P..X. }•(£ P.-X../ E P X ) . . i t i t , , i t i t , , i t i t , , i t i t i=l i=l. i=l i=l But k IPEXP = E P. X. for year t. . . i t i t J 1=1 Thus, our deflator i s simply an inverse Paasche index, D = E P.-X. / E P. X. t . . i t i t ... i t i t i=l i=l if h = E P.-X.V E E > 4, . , i t i t . , i t i=l i=l = E * L t X i t ^ E t (i.e. E f c •= IPEXP, year t ) . i=l Now, given our p l ^ t (price indices), we can define P.- = (PI.r/PI..)-P.. i t i t i t i t Thus, if D = E ( P I - / P I )-(P X../E.) t ... i t i t i t i t t 1=1 But, P..X../E. = W.. i t i t t i t which implies that it D = Z (PI -/PI. )-W. t . , i t i t i t 1=1 As an example, for 1966 we have D66 = ( 1 0 6 - 5 ) (-041) + (133.6) (.184) + (125.5) (.054) + (100.0) (.711)=!.44 (100.1) (114.5) (113.8) (63.12) To adjust for the fact that D^^ = ^986 rather than 1.0, due to accounting, and possibly roundoff, errors, this was adjusted so as to set D^ = 1.0, yielding D_ = 1.465. In a similar fashion, D was calculated for each 66 t year, and CASEXD was created as 16 3 CASEXD.^ = CASEX • D. Dt ] t (where j = 1,..,, ,87) The deflators are l i s t e d below, along with comparative Consumer Price Index Deflators computed as the inverse of the respective indices after adjustment to a 1970 base (Source: CPI figures from Canadian S t a t i s t i c a l Review): Table 5B.4: Deflators Hospital-specific Deflator CPI Deflator ( a l l items) CPI Deflator (health & personal care) 1966 1.465 1.164 1.197 1967 1.359 1.124 1.139 1968 1.202 1.080 1.095 1969 1.094 1.033 1.044 1970 1.000, 1.000 1.000 1971 0.887 0.972 0.980 1972 0.830 0.928 0.935 1973 ' 0.756 0.862 0.892 These figures make i t clear that a general Consumer Price Index, and a p a r t i a l index constructed solely from health and personal care items, both underestimate the inflationary trend in hospital-specific components for B.C. It would appear, therefore, that the extra effort entailed in constructing our own hospital-specific deflators was well j u s t i f i e d . APPENDIX 5C: Canadian Hospital Morbidity Lists TABLE 5C.1: 98 Diagnostic Category Canadian Hospital Morbidity L i s t - * H. D Case # Diagnostic Content Mean Standard Deviation 1. Tuberculosis, a l l forms 1.4388 .0.1324 2- Poliomyelitis and encephalitis 1.6611 0.3117 3. Infectious hepatitis 1.0306 0.0893 4. Other diseases attributable to viruses 0.6201 0.0714 5. Other bacterial, spirocheatal, r i c k e t t s i a l or parasitic diseases 0.5856 0.0769 6. Malignant neoplasms of buccal cavity and pharynx 2.3000 0.1962 7. Malignant neoplasm of stomach 1.3411 0.1510 8. Malignant neoplasm of large intestine except rectum 1.3607 0.1459 9. Malignant neoplasm of rectum 1.5464 0.1647 10. Malignant neoplasm of bronchus, trachea and lung 1.6404 0.1423 11. Malignant neoplasm of breast 1.3964 0.1452 12. Malignant neoplasm of cervix uteri 1.5378 0.1284 13. Malignant neoplasm of uterus other than of cervix uteri 2.0929 0.1184 14. Malignant neoplasm of ovary, Fallopian tube, and broad ligament 1.6895 0.2094 15. Malignant neoplasm of prostate 1.4190 0.1341 16. Malignant neoplasm of kidney, bladder and other urinary organs 1.9064 0.1477 17. Leukaemia and aleukaemia 1.7527 0.1598 18. Malignant neoplasm of a l l other organs and unspecified sites 1.5174 0.0821 TABLE 5C.1 (Cont'd) H * i Standard Case # Diagnostic Content Mean Deviation 19. Uterine fibromyoma and other benign neoplasm of uterus 1.1694 0.0563 20. Benign neoplasm of ovary 1.0618 0.1366 21. Benign neoplasm (excluding uterus and ovary) and neoplasm of unspecified nature 1.2346 0.0334 22. Asthma 0.6826 0.0268 23. Other allergic disorders 0.6937 0.1260 24. Diseases of thyroid gland 1.5115 0.2828 25. Diabetes mellitus 0.7627 0.0936 26. Diseases of other endocrine glands 1.6587 0.2293 27. Avitaminoses and other metabolic diseases 0.9519 0.1698 28. Diseases of the blood and blood-forming organs 0.8596 0.1933 29 Psychoses 1.4673 0.1163 30. Psychoneurotic disorders 0.8954 0.0265 31. Disorders of character, behaviour, and intelligence 1.3817 0.2625 32. Vascular lesions affecting central nervous system 1.1148 0.0526 33. Inflammatory and other diseases of C.N.S. 1.2129 0.1245 34. Diseases of nerves and peripheral ganglia 1.1816 0.0453 35. Diseases of eye 2.0519 0.1509 36. Diseases of ear and mastoid process 1.0709 0.0354 TABLE 5C.1 (Cont'd) H * j Case # Diagnostic Content Mean Standard Deviation 37. Rheumatic fever and chronic rheumatic heart disease 1.5973 0.09*0 38. Arteriosclerotic and degenerative heart disease 1.0102 0.0519 39. Other diseases of the heart 0.8373 0.1105 40. Hypertensive heart disease and other hypertensive disease 0.6605 0.0347 41. Diseases of arteries 1.6979 0.1267 42. Varicose veins of lower extremities 1.0836 0.0430 43. Haemorrhoids 1.0002 0.0310 44. Phlebitis and thrombophlebitis 0.7308 0.0433 45. Other diseases of the circulatory system 0.9389 0.1528 46. Acute upper respiratory infections 0.3881 0.0256 47. Influenza 0.4042 0.0353 48. Pneumonia 0.4843 0.0173 49. Bronchitis 0.4627 0.0463 50. Hypertrophy of tonsils and adenoids 0.8925 0.0395 51. Other diseases of respiratory system 1.2363 0.1014 52. Diseases of teeth and supporting structure 0.9395 0.1594 53. Ulcer of stomach and duodenum and jejunum 0.7738 0.0491 54. Gastritis, duodenitis and other disorders and diseases of the stomach and duodenum 0.5327 0.0328 55. Appendicitis 0.7943 0.0361 TABLE 5C.1 (Cont'd) _* H. 3 Case # Diagnostic Content Mean Standard Deviation 56. Hernia of abdominal cavity 0.9604 0.0439 57. Other intestinal obstruction 0.8770 0.0580 58. Gastro-enteritis and c o l i t i s , except ulcerative, age 4 weeks and over 0.4794 0.0413 59. Chronic enteritis and ulcerative c o l i t i s 1.2347 0.0797 60. Cirrhosis and other diseases of l i v e r 1.2917 0.1328 61. Diseases of gallbladder and pancreas 0.8782 0.0399 62. Other diseases of digestive system 0.8530 0.0532 63. Nephritis and nephrosis 4.1770 0.4299 64. Infections of kidney 0.7235 0.0891 65. Calculi of urinary system 1.2507 0.0675 66. Other diseases of urinary system 1.2804 0.1146 67. Hyperplasia of prostate 1.7470 0.1183 68. Redundant prepuce and phimosis 0.9027 0.0341 69. Infective disease of ovary, uterus, vagina, Fallopian tube, and vulva 0.8515 0.0430 70. Uterovaginal prolapse 1.3081 0.1268 71. Disorders of menstruation 0.8100 0.1281 72. Other diseases of genital organs 1.0427 0.0388 73. Complications of pregnancy 0.7152 0.0361 TABLE 5C.1 (Cont'd) _* H. 3 Case # Diagnostic Content Mean Standard Deviation 74. Abortion 1.2601 0.2198. 75. Delivery without mention of complications 0.8560 0.0299 76. Delivery with specified complication 1.0859 0.0682 77. Complications of the puerperium 0.8373 0.0669 78. Infection of skin and subcutaneous tissue 0.4855 0.0914 79. Other diseases of skin and subcutaneous tissue 0.7776 0.0477 80. Art h r i t i s and rheumatism, except rheumatic fever 0.7695 0.0697 81. Displacement of intervertebral disc 1.1196 0.0582 82. Other diseases of musculoskeletal system 1.1260 0.0661 83. Congenital malformations 1.8951 0.2080 84. Birth injuries, asphyxia, and infections of newborn and other diseases peculiar to early infancy 1.0769 0.2173 85. Symptoms, senility, and ill- d e f i n e d conditions 0.8368 0.0570 86. Fracture of skull and head injuries associated with haemorrhage in or injury to the brain 0.8855 0.0509 87. Fracture of spine and trunk 0.8685 0.0492 88. Fracture of upper limb 0.7347 0.0194 89. Fracture of femur 1.4843 0.1540 90. Other fractures of lower extremities 0.7979 0.0211 91. Dislocation without fracture, and sprains and strains of joints and adjacent muscles 0.7649 0.0275 TABLE 5C.1 (Cont'd) H j Case # Diagnostic Content Mean Standard Deviation 92. Internal injury of chest, abdomen and pelvis 1.0019 0.0661 93. Burns 0.5940 0.0400 94. Dislocations, sprains, strains, lacerations, superficial injuries, contusion, foreign body, poisoning or other injury, including adverse effects. 0.6228 0.0254 95. Medical or special examination (without sickness) 0.0727 0.2057 96. Mature newborn 0.8728 0.0401 97. Immature newborn 0.8473 0.0755 98. Other special admissions, examinations, etc. 1.0923 0.2156 * Standardized case complexities derived as described in this chapter. Means and standard deviations were computed over the eight years, 1966-1973. TABLE SC.2: 188 Diagnostic Category Canadian Hospital Morbidity L i s t _ * H. 3 Case # Diagnostic Content Mean Standard Deviation 1. Salmonella infections 1.5187 0.2570 2. Other intestinal infections 0.4250 0.0244 3. Tuberculosis 1.3688 0.1305 4. Streptococcal sore throat and scarlet fever and Erysipelas 0.8862 0.1067 5. Acute poliomyelitis — — 6. V i r a l encephalitis 1.4464 0.2777 7. Infectious hepatitis 0.9737 0.1026 8. Other virus diseases 0.5954 0.0326 9. - Venereal disease 1.4579 0.2086 10. Other infectious and parasitic diseases 0.7732 0.0578 11. Malignant neoplasm of buccal cavity and pharynx 2.2283 0.1980 12. " " of stomach 1.2349 0.0604 13. " " of intestine, except rectum 1.2287 0.0462 14. " " of rectum and rectosigmoid junction 1.3947 0.0636 15. " " other digestive organs 1.2603 0.0777 16. " " trachea, bronchus and lung 1.4981 0.0728 17. " " other respiratory organs 2.3252 0.0799 18. " " bone 1.8310 0.2326 19. " " skin 1.6824 0.1019 20. " " breast 1.2523 0.0396 TABLE 5C.2 (Cont'd) _* H. D Case # Diagnostic Content Mean Standard Deviation 21. Malignant neoplasm of cervix uteri 2.2569 0.0708 22. " " " uterus 1.9768 0.0891 23. " " " ovary 1.5017 0.1382 24. " " " other female genital organs 1.9957 0.2403 25. " " " prostate 1.2915 0.0671 26. " bladder 1.8238 0.1025 27. " " " other genito-urinary organs 1.7506 0.1082 28. " " " brain 2.2003 0.0925 29. Other primary and secondary malignant neoplasms 1.5941 0.0815 30. Leukemia 1.6916 0.1894 31. Other neoplasms-lymphatic and hematopoietic tissue 1.7881 0.1031 32. Benign neoplasm of skin 1.5931 0.1649 33. " " " breast 1.4120 0.0939 34. " " " uterus 1.0905 0.0290 35. " " " ovary 0.9359 0.0309 36. " " " other female genital organs 1.1187 0.0841 37. " " " brain and other .parts of nervous system 2.0592 0.1009 38. Other benign neoplasms 1.2372 0.0365 39. Carcinoma in si t u of cervix uteri 1.2260 0.0738 40. Other neoplasms of unspecified nature 1.1657 0.1295 \ TABLE 5C.2 CCont'd) _* H. 1 Case # Diagnostic Content Mean Standard Deviation 41. Nontoxic goiter 1.4185 0.0523 42. Thyrotoxicosis with or without goiter 1.6267 0.1793 43. Other diseases of thyroid gland 1.1992 0.1897 44. Diabetes mellitus 0.6798 0.0420 45. Other endocrine diseases 1.4452 0.0662 46. Avitaminoses and other nutritional deficiency 0.7342 0.0264 47. Congenital disorders of matabolism 2.1033 0.2059 48. Other metabolic diseases 0.9181 0.1075 49. Iron deficiency anaemias 0.8284 0.0721 50. Pernicious anaemia and other deficiency anaemias 1.1932 0.1197 51. Other diseases of blood and blood forming organs 0.7112 0.0311 52. Alcoholic psychosis 1.5048 0.2439 53. Schizophrenia 1.8572 0.1262 54. Affective psychoses 1.2168 0.0777 55. Other psychoses 1.4904 0.1241 56. Neuroses 0.8594 0.0198 57. Alcoholism 1.0409 0.2038 58. Drug dependence 1.2889 0.1181 59. Other nonpsychotic mental disorders 1.4181 0.0735 60. Mental retardation 2.4019 0.2547 TABLE 5C.2 (Cont'd) _ * H. 3 Case # Diagnostic Content Mean Standard Deviation 61. Meningitis and other inflammatory diseases of C.N.S. 1.3372 0.1139 62. Hereditary and familial diseases of nervous system 2.3924 0.1395 63. Multiple sclerosis 1.3846 0.0680 64. Paralysis agitans 1.1375 0.0982 65. Epilepsy 0.9736 0.0608 66. Other diseases of central nervous system 1.4649 0.1214 67. Diseases of nerves and peripheral ganglia 1.1251 0.0360 68. Inflammatory diseases of the eye 1.3063 0.0807 69. Strabismus 1.8368 0.0500 70. Cataract 2.1864 0.1558 71. Glaucoma 2.5130 0.0533 72. Other diseases of the eye 2.4453 0.0667 73. Ot i t i s media without mention of mastoiditis 0.9176 0.0445 74. Mastoiditis with or without o t i t i s media 1.7226 0.1267 75. Other diseases of ear and mastoid process 1.6828 0.1991 76. Active rheumatic fever 0.8299 0.1008 77. Chronic rheumatic heart disease 1.8840 0.0900 78. Hypertensive disease 0.6143 0.0244 79. Acute myocardial infarction 1.0596 0.0546 80. Other ischemic heart disease 0.8998 0.0357 TABLE 5C.2 (Cont'd) _* H. 3 Case # Diagnostic Content Mean Standard Deviation 81. Other forms of heart disease 0.8674 0.0779 82. Cerebral hemorrhage 1.6118 0.1227 83. Cerebral embolism and thrombosis 1.7946 0.0620 84. Other cerebrovascular disease 0.8619 0.0196 85. Arteriosclerosis 1.6346 0.0983 86. Other diseases of arteries, arterioles and capillaries 1.5920 0.0746 87. Pulmonary embolism and infarction 1.3607 0.0717 88. Phlebitis and thrombophlebitis and venous embolism and thrombosis . 0.7015 0.0431 89. Varicose veins of lower extremities 1.0377 0.0483 90. Hemorrhoids 0.9638 0.0220 91. Other diseases of circulatory system 1.1346 0.1179 92. Acute upper respiratory infection, except influenza 0.3597 0.0182 93. Influenza 0.3865 0.0320 94. Pneumonia 0.4601 0.0189 95. Bronchitis and emphysema 0.4698 0.0253 96. Asthma 0.6541 0.0289 97. Hypertrophy of tonsils and adenoids- 0.8552 0.0437 98. Chronic sinusitis 1.5923 0.0819 TABLE 5C.2 (Cont'd) _* H. Case # Diagnostic Content Mean Standard Deviation 99. Deflected nasal septum 2.0370 0.0731 100. Other diseases of upper respiratory tract 1.4550 0.0863 101. Empyema and abscess of lung 1.4901 0.3531 102. Pneumoconiosis and related diseases 1.1258 0.1876 103. Other diseases of respiratory system 0.7062 0.0339 104. Diseases of teeth and supporting structures 0.9228 0.1948 105. Other diseases of oral cavity, salivary glands and jaws 0.9448 0.1562 106. Ulcer of duodenum 0.8366 0.0243 107. Ulcer of stomach, and peptic ulcer site unspecified 0.6584 0.0195 108. Gastritis and duodenitis 0.4316 0.0297 109. Other diseases of esophagus, stomach, and duodenum 0.9489 0.0304 110. Appendicitis 0.7442 0.0289 111. Hernia without mention of obstruction 0.8959 0.0231 112. Hernia with obstruction 1.0445 0.0493 113. Intestinal obstruction without mention of hernia 0.8106 0.0451 114. Chronic enteritis and ulcerative c o l i t i s 1.2149 0.0773 115. Other diseases of intestines and peritoneum 0.8111 0.0302 116. Cirrhosis of li v e r 1.2571 0.1394 117. Other diseases of l i v e r 1.1511 0.0911 118. Cholelithiasis 0.9372 0.0426 J TABLE 5G.2 (Cont'd) 1 _ * H. 1 Case # Diagnostic Content Mean Standard Deviation 119. Cholecystitis and cholangitis without mention of calculus 0.5349 0.0210 120. Other diseases of gall bladder and b i l i a r y ducts 0.8387 0.0553 121. Diseases of pancreas 1.0380 0.0680 122. Nephritis and nephrosis 4.1264 0.2179 123. Infections of kidney 0.7147 0.0882 124. Calculus of urinary system 1.1643 0.0524 125. Cystitis 1.1381 0.0225 126. Other diseases of urinary system 1.2376 0.0494 127. Hyperplasia of prostate 1.5998 0.0532 128. Redundant prepuce and phimosis 0.8580 0.0284 129. Other diseases of male genital organs 1.1179 0.0500 130. Diseases of breast 1.1712 0.0226 131. Diseases of ovary, fallopian tube and parametrium 0.8670 0.0296 132. Infective disease of uterus, vagina and vulva 0.8016 0.0376 133. Uterovaginal prolapse and malposition of uterus 1.1753 0.0172 134. Disorders of menstruation 0.7027 0.0759 135. Other diseases of female genital organs 1.0393 0.0425 136. Infection of genital tract during pregnancy, and urinary infections during pregnancy and puerperium 0.7788 0.0810 137. Hemorrhage of pregnancy 0.5970 0.0300 TABLE 5C.2 (Cont'd) _ * H. 1 Case # Diagnostic Content Mean Standard Deviation 138. Toxemias of pregnancy and the puerperium 0.7648 0.0368 139. Other complications of pregnancy 0.7556 0.0140 140. Abortion 1.3281 0.1725 141. Delivery without mention of complication 0.8117 0.0321 142. Delivery complicated by: placenta previa or antepartum hemorrhage, retained placenta, or other post partum hemorrhage 1.0202 0.1159 143. Delivery complicated by abnormality of pelvis, fetopelvic dis-proportion, malpresentation or other prolonged labour 1.0845 0.0719 144. Delivery with other complications including anesthetic death in uncomplicated delivery 1.0771 0.0780 145. Complications of puerperium 0.7870 0.0778 146. Infections of skin and subcutaneous tissue 0.5312 0.0307 147. Other inflammatory conditions of skin and subcutaneous tissue 0.6442 0.0197 148. Other diseases of skin and subcutaneous tissue 0.8807 0.0663 149. Rheumatoid a r t h r i t i s and a l l i e d conditions 1.0689 0.0581 150. Osteoarthritis and a l l i e d conditions 1.0434 0.0600 151. Other arth r i t i s and rheumatism 0.4700 0.0199 152. Osteomyelitis and other diseases of bone 1.1372 0.0406 153. Displacement of intervertebral disc 1.0444 0.0462 154. Other diseases of joint 1.0498 0.0493 155. Synovitis, bursitis, and tenosynovitis 0.8252 0.0426 TABLE 5C.2 (Cont'd) _* H. 3 Case # Diagnostic Content Mean Standard Deviation 156. Other diseases of musculoskeletal system 1.2373 0.0410 157 . Spina bifida and congenital hydrocephalus 2.4751 0.1626 158. Congenital anomalies of heart 2.7556 0.0548 159. Cleft palate and c l e f t l i p 2.3336 0.1651 160. Other congenital anomalies of digestive system 1.2690 0.0879 161. Congenital anomalies of genito-urinary system 1.6876 0.0916 162. Congenital anomalies of musculoskeletal system 1.6122 0.1560 163. Other and unspecified congenital anomalies 1.7056 0.0471 164. Birth injury 1.3705 0.1485 165. Asphyxia, anoxia or hypoxia 1.2917 0.0812 166. Hemolytic disease of newborn 1.7622 0.1076 167. Immaturity unspecified 0.4906 0.1680 168. Other causes of perinatal morbidity and mortality 1.1819 0.0795 169. Observation, without need for further medical care 1.4892 0.1751 170. Symptoms, se n i l i t y and ill-defined conditions 0.7565 0.0350 171. Fractures of the skull, and other intracranial injury 0.8183 0.0173 172. Fractures of spine and trunk 0.8140 0.0501 173. Fracture of upper limb 0.7104 0.0221 174. Fracture of femur 1.3385 0.1016 175. Other fractures of lower limbs 0.7757 0.0139 TABLE 5.C.2 (Cont'd) _* H. 1 Case # Diagnostic Content Mean Standard Deviation 176. Dislocation without fracture, sprains and strains of joints and adjacent muscles 0 .7393 0.0309 177. Internal injury of chest, abdomen and pelvis 0 .9368 0.0664 178. Laceration, open wound, superficial injury, contusion and crushing with intact skin surface 0 .4337 0.0128 179. Foreign body entering through o r i f i c e 1 .0864 0.0884 180. Burns 0 .5629 0.0380 181. Injury to nerves and spinal cord 1 .6376 0.2388 182. Adverse effects of medical agents 0 .8103 0.0381 183. Toxic effects of substances chiefly non-medicinal 0 .5917 0.0338 184. Complications peculiar to certain surgical procedures, other complications of surgical procedures and other complications of medical care 1 .0790 0.0700 185. Other effects of external causes 0 .6977 0.0742 186. Special conditions and examinations without sickness 0 .9084 0.0392 187. Mature infant 0 .8189 0.0367 188. Immature infant - - -0 .7654 0.0389 * Standardized case complexities. Mean and standard deviation based on five years, 1969-1973 inclusive. TABLE 5C.3: Aggregation Formula For Compatibility  of 188 and 98 Diagnostic Category  Canadian Hospital Morbidity Lists l 98 L i s t # 188 Lis t Combinations # # # # # # # 1 2 3 4 5 6 7 # 8 # 9 # 10 # 11 # 12 # 13 # 14 # 15 # 16 # 17 # 18 # 19 # 20 # 21 # 22 # 23 # 24 # 25 # 26 # 27 # 28 # 29 #3 #5 + #6 #7 .05#2 + #8 + .05#9 #1 + .25#2 + .80#4 + .95#9 + #10 #11 #12 •80#13 + .10#14 .90#14 #16 #20 #21 + #39 #22 #23 + .50#24 #25 #26 + .75*27 #30 #.20#13 + #15 + #17 + #18 + #19 + .50#24 +.25#27 #28 + #29 + #31 + .90#40 #34 #35 #32 + #33 + #36 + #37 + #38 + .10#40 #96 .10#100 + .40#147 #41 + #42 + #43 #44 #45 #46 + #47 + #48 #49 + #50 + #51 #52 + #53 + #54 + #55 TABLE 5C.3 (Cont'd) 181 98 L i s t # 188 L i s t Combinations # 30 #56 # 31 #57 + #58 + #59 + #60 # 32 #82 + #83 + #84 # 33 #61 + #62 + #63 + #64 + #65 + #66 # 34 #67 # 35 #68 + #69 + #70 + #71 + #72 # 36 #73 + #74 + #75 # 37 #76 + #77 # 38 #79 + #80 # 39. #81 # 40 #78 # 41 #85 + #86 # 42 #89 # 43 #90 # 44 .85#88 # 45 #87 + .15#88 + #91 # 46 #92 # 47 #93 # 48 #94 # 49 .90#95 # 50 #97 # 51 #98 + #99 + .90#100 + .10#95 + #101 + #102 + #103 # 52 #104 + .25#159 # 53 #106 + #107 # 54 #108 + .90#109 # 55 #110 # 56 #111 + #112 # 57 #113 # 58 • 70#2 + .40*115 # 59 #114 # 60 #116 + #117 # 61 #118 + #119 + #120 + #121 182 TABLE 5C.3 (Cont'd) 98 L i s t # 188 L i s t Combinations # 62 #105 + .10#109 + .60#115 # 63 #122 # 64 #123 # 65 #124 # 66 #125 + #126 # 67 #127 # 68 #128 # 69 #131 + #132 # 70 .95#133 # 71 #134 # 72 #129 + #130 + .05*133 + #135 # 73 #136 + #137 + #138 + #139 # 74 #140 # 75 #141 # 76 #142 + #143 + #144 # 77 #145 # 78 #146 + .20#4 # 79 .60#147 + #148 # 80 #149 + #150 + #151 # 81 #153 # 82 #152 + #154 + #155 + #156 # 83 #157 + #158 + .75#159 + #160 + #161 + #162 + #163 # 84 #164 + #165 + #166 + #167 + #168 # 85 #169 + #170 # 86 #171 # 87 #172 # 88 #173 # 89 #174 # 90 #175 # 91 #176 # 92 #177 # 93 #180 TABLE 5C.3 (Cont'd) l 8 3 98 L i s t # 188 L i s t Combinations # 94 #178 + #179 + #181 + #182 + #183 + #184 + #185 # 95 No cases # 96 #187 # 97 #188 # 98 #186 1 8 it Appendix 5D: Hospital Statistics Table 5D.1; Selected Hospital Statistics - 1970 HOSPITAL SEQUENCE # RATED BED CAPACITY CMPXC1 CMPADJ SPCLC1 001 109 0.9150 0.8932 0.5793 002 61 0.8039 0.7848 1.9339 003 16 0.8063 0.7870 2.5530 004 29 0.7698 0.7514 1.4893 005 25 0.7632 0.7450 2.9268 006 25 0.7914 0.7725 2.2798 007 242 0.9391 0.9168 0.5250 008 110 0.8905 0.8693 0.4829 009 33 0.8093 0.7900 1.2638 010 95 0.8784 0.8574 0.7197 Oil 60 0.8579 0.8375 0.7319 012 33 0.8722 0.8515 0.9823 013 184 0.9207 0.8988 0.3215 014 119 0.8853 0.8643 0.3941 015 44 0.9016 0.8801 6.7391 016 41 0.8611 0.8406 1.6065 017 100 0.8658 0.8452 0.6539 018 148 0.8476 0.8275 0.5273 019 23 0.8495 0.8293 0.9907 020 43 0.8432 0.8231 0.7146 021 31 0.7545 0.7365 2.1848 022 33 0.7576 0.7396 2.4994 023 100 0.8680 0.8474 0.7762 024 21 0.9086 0.8869 1.0367 025 35 0.8699 0.8491 0.6841 026 25 0.8243 0.8046 1.2824 027 35 0.8702 0.8494 0.6439 028 153 0.9387 0.9163 0.5351 029 106 0.8921 0.8708 0.4671 030 50 0.7466 0.7288 3.1845 TABLE 5D.1 (Contd) HOSPITAL SEQUENCE # RATED BED CAPACITY CMPXC1. CMPADJ SPCLC1 031 30 0.8472 0.8270 1.0015 032 24 0.8259 0.8063 1.1906 033 313 1.0074 0.9834 0.2568 034 19 0.7607 0.7425 2.9269 035 254 0.9682 0.9451 0.2716 036 50 0.9281 0.9060 0.5103 037. 113 0.8653 0.8447 0.9436 038 43 0.8494 0.8292 0.9897 039 30 0.7901 0.7713 1.9765 040 27 0.7551 0.7372 3.4686 041 21 0.8501 0.8299 1.1087 042 41 0.8306 0.8108 0.9247 043 17 0.7944 0.7755 2.2538 044 54 0.8967 0.8754 0.6334 045 157 0.8973 0.8759 0.6762 046 15 0.8283 0.8086 2.3939 047 225 0.9577 0.9349 0.3968 048 94 0.9260 0.9039 0.3664 049 21 0.7142 0.6972 5.1513 050 445 0.9605 0.9376 0.5473 051 256 0.9816 0.9583 1.0228 052 264 0.9215 0.8996 0.9645 053 485 0.9843 0.9608 0.3028 054 31 0.8599 0.8394 1.8972 055 37 0.8816 0.8606 0.7054 056 121 0.9573 0.9345 0.4781 057 111 0.8493 0.8291 0.8581 058 151 0.8809 0.8599 0.4922 059 246 0.8848 0.8637 0.6594 060 88 0.8694 0.8487 0.5643 TABLE 5D.1 (Cont'd) 1 86 HOSPITAL SEQUENCE # RATED BED CAPACITY CMPXC1 CMPADJ SPCLC1 061 25 0.8404 0.8204 1.4135 062 26 0.8251 0.8054 1.1954 063 100 0.8756 0.8548 0.5326 064 30 0.9006 0.8791 0.8549 065 45 0.8587 0.8383 2.1895 066 56 0.8535 0.8332 0.6818 067 40 0.8941 0.8728 0.7240 068 63 0.8026 0.7835 1.1736 069 21 0.8158 0.7964 1.3270 070 9 0.7652 0.7470 3.8622 071 28 0.8662 0.8456 1.3196 072 87 0.8667 0.8461 0.6540 073 21 0.8066 0.7874 2.5113 074 238 - 1.0039 0.9800 0.5614 075 93 0.9489 0.9263 6.-2 82 9 076 144 0.9520 0.9293 3.2713 077 489 1.0377 1.0130 0.4319 078 180 0.9622 0.9393 0.7225 079 26 0.7620 0.7439 7.7254 080 83 0.9361 0.9138 6.1823 081 1762 1.4511 1.4165 1.1507 082 45 0.7922 0.7733 1.2464 083 177 0.9613 0.9384 0.3850 084 705 1.0483 1.0233 0.3726 085 449 0.9711 0.9480 0.4325 086 227 0.8976 0.8762 0.8457 087 75 0.8081 0.7889 1.0436 TABLE 5D.2 HOSPITAL COMPLEXITY MEASURES 18 7 CMPXC1 HOSPITAL SEQUENCE # 1967 1968 1969 1970 001 0.9461 0.9205 0.9197 0.9150 002 0.7793 0.7988 0.7890 0.8039 003 0.8088 0.8625 0.8224 0.8063 004 0.7860 0.7931 0.8014 0.7698 005 0.7264 0.7817 0.7600 0.7632 006 0.8078 0.8163 0.8226 0.7914 007 1.0092 0.9913 0.9762 0.9391 008 0.9017 0.9193 0.8957 0.8905 009 0.8319 0.8258 0.8110 0.8093 010 0.9061 0.8991 0.8972 0.8784 Oil 0.9027 0.8922 0.8805 0.8579 012 0.8610 0.8797 0.8692 0.8722 013 0.9571 0.9403 0.9336 0.9207 014 0.9341 0.9320 0.8950 0.8853 015 0.9071 0.8868 0.9066 0.9016 016 0.8530 0.8447 0.8496. 0.8611 017 0.9141 0.894 8 0.8694 0.8658 018 0.9194 0.8958 0.8731 0.8476 019 0.8897 0.8412 0.8551 0.8495 020 0.9138 0.8835 0.8654 0.8432 021. 0.8355 0.8066 0.7873 0.7545 022 0.7827 0.7590 0.7762 0.7576 023 0.8460 0.8472 0.8673 0.8680 024 0.9164 0.8642 0.8657 0.9086 025 0.9027 0.8734 0.8591 0.8699 026 0.8478 0.8429 0.8462 0.8243 027 0.8928 0.8994 0.8725 0.8702 028 0.9637 0.9548 0.9430 0.9387 029 0.9001 0.8873 0.8851 0.8921 030 0.7557 0.7312 0.7712 0.7466 1 8 8 TABLE 5D.2 (Cont'd) CMPXC1 HOSPITAL SEQUENCE # 1967 1968 1969 1970 031 0.8762 0.8669 0.8388 0.8472 032 0.8942 0.8773 0.8448 0.8259 033 0.9865 0.9830 0.9896 1.0074 034 0.8167 0.8332 0.7707 0.7607 035 0.9850 0.9988 0.9744 0.9682 036 0.9570 0.9339 0.9306 0.9281 037 0.8598 0.8531 0.8651 0.8653 038 0.8649 0.8383 0.8454 0.8494 039 0.8286 0.8145 0.8127 0.7901 040 0.7388 0.7499 0.7593 0.7551 041 0.8273 0.8431 0.8220 0.8501 042 0.8325 0.8350 0.8474 0.8306 043 0.8575 0.7996 0.7921 0.7944 044 0.9189 0.9169 0.9058 0.8967 045 0.9339 0.9115 0.9101 6.8973 046 0.8183 0.8014 0.7903 0.8283 047 0.9952 0.9840 0.9573 0.9577 048 0.9218 0.9692 0.9663 0.9260 049 0.7813 0.7246 0.7553 0.7142 050 0.9993 0.9958 0.9740 0.9605 051 0.9756 1.0082 0.9883 0.9816 052 0.9471 0.9178 0.9165 0.9215 053 1.0174 1.0003 0.9860 0.9843 054 0.8095 0.8717 0.8960 0.8599 055 0.9151 0.8946 0.8828 0.8816 056 0.9761 0.9977 0.9583 0.9573 057 0.9088 0.8839 0.8697 0.8493 058 0.8981 0.9018 0.8874 0.8809 059 0.8921 0.8806 0.8838 0.8848 060 0.8827 0.8646 0.8560 0.8694 TABLE 5D.2 (Cont'd) 1 8 9 CMPXC1 HOSPITAL SEQUENCE # 1967 1968 1969 1970 061 0.8889 0.8507 0.8678 0.8404 062 0.8049 0.8277 0.8213 0.8251 063 0.9124 0.8829 0.8871 0.8756 064 0.8867 0.8925 0.8899 0.9006 065 0.9085 0.8931 0.8868 0.8587 066 0.8805 0.8673 0.8573 0.8535 067 0.9307 0.9176 0.8930 0.8941 068 0.8043 0.8064 0.8019 0.8026 069 0.8620 0.8397 0.8220 0.8158 070 0.8454 0.8024 0.8133 0.7652 071 0.9168 0.9002 0.9101 0.8662 072 0.8840 0.8650 0.8597 0.8667 073 0.7903 0.8079 0.8065 0.8067 074 1.0478 1.0375 1.0044 1.0039 075 0.9737 0.9618 0.9708 0.9489 076 0.9997 0.9830 0.9662 0.9520 077 1.0964 1.0654 1.0559 1.0377 078 0.9925 0.9889 0.9655 0.9622 079 0.8276 0.7709 0.8094 0.7620 080 1.0137 1.0335 0.9811 0.9361 081 1.2834 1.3439 1.4032 1.4511 082 0.8081 0.8116 0.8286 0.7922 083 0.9765 0.9829 0.9703 0.9613 084 1.0721 1.0550 1.0461 1.0483 085 1.0309 1.0019 0.9798 0.9711 086 0.9348 0.9216 0.9005 0.8976 087 0.8180 0.8287 0.8173 0.8081 TABLE 5D.3: HOSPITAL WAGE1 AND WAGE2 VALUES, SELECTED YEARS 1 9 0 1967 1970 1973 HOSPITAL SEQUENCE # WAGE1 WAGE 2 WAGE1 WAGE 2 WAGE1 WAGE 2 001 0 .99 1 .02 1 .04 0 .99 1 .00 1 .00 002 0 .98 0 .98 0 .97 1 .05 1 .00 1 .03 003 1 .06 0 .91 1 .09 1 .09 1 .06 1 .00 004 1 .01 0 .94 1 .02 0 .99 1 .01 1 .01 005 0 .99 0 .93 1 .10 1 .02 1 .04 0 .77 006 1 .00 0 .93 0 .99 0 .91 0 .99 0 .98 007 1 .07 1 .05 1 .00 1 .02 1 .00 0 .99 008 1 .02 0 .98 0 .99 0 .96 1 .01 0 .99 009 0 .97 0 .92 1 .02 0 93 0 .99 0 .99 010 1 .02 0 .98 0 .97 0 98 0 .99 1 .02 Oil 1 02 0 99 0 .96 0. 96 0 .98 1 .02 012 0 99 0 96 1 03 1. 00 1 .01 1 .05 013 0 99 0 98 0 99 0. 98 0 99 0 98 014 1. 03 1 00 0 97 1. 00 0 99 . 0 99 015 1. 03 1. 17 1 00 1. 09 1 01 1 06 016 1. 01 1. 02 1. 04 1. 07 1. 02 1. 06 017 1. 06 0. 92 1. 01 0. 95 1. 01 0. 96 018 0. 98 1. 03 1. 01 1. 00 0. 98 1. 00 019 1. 04 1. 00 1. 02 0. 98 1. 01 0. 98 020 1. 00 1. 01 1. 00 1. 10 1. 01 1. 02 021 1. 05 0. 89 0. 99 0. 94 0. 95 0. 98 022 1. 01 1. 08 1. 00 0. 87 0. 89 0. 87 023 1. 06 0. 96 1. 00 0. 97 1. 00 1. 00 024 1. 00 0. 94 1. 04 0. 96 1. 09 1. 01 025 1. 01 1. 02 1. 01 0. 97 1. 00 1. 00 026 0. 99 1. 04 1. 03 1. 05 1. 00 1. 03 027 1. 00 0. 99 1. 01 1. 00 0. 98 1. 04 028 1. 00 1. 00 1. 00 1. 01 1. 00 0. 98 029 0. 97 1. 05 1. 00 1. 00 1. 00 1. 00 TABLE 5D.3 (Cont'd) l 1967 1970 1973 HOSPITAL SEQUENCE # WAGE1 WAGE 2 WAGE1 WAGE 2 WAGE1 WAGE 2 030 1 .04 0 .86 0 .96 0 .91 0 .95 0 .88 031 0 .99 1 .08 0 .96 0 .94 1 .00 0 .99 032 1 .01 0 .93 0 .99 0 .97 1 .01 1 .04 033 0 .89 0 .98 0 .86 0 .98 0 .95 0 .99 034 1 .08 0 .92 1 .10 0 .86 1 .04 0 .90 035 1 .06 1 .01 1 .02 1 .02 1 .03 0 .99 036 1 .14 1 .00 1 • 0§ 1 .09 1 .03 1 .06 037 1 .00 1 .09 1 .01 1 .08 1 .00 1 .05 038 0 .97 1 .01 1 .00 1 .05 1 .00 1 .02 039 0 .97 0 .93 0 .99 0 .98 1 .02 0 .99 040 1 .08 0 .93 0 .98 0 .99 . 1 .01 0 .97 041 0 .96 0 .89 0 .94 0 .87 1 .01 0 .89 042 1 .01 0 .99 1 .00 0 .99 0 .96 1 .01 043 0 98 0 .91 1 .01 0 .89 0 .99 . 1 02 044 0 98 1 05 0 98 1 .03 1 00 1 .02 045 1. 00 1. 04 1 00 0 94 0 98 0 99 046 0. 99 0. 95 1 03 1. 10 1. 02 1. 02 047 1. 07 0. 95 0. 99 1. 02 1. 00 1. 00 048 1. 07 1. 01 0. 98 0. 98 1. 00 1. 00 049 1. 00 0. 91 1. 03 0. 97 1. 06 0. 84 050 0. 88 1. 00 0. 92 1. 04 0. 92 1. 03 051 1. 01 1. 01 1. 00 0. 98 1. 00 0. 99 052 0. 99 1. 03 1. 00 1. 05 1. 00 0. 99 053 1. 08 0. 91 1. 00 0. 95 1. 00 0. 98 054 1. 05 0. 95 1. 03 0. 96 1. 00 0. 96 055 1. 01 0. 95 1. 01 1. 02 1. 00 1. 00 056 1. 04 0. 99 0. 99 1. 04 1. 00 1. 00 057 1. 02 1. 03 0. 99 1. 04 1. 00 0. 99 058 0. 99 1. 05 0. 99 1. 01 1. 00 1. 00 059 1. 09 0. 96 1. 01 0. 98 1. 00 0. 99 TABLE 5D.3 (Cont'd) 192 1967 . 1970 1973 HOSPITAL SEQUENCE # WAGE1 WAGE 2 WAGE1 WAGE2 WAGE1 WAGE 2 060 0 .99 1. 01 1 .01 1 .05 1 .00 1 .04 061 1 .00 0. 97 0 .76 0 .96 0 .97 0 .95 062 1 .06 0. 77 1 .00 0 .81 1 .00 0 .71 063 1 .09 0. 99 1 .02 1 .02 1 .00 0 .97 064 1 .03 1. 04 1 .00 1 .09 0 .99 1 05 065 0 .99 1. 04 1 .00 1 .06 0 .98 1 04 066 1 .00 1. 03 0 .99 1 .06 1 .00 1 00 067 0 .99 0. 91 0 .99 1 .00 1 .00 1. 02 068 0 .98 0. 83 0 .98 0 .98 0 .99 1. 06 069 1 .02 0. 98 1 .02 1 .00 1 .01 1. 01 070 1 25 1. 10 1 33 1 32 1 .02 1. 08 071 1 02 1. 01 1 .03 1 04 1 00 1. 02 072 1 00 1. 00 1 01 1 06 0 97 1. 00 073 1. 02 0. 95 1 00 0 96 1 02 1. 00 074 1. 07 0. 98 0 98 0 95 0 99 1. 03 075 1. 00 1. 00 0 96 1 00 0 97 0. 99 076 0. 96 1. 04 1 00 0. 94 1. 00 0. 99 077 0. 93 0. 99 0. 94 1. 01 0. 99 1. 00 078 1. 01 1. 03 . 0. 99 1. 01 0. 99 1. 00 079 0. 95 1. 14 1. 01 1. 04 1. 06 1. 03 080 1. 03 1. 04 1. 00 1. 00 1. 00 1. 01 081 0. 96 1. 02 0. 96 1. 00 0. 95 0. 99 082 1. 00 0. 88 0. 98 0. 92 1. 00 0. 96 083 1. 05 0. 98 1. 00 0. 96 0. 98 1. 01 084 0. 94 0. 98 0. 91 0. 98 0. 91 1. 03 085 0. 98 1. 04 0. 96 1. 05 0. 95 1. 04 086 0. 99 1. 02 0. 99 1. 00 0. 99 0. 99 087 1. 06 0. 99 1. 00 0. 99 1. 00 0. 99 Chapter 6: Econometric Analysis - From OLS to MLE In the past two chapters attention was devoted to specification of an average cost equation for B.C. acute care hospitals. We now proceed to discuss the various stages involved i n estimation of the relevant parameters. In particular, the analysis contained in Evans and Walker (1972) i s expanded through e x p l i c i t consideration of econometric complexities entailed in an extension to time series analysis. Ordinary least squares estimation (hereafter OLS) is found to be inadequate i n that i t yields i n e f f i c i e n t parameter estimates (in the sense that there exist lower-variance unbiased estimators) as a result of autoregressive residual values. In addition, evidence of heteroskedasticity i n the cross section analysis leads to the necessity of an appropriate data transformation. Each stage i n the procedure i s considered i n some det a i l , as i t i s l i k e l y that any related future analysis of hospital costs w i l l encounter similar empirical regularities. The multivariate analysis u t i l i z e s a regression model consisting of 17 independent variables (including a constant term). I n i t i a l l y ordinary least squares estimation, with i t s inherent assumptions, was employed. In particular, we assumed E(ee') = 02l in undertaking (i) year by year ordinary least squares estimation for eight years, 1966-1973. (ii ) pooled time-series-cross-section OLS estimation. The intent was to provide a comparison of results with those reported by Evans and Walker, and a f i r s t cursory indication of the degree of s t a b i l i t y of the parameter estimates over time. The pooled regression estimates were to be used for the case cost analysis i f we could show that there was basis for accepting a l l the c l a s s i c a l assumptions associated with OLS regression analysis. This pooling simply involved 'stacking' the eight years of variable values and using OLS c r i t e r i a to obtain coefficient estimates,. as*i we were considering 696 hospitals at one point in time, or one hospital over 696 time periods. The results of this entire analysis are displayed in Table 6.I. 1 It i s useful at this point to r e c a l l the intent of this estimation procedure. The primary goal of this segment of the project i s to estimate average cost equation parameters which w i l l accurately represent the behaviour of a particular set of hospitals over a specific period of time. In addition, the estimation w i l l provide new evidence regarding the shape of hospital cost equations and the importance of various factors in explaining unit cost variations. The estimated equation i s then to be employed as a single equation simulation model which provides us with estimated cost per case figures for a wide variety of cases. Clearly, one has an alternative (and eventually adopted) option, that being the use of one equation per year. However, this method would add considerable time and effort to an already complex task, and would essentially be superfluous i f i t can be i l l u s t r a t e d that the parameters are s u f f i c i e n t l y stable over time to allow use of a single set of parameters to represent the eight years. Before we proceed to a closer examination of the underlying assumptions inherent i n the pooled OLS estimation, brief consideration i s given to the 1967 cross-sectional results. In comparing our equation with equation Cl of Evans and Walker (1972,409) we must r e c a l l that our dependent variable differs in that CASEXD i s a deflated value. In addition, our sample size i s s l i g h t l y smaller (87 hospitals vs. 90), and we employ one less factor score. I t i s , nonetheless, interesting to note that Evans and Walker 2 'stumbled upon' the year producing our highest R , for their analysis. Note also that, whereas their BEDS, OCC, ALS and CFR coefficients were not significantly different from zero, our re-specification of the equation TABLE 6.1: OLS Estimation R e s u l t s Dependent Variable: CASEXD 1966 1967 1968 1969 Variable Parameter Estimate t Statistic Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant -252.44 -2.82 -441.96 -4.88 - 507.65 -4.63 - 671.62 -3.69 BDCFR 0.43 0.71 - 0.24 -0.38 1.55 -1.84 4.27 -3.67 ALS 19.23 5.81 18.74 5.71 15.66 5.62 22.62 7.90 INVCFR 2532.5 7.33 2855.7 5.38 1854.6 4.94 3126.5 6.86 EDRAT 891.42 3.21 1451.4 5.67 1897.3 6.24 1532.0 4.33 DEPRAT - 22.70 -0.34 - 65.25 -0.95 - 79.31 -0.92 2.46 0.02 CMPADJ 391.61 5.35 418.19 5.21 518.40 6.29 613.09 6.75 SPCLC1 2.11 0.73 - 1.03 -0.31 0.67 0.20 3.99 -0.84 FI - 3.08 -1.07 - 8.33 -3.46 - 6.63 -2.03 0.47 -0.12 F2 10.44 3.15 10.28 3.02 14.59 3.97 0.12 0.03 F3 - 8.98 -2.53 - 2.45 -0.67 - 7.76 -2.18 1.95 -0.44 F4 - 1.98 -0.55 - 5.83 -1.63 - 2.45 -0.64 0.34 -0.08 F5 10.51 2.94 4.61 1.39 10.22 2.90 20.11 3.90 F6 4.18 1.41 0.96 0.30 3.14 0.93 9.49 -2.19 OUTXPR 171.35 1.05 36.92 0.26 100.74 0.63 184.89 1.01 WAGE1 -118.88 -1.74 28.96 0.39 62.02 0.77 88.28 0.59 WAGE 2 85.55 1.85 114.66 2.22 118.34 1.94 112.10 1.70 R2 ESS* • 90547 41921 • 91721 41573 .91454 52559 • 88960 68931 Error Sum of Squares TABLE 6:1 (Cont'd) 1970 1971 1972 1973 POOLED Variable Parameter /. Estimate t Sta-t i s t i c Parameter Estimate t Sta-t i s t i c Parameter Estimate t Sta-t i s t i c Parameter Estimate t Sta-t i s t i c Parameter Estimate t Sta-t i s t i c Constant -366.75 -3.07 -114.30 -0.97 -137.58 -0.91 -554.00 -2.01 -251.99 -5.19 BDCFR - 2.23 -1.86 - 0.65 -0.68 - 0.11 -0.10 - 0.59 -0.39 - 0.65 -1.67 ALS 24.68 8.11 16.98 5.76 13.55 4.13 10.17 2.72 15.76 13.20 INVCFR 2075.8 4.89 3727.3 6.21 3099.6 4.43 7079.2 11.57 3491.3 18.55 EDRAT 1374.9 3.91 1324.7 3.44 2138.8 3.83 2558.9 3.59 1369.4 9.20 DEPRAT - 18.42 -0.17 -301.90 -2.64 - 42.35 -0.34 191.41 1.01 - 61.13- -1.45 CMPADJ 423.29 4.54 294.09 4.24 188.55 2.23 282.68 2.44 371.17 12.72 SPCLC1 1.93 0.45 - 9.60 -2.14 - 6.04 -1.05 - 6.12 -0.94 - 2.00 -1.25 FI - 3.49 -0.72 - 2.78 -0.63 0.60 0.08 17.94 1.56 - 3.90 -2.38 F2 4.55 1.17 5.27 1.42 5.81 1.22 6.82 0.82 5.83 3.57 F3 - 4.05 -0.93 7.48 1.78 0.80 0.13 5.20 0.79 - 0.58 -0.36 F4 1.24 0.21 - 4.17 -0.94 - 4.82 -0.68 - 0.12 -0.01 - 2.80 -1.59 F5 1.26 0.31 - 0.21 -0.05 - 8.33 -1.62 - 9.40 -1.24 3.21 2.08 F6 - 11.52 -2.71 - 6.63 -1.30 5.73 1.01 - 3.81 -0.41 - 2.98 -1.83 OUTXPR 61.73 0.35 174.77 1.08 -147.28 -0.72 115.84 0.40 129.37 1.88 WAGE1 - 64.15 -0.72 -43.86 -0.52 66.10 0.53 346.52 1.44 -58.23 -1.56 WAGE 2 127.19 1.85 - 9.80 -0.16 41.03 0.51 - 3.62 -0.03 72.40 2.84 R2 .88473 .88019 .83374 .84103 .79804 ESS* 67451 67710 100110 1.6908 x 10 5 1.0579 x 10 6 Error Sum of Squares £ on produces a strikingly significant parameter estimate on the INVCFR term (which replaces their BEDS), and a similarly significant coefficient for ALS, which concurs with the notion that length of stay is crucial to cost per case. Based on our ear l i e r methodology the 1967 equation implies that an 'average' hospital's total yearly inpatient expenditure was comprised of approximately $2856 per bed, plus an additional $18.74 for each day i n which a bed was f i l l e d , after standardizing for case load and other hospital characteristics. We also note, in passing, the similarity of the CMPXC1 effect i n the two analyses (Evans/Walker reported a parameter estimate of 435.6, as compared to our present 418.2). Turning b r i e f l y to longitudinal considerations we note that nothing resembling a stable relationship i s evident over the entire period of analysis, for any of the coefficients. Further discussion of parameter s t a b i l i t y follows a reconsideration of the legitimacy of u t i l i z i n g OLS for this type of analysis. Our pooled time series-cross section equation estimates are e f f i c i e n t only i f the standard conditions are assumed to hold; i.e i f E(£?) = a2 and E(£^£_.) = 0, i , j = l , 696; i ^ j . In particular, we would require (£. £. ) = 0 etc. Equivalently, i f we l e t E(££') = 9. then our assumption is that 1 9 8 For ft to have the illu s t r a t e d form, two distin c t sets of interactions are ruled out: (i) the variance of the disturbance Cor residual) term i s unrelated to the absolute magnitudes of the dependent and explanatory variables; (ii) the size of the residuals in year t i s not correlated with the disturbance terms in any other year. Thus, our normal regression model includes assumptions of homoskedasticity . and non-autocorrelation. We leave the f i r s t of these relationships for the time being, and consider the implications of the non-autoregressivity assumption. We would, a p r i o r i , not be surprised to find a hospital with a large error (residual) term in one year having a disturbance term of related magnitude, or at least of similar sign, i n following years. Any 'outlying' hospital (in the.sense of a large positive or negative residual) i s l i k e l y to be in that position for some reason not captured within our functional form (i.e. managerial inefficiency). It i s reasonable to presume that a f a i r proportion of hospitals i n such a position w i l l be unable or unwilling to alter their mode of operation i n the very short term, or are unaware of their position relative to other hospitals. To test for inter-year residual correlation, we set up a multiple equation model comprised of eight equations, one per year, and u t i l i z e d 2 the maximum likelihood estimation (MLE) technique. This procedure adjusts for cross equation covariance amongst the disturbance terms and provides 3 asymptotically e f f i c i e n t , consistent estimators. It also provides us with an indication of the nature of the autoregressive pattern, i f any. Thus, i f we assume that f2 has the form 19 9 ft = c r i i P 1 2 P 1 2r 18 so that we allow for any and a l l cross-equation residual interactions, the maximum likelihood estimation w i l l provide us with estimates for the P ^ j ' 3 -As a f i r s t step the eight equation system was estimated with no parameter restrictions. The results are displayed as Table 6.2. Again, over the entire time range, there appears to be no evidence of s t a b i l i t y amongst the parameter estimates. However, specific likelihood tests which confirm this casual observation are reported i n Appendix 6A. What was of more interest than the parameter estimates themselves, at this stage, was the form of the residual correlation matrix, which may be found in Table 6.3. From the date in this table the following information regarding the p values i n the above ft matrix was computed. Consider the s t a t i s t i c 7 Z P . .,,/7 = .8362 1=1 which i s the average correlation of residuals separated by one year. Similarly, . f 1 P i , i + 2 / 6 " - 7 3 1 2 from which we note that /.7312 = .8550. If we denote the average correlation by p , where t refers to the time span, then similar calculations y i e l d the following results: TABLE 6.2: Maximum Likelihood Estimation Results (1) Dependent Variable: CASEXD 1966 1967 1968 1969 Variable Parameter Estimate t Stati s t i c Paramete r Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant - 9.7305 -0.14 - 8.7070 -0.13 9.9624 0.13 - 151.04 : -1.30 BDCFR 1.2372 2.33 1.3815 2.48 0.9472 1.36 1.0325 -1.10 ALS 11.285 4.49 14.270 7.09 10.146 5.63 15.899 7.04 INVCFR 2784.0 12.69 2070.0 7.13 1604.1 7.20 1879.7 6.17 EDRAT 1164.8 4.77 1573.9 6.78 1971.6 7.12 1703.1 5.36 DEPRAT - 51.930 -1.00 4.0227 0.08 - 40.103 -0.63 37.336 0.49 CMPADJ 230.24 3.91 168.22 3.02 183.69 3.11 285.48 4.35 SPCLC1 0.9198 0.38 1.2729 0.49 1.6518 0.61 1.3975 0.37 F l 2.8638 1.17 - 0.7863 -0.37 3.9006 1.32 11.030 3.08 F2 1.9277 0.71 4.3913 1.82 6.5416 2.26 - 1.5938 -0.52 F3 - 1.9196 -0.75 2.5338 1.14 - 2.2333 -0.99 - 1.4031 -0.54 F4 - 3.2454 -1.23 - 5.8705 -2.31 - 6.5283 -2.48 - 4.3004 -1.47 F5 2.5359 0.96 - 1.4195 -0.68 - 2.2180 -0.85 8.3958 2.55 F6 2.5958 1.12 1.1357 0.52 0.9291 0.40 - 1.8157 -0.54 OUTXPR - 19.380 -0.15 -149.08 -1.53 -146.85 -1.36 - 66.326 -0.52 WAGE1 -130.05 -2.81 - 80.575 -1.91 - 37.981 -0.87 - 28.203 -0.34 WAGE 2 51.73 1.66 54.549 1.87 39.922 1.14 64.888 1.66 R2 .86804 .85775 .85140 .82438 TABLE 6.2 (Cont'd) 1970 1971 1972 1973 Parameter t Parameter t Parameter t Parameter t Variable Estimate Sta t i s t i c Estimate Sta t i s t i c Estimate S t a t i s t i c Estimate St a t i s t i c Constant 34.720 0.36 75.167 1.21 215.76 2.56 - 67.199 -0.42 BDCFR 0.2538 0.25 1.1300 1.56 1.6395 1.81 1.8394 1.40 ALS 16.412 6.17 9.0524 5.26 3.0708 1.50 - 1.2041 -0.41 INVCFR 1624.7 5.13 3664.8 11.30 3788.2 9.68 6158.8 14.2 EDRAT 1415.4 4.33 1253.9 3.90 1791.1 3.99 1808.8 2.97 DEPRAT 51.179 0.61 -110.41 -1.73 -154.69 -2.22 - 21.351 -0.17 CMPADJ 198.06 2.76 157.67 3.77 90.622 1.74 172.59 2.02 SPCLC1 6.3224 1.65 - 1.4316 -0.42 - 5.1614 -1.21 4.3492 -0.81 FI 12.611 2.82 11.178 3.28 12.851 2.64 28.611 3.90 F2 0.6534 0.22 1.6547 0.59 - 0.6116 -0.17 4.8706 -0.77 F3 3.7194 1.14 - 2.4404 -1.00 9.8927 2.91 12.270 2.44 F4 1.4298 0.37 0.9930 0.42 - 7.2392 -2.16 1.5013 -0.29 F5 8.1123 2.43 4.4552 1.68 - 7.5264 -2.00 1.4126 0.26 F6 - 6.2673 -1.91 - 1.4586 -0.57 - 1.4482 -0.49 0.7108 -0.13 OUTXPR - 202.95 -1.48 -33.936 -0.35 -225.73 -1.78 - 143.11 -0.71 WAGE1 - 201.79 -3.26 -112.26 -3.07 - 56.538 -1.06 170.31 1.40 WAGE 2 127.88 2.67 37.165 1.27 - 36.077 -0-i 87 - 82.757 -1.18 2 R .82535 .82355 • 76684 • 78707 TABLE 6.3: Residiial Correlation Matrix - Unrestricted MLE 1966 1967 1968 1969 1970 1971 1972 1973 1966 1.0000 0.8182 0.7312 .0.6873 .0.6034 0.6126 0.4795 0.2039 1967 1.0000 0.8649 0.8165 0.7249 0.7870 0.6250 0.4142 1968 1.0000 0.8680 0.7664 0.7808 0.6485 0.3928 1969 1.0000 0.8040 0.7358 0.5470 0.3065 1970 1.0000 0.7636 0.6343 0.4759 1971 1.0000 0.8739 0.7028 1972 1.0000 0.8605 1973 1.0000 1 = '.8362 = .8362 2 p = .7312 / - = .8550 ? P 2 3 p = .6432 = .8632 P 3 ' p = .5864 Z" 1 = .8751 P k 5 p = .5435 i T 1 = .8852 5 P 5 6 p = .4469 Z" 1 = .8744 P 6 7 p = .2039 = .7968 7 P 7 average = .8551 P t Thus, there i s some indication that the yearly interdependence can be reasonably approximated by a first-order autoregressive pattern i n the residuals, with p-.85. This appears to provide sufficient evidence against any further use of OLS i n time series analysis of hospitals, at least for this particular data base. In addition i t appears to confirm the above-noted suspicion, that the reasons for hospitals having large residuals tend to be other than random. One suspects that similar patterns would surface in other sets of data. Having established the illegitimacy of using pooled OLS regressions to provide e f f i c i e n t , unbiased parameter estimates, we now focus our attention on the estimates reported in Table 6.2. The parameter estimates suggest that we could consider eliminating certain variables, without 20 3 l i k e l y loss of a significant degree of explanatory power. In particular, the t - s t a t i s t i c s associated with SPCLC1 and OUTXPR indicate that in no case can we reject the null hypothesis that the true parameters are not different from zero at the 5% significance level. In addition, for a l l years except 1972, a similar conclusion may be drawn regarding DEPRAT and, since the data comprising that variable are somewhat 'soft', i t was decided that a maximum likelihood estimation would be undertaken using 4 only fourteen explanatory variables (including constant). The results from this estimation appear in Table 6.4. As expected, the remaining coefficients changed only minimally, and the explained proportion of tota l variance in our dependent variable did not s h i f t markedly. The variable deletions were apparently not surgery of a c r i t i c a l nature. The u t i l i z a t i o n of MLE to r e s t r i c t each variable's parameter estimates to be equal over time would allow estimation of a single equation. This would, i n turn, greatly f a c i l i t a t e later stages of the cost analysis. One rather subtle consideration prevented such a route being adopted, irrespective of the parameter s t a b i l i t y issue. In effect, the factor scores F l through F6 are not identical variables in each year, as they are scores derived using parameters from regressions employing principal factors as dependent variables. These factors, however, represent different proportions of the total variance i n the age-sex proportion matrix, in each year, and the resulting scores must thus be considered as 'different' variables in each year. It seems illegitimate, therefore, to r e s t r i c t the factor score parameters to be equal over the entire time period. This consideration aside, a l l likelihood ratio tests indicated the necessity of rejecting the null hypothesis that various subsets of the parameters were stable over time and, in fact, there was no case in which the s t a t i s t i c s indicated we were even close to being able to accept such a hypothesis. Table 6.4: Maximum Likelihood Estimation Results (2) Dependent Variable: CASEXD 1966 1967 1968 1969 Variable Parameter Estimate t Stati s t i c Parameter Estimate t Stati s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant - 7.7617 -0.12 - 27.116 -0.41 - 8.8499 -0.12 -128.47 -1.19 BDCFR 1.2556 2.37 1.2514 2.29 0.8011 1.17 - 1.0962 -1.19 ALS 11.311 4.79 13.767 6.94 10.129 5.82 15.879 7.31 INVCFR 2727.5 13.79 2191.8 8.12 1752.3 8.49 1852.8 7.23 EDRAT 1213.0 4.98 1593.5 7.00 1987.4 7.29 1661.0 5.27 CMPADJ 210.23 3.72 182.71 3.36 195.64 3.41 287.21 4.51 F l 2.8842 1.18 - 1.6672 -0.81 2.7223 0.97 10.454 2.98 F2 2.4597 0.92 5.4754 2.29 7.5092 2.68 - 1.4913 -0.53 F3 - 1.2716 -0.52 2.4611 1.16 - 1.9860 -0.96 - 2.1837 -0.91 F4 - 3.4365 -1.38 - 5.7631 -2.42 - 5.4848 -2.26 - 4.3854 -1.58 F5 2.0080 0.82 - 1.0214 -0.51 - 1.5893 -0.62 8.5739 2.66 F6 2.9568 1.28 1.3711 0.64 0.4279 0.19 - 3.1755 -0.97 WAGE1 -125.32 -2.71 - 70.423 -1.66 - 34.087 -0.78 - 41.847 -0.52 WAGE 2 60.012 1.97 46.784 1.61 33.728 1.00 56.509 1.46 R2 0.8660 .8673 .8565 0. 8282 ESS 59425 66613 88285 107280 o (71 TABLE 6.4 (Cont'd) ] .970 1971 1972 1973 Variable Parameter Estimate t S t a t i s t i c Parameter Estimate t Stati s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant - 23.601 -0.25 73.153 1.17 159.59 1.92 - 67.451 -0.44 BDCFR - 0.2416 -0.24 1.2632 1.72 1.7755 1.98 1.9382 1.48 ALS 16.971 6.61 9.2818 5.25 4.9485 2.41 - 0.1962 -0.07 INVCFR , 1962.4 6.71 3515.3 12.23 3530.5 9.83 6054.2 15.32 EDRAT 1449.8 . 4.58 1173.6 3.62 1634.5 3.73 1585.9 2.64 CMPADJ 228.67 3.19 159.06 3.67 106.90 2.02 191.86 2.22 FI 9.1408 2.12 11.590 3.40 11.362 2.47 30.060 4.20 F2 1.8070 0.62 2.1519 0.78 - 1.3043 -0.38 - 6.7830 -1.22 F3 2.4695 0.77 - 2.5199 -1.06 8.0482 2.58 11.383 2.29 F4 1.8523 0.46 1.8977 0.81 -10.328 -3.20 - 1.1645 -0.23 F5 4.6762 1.52 3.6801 1.41 - 7.3554 -2.05 2.8619 0.52 F6 - 8.1309 -2.56 - 0.7768 -0.32 - 1.1480 -0.38 - 1.1944 -0.23 WAGE1 -145.61 -2.42 -130.20 -3.54 -52.385 -1.01 134.34 1.16 WAGE 2 92.429 2.06 49.100 1.66 -33.805 -0.79 - 83.381 -1.18 2 R • 8444 .8183 .7727 7894 ESS 91074 102669 136878 223989 ro o An outline of the likelihood tests to which the regression results were subjected, and a description of a few specific examples, are included in Appendix 6A. The nature of the factor score variables and the results of the likelihood ratio testing determined that the research proceed under the assumption that one equation per year would be u t i l i z e d for the cost analysis. As a f i n a l refinement to the equation, an investigation into evidence of heteroskedasticity i n the data was undertaken. Potential violation of the homoskedasticity assumption may be exposed through examination of the residuals from the FIML estimation reported i n Table 6.4^ . In particular, i f we were to plot our e ^ ' s (estimated residuals) against our estimated dependent variable values, Y_^ , homoskedasticity would be confirmed by a horizontal or v e r t i c a l band plot; i.e. a l l residuals f a l l i n g within a specified range, and in seemingly random fashion. However, i f the absolute magnitude of the residuals tends to be positively correlated with the absolute value of Y^, we may conclude that our model, which included the homoskedasticity assumption, i s incorrectly specified. An alternative to plotting the residuals in the manner described above, employs a further OLS regression analysis, wherein the equation takes the form Y. = a + b e 2 + u. , , . _ i o o i i (where u. i s the new i disturbance term). Thus, the f i t t e d dependent variable values from the equations reported in Table 6.4 were regressed on the squares of their respective estimated residuals, on a year by year basis. The results appear in Table 6.5. It i s clear from the figures in this table that for six of the eight years we can reject the hypothesis H : 8 = 0 (where b i s the estimator o o o 20 3 TABLE 6.5: OLS Estimation Results From  Test for Heteroskedasticity Dependent Variable: CASEXD VARIABLE Constant 2 e. i 2 R 1966 Parameter Estimate t S t a t i s t i c 271.84 (31.61) 0.0120 (1.30) .0195 1967 Parameter Estimate t S t a t i s t i c 279.23 (28.95) 0.0103 (0.89) .0092 1968 Parameter Estimate t S t a t i s t i c 290.68 (28.16) 0.0220 (2.30) .0584 1969 Parameter Estimate t S t a t i s t i c 302.73 (31.49) 0.0136 (2.39) .0627 1970 Parameter Estimate t S t a t i s t i c 300.19 (31.27) 0.0156 (2.35) .0612 1971 Parameter Estimate t S t a t i s t i c 293.13 (31.42) 0.0169 (2.95) .0927 1972 Parameter Estimate t S t a t i s t i c 301.53 (33.24) 0.0154 (3.68) .1374 1973 Parameter Estimate t S t a t i s t i c 320.96 (31.06) 0.0096 (5.07) .2319 of 3 ) with 95% confidence. Thus, there does appear to be a correlation 2 0 9 o between the magnitude (in absolute terms) of the residuals and the estimated dependent variable values. It was f e l t that this j u s t i f i e d a respecification of the equations to incorporate this new information. The data were subjected to a transformation (described below) after which the system of equations was re-estimated. The indication in Table 6.5 i s that the disturbance variance i s of the following form. 2 Var (£.) = 0", A Y . where A i s a constant l l Or, the variance of the residuals i s proportional to the value of the dependent variables. Now, i f we l e t K. = 1 I X and create a new dependent variable K . Y . , then x i 2 2 2 Var (e) = Var ( K Y ) = K Var ( Y ) = a A Y = o A , a constant, Y which implies that this transformation f u l f i l l s the homoskedasticity assumption. Thus, we proceeded to divide the dependent and fourteen 6 independent variables, for each observation, by 1 / / Y ^ . The parameter estimates i n Table 6.6 are those deriving from our f i n a l eight equation system estimation. The data for this estimation were transformed as described above. Table 6.7 reproduces the residual correlation matrix deriving from the estimation. Calculations similar to those undertaken for Table 6.3 yield the following s t a t i s t i c s : Table 6.6: Maximum Likelihood Estimation Results (3) Dependent Variable: / CASEXD 1966 1967 1968 1969 * Variable Parameter Estimate t Stati s t i c Parameter Estimate t Stati s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant 0.1508 0.00 - 30.308 -0.47 - 24.428 -0.36 -114.66 -1.21 BDCFR 1.2483 1.85 1.2510 1.84 0.9232 1.15 - 0.8971 -0.88 ALS 10.877 4.75 13.637 6.95 10.748 6.16 15.699 7.34 INVCFR 2562.4 12.76 2127.3 7.93 1695.5 8.08 1637.2 6.58 EDRAT 1289.6 4.56 1587.8 5.86 1972.9 6.22 1762.4 4.78 CMPADJ 205.81 3.77 190.22 3.56 194.26 3.52 266.90 4.46 F l 2.6027 1.10 2.2031 -1.12 2.4943 0.94 9.7984 3.03 F2 1.9027 0.75 4.3743 1.90 6.2844 2.42 - 2.3814 -0.90 F3 - 1.1805 -0.49 2.1847 1.05 - 1.0661 -0.53 - 0.7417 -0.34 F4 - 3.3911 -1.51 - 5.8382 -2.63 - 5.3838 -2.53 - 4.2654 -1.67 F5 1.3879 0.58 - 1.6079 -0.80 - 1.6805 -0.67 4.8907 1.63 F6 1.8451 0.79 0.0440 0.02 1.0025 0.47 - 3.8137 -1.26 WAGEl -119.26 -2.69 - 80.748 -1.95 - 45.760 -1.15 - 48.006 -0.69 WAGE 2 47.755 1.70 45.552 1.67 45.451 1.50 57.526 1.73 A l l variable values have been transformed as described in the text. TABLE 6.6 (Cont'd) 1970 1971 1972 1973 • • * Variable Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Parameter Estimate t S t a t i s t i c Constant - 13.852 -0.16 28.470 0.47 116.32 1.58 -135.25 -1.09 BDCFR 0.0565 0.05 1.7623 2.11 2.2823 2.37 2.6494 2.05 ALS 15.618 6.11 10.158 5.68 7.3711 3.70 5.6014 2.03 INVCFR 1867.1 6.81 3200.4 11.2 2941.8 8.43 4454.5 10.51 EDRAT 1544.8 4.16 1085.6 2.91 1534.5 3.25 1577.8 2.67 CMPADJ 207.92 3.08 157.14 3.67 97.081 1.97 141.36 1.89 FI 10.739 2.59 11.216 3.43 11.673 2.80 26.734 4.50 F2 0.9205 0.32 1.5984 0.60 - 1.2965 -0.43 - 3.9142 -0.83 F3 3.8333 1.34 - 2.0943 -0.92 6.4657 2.29 6.9964 1.65 F4 2.1880 0.61 2.7786 1.26 - 7.2912 -2.45 - 0.6885 -0.16 F5 4.5396 1.61 3.8158 1.62 - 6.7116 -2.13 3.2512 0.74 F6 6.2778 -2.10 - 0,7728 -0.34 - 1.8707 -0.70 0.6643 0.15 WAGE1 - 147.34 -2.71 -123.04 -3.34 - 50.609 -1.09 176.63 1.80 WAGE 2 101.04 2.59 74.25 2.81 - 3.0489 -0.08 - 31.779 -0.55 A l l variable values have been transformed as described in the text. TABLE 6.7: Residual Correlation Matrix - Unrestricted 'MLE After Data Transformation 1966 1967 1968 1969 1970 1971 1972 1973 1966 1.0000 0.8319 0.7606 0.7159 0.6358 0.6510 0.5624 0.2849 1967 1.0000 0.8690 0.8293 0.7194 0.7659 0.6438 0.4532 1968 1.0000 0.8815 0.7748 0.7907 0.6901 0.4557 1969 1.0000 0.8468 0.7656 0.6180 0.4079 1970 1.0000 0.7318 0.6106 0.4433 1971 1.0000 0.8859 0.7497 1972 1.0000 0.8504 1973 1.0000 p = .8425 / -l p- = .8425 i 2; p = .7484 / -P 2 3 p = .6575 3 P 3 ,8651 .8695 P = -6249 / - = .8891 f p 5 p = .5835 / -5 p 5 6 P = .5078 /~^~" 6 p 6 7 P = .2849 / -7 p 7 .8979 .8932 .8358 Average V~-P t .8704 Again the figures suggest a first-order autoregressive disturbance, with p=.87. The parameter estimates in Table 6.6 are those which are carried forward to the analysis of the following chapter. Brief consideration i s thus given to the interpretation and implications of these coefficients and, in particular, to the extent to which they concur with our a p r i o r i expectations. Unfortunately much of the i n s t a b i l i t y of the parameter estimates over time appears to defy complete and decisive explanation. However, an attempt i s made to consider each variable in turn, and some variables jointly . The BDCFR parameter i s of roughly the same magnitude and t-value for 1966-'68 and 1971-'73. We would expect this parameter to have 2 2 1 a positive sign. An increase i n the value of BDCFR = B /C may be the result of one of three effects. If B increases, without a concurrent increase i n patient load, fixed costs w i l l increase and w i l l have to be spread over an unchanged case load, tending to increase CASEXD. Similarly, i f C declines while capacity remains unchanged, the base over which fixed costs may be allocated shrinks. If a given percentage increase i n BDCFR i s comprised of shifts in both B and C, the effects are harder to separate. A 5% increase i n both B and C w i l l lead to an identical increase i n B2/C, with an a p r i o r i unknown effect on CASEXD. A 2% increase in beds plus a 2% decrease i n cases yields a 6.16% increase in BDCFR and a l i k e l y increase in CASEX. So the source of the change i n BDCFR may be cruci a l . Using the 1973 parameter estimate for i l l u s t r a t i v e purposes, assuming a capacity of 400 beds an increase of 5% in a case load of 10000 cases per year would decrease average cost per case by $2.02, through the change i n 7 BDCFR only. Similarly, i f a 5% increase i n rated bed capacity i s proposed in this hypothetical hospital, but number of cases i s not expected to respond, the 1973 estimate would lead us to predict an increase i n cost 2 2 per case of approximately $4.35 : ((420 /10000) - (400 /10000)) x 2.6494). The effects of B and C on CASEXD are not limited to derived effects through BDCFR; INVCFR i s also an ex p l i c i t function of both variables . We consider the joint effect subsequently. Clearly, an increase in cases w i l l affect not only BDCFR and INVCFR, but also F1...F6, depending on changes in the age-sex distribution of discharge patients, and CMPADJ. However, considerations of this sort are best l e f t to Chapter 7. In 1969, the coefficient on BDCFR i s of the 'wrong' a p r i o r i expected sign, but the t - s t a t i s t i c indicates, with a high probability, that i t i s not significant. Recall that the coefficient on INVCFR, the second term which i s a direct function of B and C, i s theoretically an estimate of fixed cost per hospital bed, after case load standardization. The figures resulting from our analysis indicate that this fixed cost component ranged from $1600 to $4500 per bed over the time of analysis. Note also that the effect of increasing cases or beds (ceteris paribus) as in the exercise above with BDCFR, w i l l produce similar qualitative effects. Again using the 1973 parameter estimate, and the i l l u s t r a t i v e figures from that example, we see that a 5% increase in the case load, given a fixed bed capacity, leads to a decline i n cost per case of $8.48. Thus, the total direct effect of a 5% case load increase on cost per case, through BDCFR and INVCFR, i s a decline of $8.48 + $2.02 = $10.50. Having case load unchanged, but increasing bed capacity by 5%, to 420 beds, yields an INVCR related increase in cost per case of $8.91= ((420-400) _ 4454.5). 10000 The total direct effect through both variables i s to raise cost per case by $8.91 + 4.35 = $13.26, an increase of $132,600 for the 10000 cases. If a 5% increase i n rated bed capacity i s followed instantaneously by a 5% increase in throughput, the effect w i l l be limited to that deriving from a change in the value of BDCFR, as INVCFR w i l l remain unaltered. The magnitude of the change i s a $2.12 increase in cost per case, indicating that the capacity effect sl i g h t l y outweights the case load effect in that year. Returning to capacity, or scale, effects in isolation, i f instead of a 5% increase, we consider a 10% increase, to 440 beds, the joint (BDCFR and INVCFR) implication i s an increase in cost per case of $26.72. This i s indicative of a diseconomy of scale effect, which i s confirmed i f we consider 3CASEXD/3B and ignore a l l potential indirect bed related influences outside of the derived BDCFR and INVCFR effects: 2 16 3CASEXD = a 3B 1 1 + 2a B > 0 for a ,a > 0 as i n 1973. This suggests that cost per case w i l l rise over the entire scale range. Turning to the estimate of the ALS coefficient, we see that i t too meets with our a p r i o r i expectations, being positive and significant in a l l cases. This is in marked contrast to the Evans/Walker (1972) results wherein the authors were somewhat puzzled as to the lack of explanatory power contributed by this variable. Note that i n our CASEXD equation specification, the ALS parameter represented the average variable cost per day. The figures presented i n Table 6.6, ranging from 5.6 to 15.7, do nothing to suggest rejection of that interpretation. Thus, ceteris paribus, an increase in hospital average length of stay of 1 day, assuming the occupancy of the hospital i s such that this increase could be f a c i l i t a t e d , would be expected to lead to increased average case costs i n the neighbour-hood of $5 - $16. Whereas the figures for 1966-1971 tend to stay within a f a i r l y well-defined range, the values for the last two years take a dramatic drop. Although an obvious explanation does not present i t s e l f , i t would appear that there i s some tradeoff operating between the INVCFR coefficient representing fixed costs, and the ALS coefficient representing variable costs. It i s possible that the increased influence of wages and salaries i n t o t a l hospital expenditure has caused a s h i f t i n the fixed/ variable cost ratio over time. In particular, i f hospitals staff for a certain rated bed capacity, then the wages and salaries may tend to dominate cost per case, indicating that over time, an empty bed has grown more costly as a proportion of the cost of a f i l l e d bed. Complementing the decline i n the magnitude of the ALS coefficient, and the general increase in the INVCFR coefficient in the later years of the analysis, i s the trend evident in the WAGE1 and WAGE2 coefficients. The dramatic reversal of sign for both these parameters hints at the p o s s i b i l i t y that the wage and skill-mix structure of the hospitals in the later years was affecting the fixed/variable cost ratio. For example, we note that, u n t i l 1973, the coefficient on WAGE1 was negative, perhaps contrary to i n i t i a l theoretical reasoning which would suggest that a hospital with a rela t i v e l y costly service mix i s l i k e l y to exhibit relatively higher case costs. However, i f we posit that more highly s k i l l e d (and thus costly) personnel give rise to a higher marginal product/factor price ratio, which i s reflected i n the hospital's a b i l i t y to move their patients through more quickly than other hospitals (for similar case types), then this negative sign i s less of a surprise. If wages increased to such an extent as to overwhelm this increased case flow in high skill-mix hospitals, we could expect the WAGE1 parameter sign to change, as i t has done, and we would also not be surprised to see this effect dwarfing the ALS effect, as differences in ALS would be p a r t i a l l y captured by the s k i l l mix variance. The WAGE2 coefficient i s , from 1966-1971, positive and significant (for every year except 1968, at a 90% confidence level). In 1972 and 1973 the coefficient i s not significantly different from zero. Clearly we would expect relatively high wage hospitals to exhibit relatively high case costs, especially, as suggested below, in recent years. This i s borne out for early years, but 1972 and 1973 cause some confusion. In the former case, part of that influence appears to have been captured by the constant term, perhaps indicating that wage levels in general were causing average costs to increase while inter-hospital wage level dis-crepancies were of l i t t l e importance. One i s inclined, however, to remain 218 puzzled at the 1972 estimates. For 1973, we can only suggest that any possible relative wage effect has been captured in the INVCFR and WAGE1 variables. The EDRAT variable i s of particular interest i n that i t s purpose was to check on the efficiency of our attempt to isolate inpatient expenditures. Thus, a significant EDRAT coefficient would indicate that educational costs had not been completely deleted from TOTEX, i n deriving inpatient expense. As the figures i n Table 6.6 indicate, the parameter estimate for EDRAT i s , indeed, significant in a l l years and i s of relatively stable magnitude over time. On reflection, the significance i s not surprising, as educational influence within a hospital undoubtedly extends above and beyond the s t r i c t education accounting items. Our: expectation would be that teaching hospitals, and other hospitals serving any educational or research function, would tend to be relatively more expensive on an inpatient case cost basis, 8 as borne out by these figures. As an indication of the magnitude involved here, the educational component never exceeded 8% of total expenditure, the range thus being 0.00 to 0.08 (education-expenses as a ratio of TOTEX). An increase in the educational portion of TOTEX, say from .06 to .07, would lead to an increase i n average cost per case of anywhere from $10.86 (1971) to.$19.73 (1968). Thus, i t i s evident that educational a c t i v i t i e s are of considerable importance'in explaining inter-hospital case cost di f f e r e n t i a l s . The case-mix complexity coefficient i s significantly different from zero (at a 90% confidence level) over a l l eight years and, while the magnitude does tend to vary in the time span considered, the coefficient never comes close to losing i t s expected positive sign. It i s interesting to note that the parameters are less than one-half the magnitude of those reported by Evans and Walker (1972) indicating that although case complexity continues to play an important role i n the analysis of the variance in average costs, the respecification of the equation has led to a significant drop i n i t s explanatory power. The major explanatory variable now appears to be the case flow rate - the higher the case flow rate, the lower the cost per case - emphasizing again the importance of empty beds in hospital costs. The majority of hospital complexity measures f a l l in the range..75 to 9 1.25, indicating that there i s a good deal of variation in the measure. Thus, a hospital with case complexity of 1.0 may be expected to experience case costs $20 - $50 higher than another hospital which, ceteris paribus, has a case complexity of .80. The factor scores must be l e f t largely unexplained, as no apparent interpretation of any particular score i s possible. No significant patterns were evident amongst the loadings of the factors on the original variables. Suffice i t to note that, i n a l l years except 1966, at least one score appears to have a significant coefficient, but no consistent pattern emerges. Perhaps the most striking feature evident here i s the discontinuity in magnitude of FI between the 1966-'68 period, and the remaining years. Although one might suspect problems in meshing the two different data bases, we would he hard pressed to explain why any such problem would only surface here. This chapter has provided a summary of the empirical analysis which led to the estimation of parameters suitable for our case cost derivations. Although some of the less f r u i t f u l approaches, and dead ends, have been alluded to, space/energy constraints limit the completeness of such documentation. In this chapter we have subjected the cost equation developed in the previous two chapters to rather rigorous econometric scrutiny. The parameter estimates which were ultimately passed on to the next phase in this project are found in Table 6.6. Enroute to their estimation, we have provided strong evidence of f i r s t order autoregret-sive disturbances i n hospital time series analysis. Chapter 7 describes an application of the estimated coefficients. Chapter 6 - Footnotes 2 2 1 1.. ALS i s used interchangeably with L, used earlier, to denote average length of stay. In particular, the ALS form appears i n a l l tables. 2. The equations were not identical. The factor scores are derived from different proportions of total age-sex proportion variance, as described later, and are thus,, s t r i c t l y speaking, different variables in each year. 3. See, for example, Kmenta (1971), pp. 578-581. 4. Decisions regarding the estimations to be carried out were not to be taken l i g h t l y . Maximum Likelihood Estimation of a system of this size was an extremely costly exercise with respect to computer time. 5. A concise discussion of the information inherent i n residuals may be found i n Draper and Smith (1966, 86-97). 6. The reader i s referred to Goldberger (1964) for a discussion of similar data transformation techniques. This particular methodology i s due to Ernst Berndt. 7. This refers, of course, to $1970, as do a l l other figures in the subsequent discussion. 8. It was equally gratifying to be able to delete the OUTXPR and DEPRAT -variables at an ea r l i e r stage i n the analysis. The reader may r e c a l l that their purpose was identical to that of the EDRAT variable. In those two cases however, we were apparently more successful in deleting non-inpatient related expenses. This i s also not surprising, as outpatient a c t i v i t i e s and interest, depreciation and non-departmental expenses are less l i k e l y to affect inpatient care costs. 9. In contrast, case complexities ranged anywhere from a low of .35 to a high of 4.57 for the 98 diagnostic categories over the eight years. 222 Appendix 6A: Testing for Time Sta b i l i t y of Parameter Estimates At various stages i n the estimation process, hypothesis testing was undertaken to ascertain the acceptability of using identical parameter estimates for the entire time span, for a l l , or a subset, of the coefficients. Maximum Likelihood estimation f a c i l i t a t e d this procedure. (The interested reader should consult the F u l l Information Maximum Likelihood User's Guide, U.B.C. S t a t i s t i c a l Centre, for a detailed description of the programming technique employed in the restricted estimations). The test u t i l i z e d consists of a comparison of log likelihood function values for restricted and unrestricted (but otherwise identical) regressions. More s p e c i f i c a l l y , the s t a t i s t i c 2 A log L i s distributed approximately as X c where L i s the value of the likelihood function, A log L i s the change i n the value of the log likelihood function as we move from restricted to unrestricted, and c i s the number of constraints imposed in the restricted simultaneous equation estimation. Further details may be found i n Silvey 2 (1970, 108-115). If the value of this s t a t i s t i c exceeds the y c r i t i c a l c value for a chosen confidence level we are forced to reject our null hypothesis. In the majority of cases described below, the null hypothesis i s comprised of a group of hypotheses (or constraints) which must jo i n t l y hold i f we are to be able to accept i t (them). Thus, for example, the value of log L for the unrestricted FIML estimation on 14 independent variable parameters, 3 3 for 1966-1973, i s -3.05067 x 10 , as opposed to a value of -3.2295 x 10 for the f u l l y constrained regression. In the latter case, i f we denote the parameters by b^ , i=l, 14; j=l, — , 8 years, then the null hypothesis i s Ho : b l l - b12 = b l l " b13 = b l l " b14 = = b H " b 1 8 " ? b21 b22 - b21 " b 2 3 = b 2 1 " b 2 4 " - " b 2 l ' fa28 = ° b14 , r b14,2 = b14 , r b14,3 = b14 , r b14,4 ••• = b14 , r b14,8 = ° 2 o The value of 2A log L = 2(1.7884 x 10 ) = 357.68. Consulting a X table of c r i t i c a l values, and noting that the constrained estimation imposed 98 constraints, we see that for 120 constraints, the c r i t i c a l value i s 158.95 at the 99% confidence le v e l . Since our value f a l l s well beyond the c r i t i c a l range, we impose very minimal risk of being incorrect when we unequivocally reject the above n u l l hypothesis. The residual cross product matrix may also be used to perform likelihood ratio tests, and one's choice i s solely dependent on the information provided by the particular program being u t i l i z e d . The tests are numerically equivalent. If S i s the 8X8 matrix comprised of the e | e j (where i , j = 1, , 8) and we denote S and S as the respective matrices for the constrained con unc and unconstrained estimation, then T In l s c o n | 1 S distributed approximately as xf» | S i | unc| where T = # of observations. Thus, using the same example, we have T ln |s con . . 22 ,S = 8 7 l n <2-4775 x 10 Z Z) = 357.68 unc ' 70 (4.0602 x 10 ) A number of other likelihood test examples (in no particular order) which were performed at various stages i n our analysis, are b r i e f l y described below. A l l c r i t i c a l values cited are those available in Table A-3 of Johnston (1963), which most closely approximate, but always overstate, the actual 99% confidence level values for our particular number of constraints: (i) 1966-1973; 17 independent variables, 119 constraints (i.e. f u l l y contrained). 2A log L = 338.12 vs c r i t i c a l value of 158.95 (ii) 1966-1971; 17 independent variables, a l l parameters save those for FI through F6 constrained - 55 constraints. 2A log L = 187.58 vs c r i t i c a l value of 79.08 ( i i i ) 1966-1971; 17 independent variables, only BDCFR, ALS, INVCFR and CMPADJ parameters constrained - 20 constraints. 2A log L = 57.13 vs c r i t i c a l value of 31.41 (iv) 1966-1973; 17 independent variables, only BDCFR, ALS, INVCFR and CMPADJ constrained - 28 constraints. 2A log L = 128.44 vs c r i t i c a l value of 43.77 (v) Consider the.OLS regression using pooled time series-cross section data as employed early in this chapter. If we denote D72 as a dummy variable which takes the value 0 except for the 87 1972 observations, and similarly denote D73 for 1973, we may.create the following 8 variables: ALS72 r r ALS*D72 ALS73 = ALS*D73 INVC72 = INVCFR*D72 INVC7.3 = INVCFR*D73 WAGE172 = WAGE1*D72 WAGE173 = WAGE1*D73 WAGE272 = WAGE2*D72 WAGE273 — WAGE2*D73 225 Now, a pooled time series-cross section OLS regression u t i l i z i n g 25 variables (our original 17 plus the above 8 'interaction' variables) yielded an error sum of squares of 8.5498 x 10^. Thus, the average yearly error sum of squares i s 1.068725 x 10^. We note that NO2 = 1.068725 x 10 5; N = sample size Now, let Q denote the residual covariance matrix, 0, = where i s an 8 x 8 matrix , A. % 8 24 Then |fi| = (a ) = 5.1853 x 10 . But this i s the determinant of the aforementioned S matrix for a constrained regression, the constraint being on the form of the 0, matrix. Thus, i t can be compared with the unconstrained MLE estimation using a l l parameters restricted to be equal across years except for ALS, INVCFR, WAGE1 and WAGE2 which are to have parameters restricted only for 1966-1971, implying a total of 111 parameter restrictions. In both regressions, there are 25 free parameters, the only difference in the systems being that the MLE estimation imposes no constraint on the form which the Q matrix w i l l take. 22 The value of \Q,\ was 1.1617 x 10 for the FIML estimation, which yields T In |fl I C O n | = 87 ln (5.1853 x 10 ) = 530.79 unc 1 (1.1617 x 10 2 2) This clearly exceeds even the 99% c r i t i c a l value of 158.95 for 120 constraints. Thus, we are forced to reject use of the pooled time series-cross section OLS. parameter estimates. In this example, the OLS estimation imposed constraints on ft, i.e. i t had the diagonal form with a 2 as diagonal elements. In comparison, the ML, estimation, while imposing the same number of parameter constraints, imposed no restrictions on the form of the ft matrix.^ Thus, in effect our null hypothesis here was one regarding an ex p l i c i t form for the ft matrix and, since i t was rejected, we may conclude, at a high confidence level, that we are not i n error when we assume that ft i s not of a diagonal form, or equivalently, when we assume that OLS provides i n e f f i c i e n t parameter estimates as a result of autoregressive disturbances. This appendix has outlined a number of examples u t i l i z i n g the likelihood ratio test. The result of this portion of our analysis was clearly that these tests provided no j u s t i f i c a t i o n for the intended route of u t i l i z i n g one set of parameter estimates for a l l years. In addition, they provided definitive evidence against using OLS for pooled time series-cross section hospital cost analysis. Appendix 6A - Footnotes 1. This test was u t i l i z e d by Berndt and Wales (1974) and I am indebted to the former for suggesting i t s applicability here. 2 2 7 Chapter 7: Marginal Case Costs - Application of a Behavioural Hospital Average Cost Equation The past three chapters have described the specification and estimation of an equation relating average cost per hospital separation to a number of exogenous variables. The intent of the present chapter i s to employ the estimated parameters from that equation to derive marginal costs of various I.CD.A. diagnostic categories. The methodology involves consideration of the comparative static implications of changing a hospital's case mix, through additions i n the number of discharges for a particular diagnostic category. For example, let us consider a hospital which discharged twenty-five patients for whom the recorded principal diagnosis was infectious hepatitis. We further assume the hospital's yearly case load was 3000 discharged cases. The question to which we address ourselves i s : what would the average hospital case cost implications have been, ceteris paribus, i f this particular hospital had treated and discharged three (10% of twenty-five) additional hepatitis cases during the year? The hospital BDCFR and INVCFR values would be expected to f a l l , for reasons outlined in the previous chapter. The ALS would change, the direction being dependent on the length of stay of these three patients relative to the hospital average. CMPXC1 would also change, as i t i s dependent on the resultant case mix distribution which incorporates the added cases. From these shifts i n variable values we are able to calculate a new CASEXD estimate, and comparison of the old and new CASEXD values gives rise to an estimated marginal case cost. The analysis i s based on some suspect assumptions, but they would l i k e l y make l i t t l e difference to the ultimate results, and are necessary either i n the interest of expense or p r a c t i c a l i t y . In particular, i t i s assumed that an addition to the case load does not alter EDRAT, WAGE1 or WAGE2, or FI through F6. It i s not unrealistic to assume that any educational ac t i v i t y influence on inpatient care w i l l continue to be distributed as the same proportion of tot a l expenditures. Thus, there i s no persuasive reason for presuming that this variable value ought to change and, in any case, the direction of change would be d i f f i c u l t to determine at this level of sophistication. The relative wage levels and s k i l l mixes of non-medical staff personnel are not l i k e l y to change, as in the majority of cases we are considering the addition of less than fifteen cases over a year's time. Additions to tot a l case load of this magnitude are not l i k e l y to induce staffing changes. Additional cases w i l l alter the age-sex structure of the discharge patient population. The values of the FI F6 variables would, in rea l i t y , change with any change in this age-sex distribution. However, the only information which we could apply i n estimating the new distribution"would be the relationship of the original case-specific age-sex structure to that for the hospital as a whole. It w i l l be recalled that our or i g i n a l age-sex data were compiled only on a hospital specific basis. To compile this data for each year at a level disaggregated on a hospital- and case-specif i c . basis , would have involved creating eight three-dimensional arrays with 341,040 entries (87-98-40). Needless to say, as measured against the expected information gain of this route, the costs of data manipulation and storage are prohibitive. Consider, for example, the complexity and time consumption of a program which, for each case in each year (98-8 = 784 times) recalculated the age-sex proportion matrix and computed the resultant factor scores. The f i n a l assumption necessary in this exercise i s that any hospital could accommodate the added cases without undue occupancy stress, and without the addition of beds or personnel. In that sense, this i s s t r i c t l y a short run, stat i c analysis. Again, as most hospitals operate at less than 100% occupancy, and as the number of cases added i s generally small, we assume away problems related to these considerations. One possible related d i f f i c u l t y arises due to the i n d i v i s i b i l i t y problem. Beds are often not interchangeable across treatment areas. A hospital reporting only an 85% occupancy rate may s t i l l be unable to accommodate additional cases of a particular type. However, the incidence of this type of occurrence i s not l i k e l y to be of sufficient impact to affect the basic methodology and results. Thus, the general analysis involves a quantitative consideration of the impact on each of the four variables (BDCFR, ALS, INVCFR, CMPADJ) subject to change, brought about by alterations in the hospital case mix. The implications of changes i n these variables for cost per case are calculated. This entire process i s undertaken a to t a l of 68208 times (8 years, 87 hospitals, 98 cases). The results of this i n i t i a l phase are the marginal costs of a l l case types for each hospital and each year. Two distin c t aggregations are then applied to these figures. The f i r s t involves aggregrating across hospitals in a given year, and the f i n a l set of figures i s derived by aggregating the cost vectors across years. Each step i s discussed i n detail below. For each year, the following steps were undertaken for phase one of the analysis: 1 (i) The year's C matrix (where each c.. entry refers to the number th th "^ ^  of j category cases in the i hospital; i=l,...,87; j=l,...,98) was altered by adding 10% of the total cases of type j in 230 hospital i to that hospital's type j case load. If c^ _. > 0, a minimum of one case was added. C_. , the total provincial type j cases, was adjusted accordingly. Also, the last case type to have been adjusted was reset to i t s original value. Thus, i f hospital #3 discharged 40 cases of type #72, no cases of type #73, and 26 cases of type #74, when the analysis reached case #74, c., 0 would be reset to 40 from 44 and c. would be set at 29. 172 X7l* I t goes without saying that the value for the previously considered case type was also reset to i t s original value. Total provincial cases, C, were also recomputed at each step. (ii) At the time the original C matrices were created, total length of stay (TLS) matrices were also generated, their ultimate purpose being to create case- and hospital-specific ALS figures. Thus, for the case and hospital being considered a case-specific ALS was calculated using the C and TLS matrices. This figure was multiplied by the number of cases added to the C matrix i n step ( i ) , and the resulting total days stay figure for new cases was added to the hospital's actual total days stay of discharged patients. The result was divided by actual hospital separations plus the new cases, to arrive at a new hospital ALS. This step i s dependent upon the assumption that the new cases w i l l , on average, involve lengths of stay equal to past cases of similar type in the same hospital. ( i i i ) New P and Q matrices, comprised of recomputed p ^ and q^. values (refer back to Chapter 5 for definitions) were constructed, after which the entire CMPXC1 methodology was repeated to compute a value based on the revised case mix. S t r i c t l y speaking, changing even one hospital's case mix by a few cases w i l l alter a l l the individual case complexities, as their construction i s based upon the provincial dispersion of a l l cases. However, as i t was f e l t that the effects of recomputing would be minimal, the original yearly case complexities were used. To determine the bias introduced by this procedure, a program check computed EH.Q. j 3 3 which should equal 1.0, by construction (see Chapter 5). In fact, for 1966, there were three occurrences, out of a tot a l of 87*98 = 8526 passes through the program, for which the error was greater than or equal to 0.0003. Thus, i t would appear that this slight simplification's merits far outweighed the additional time and expense involved i n recomputing a l l case complexities for each iteration of the procedure. The revised CMPXC1 value, created as described above, was then adjusted, depending on the year being considered, to yield a new CMPADJ value for the i * " * 1 hospital. (iv) A new hospital case flow rate (CFR) was computed using the new case t o t a l . This value was, in turn, employed in the calculation of new INVCFR and BDCFR values. (v) For the hospital under consideration, CASEXD was determined using the parameter estimates from the previous chapter, and the original values of a l l independent variables. We denote the resultant figure by CASEXD^. Similarly, a new CASEXD figure, CASEXD , based on the adjusted values for the independent n variables, was computed. Letting N refer to the number of new, or added, cases, and MC. . to the 'marginal cost* for the j*"* 1 case th X 3 type i n the i hospital, we have the following: IPEXP = CASEXD • CASES o o where CASES i s actual hospital case total for the year in question; IPEXP = CASEXD • (CASES + N) n n MC.. = (IPEXP - IPEXP )/N i ; j n o These five steps were repeated for each case type and each hospital. It i s clearly impossible to include a l l the results from this phase of the analysis. For i l l u s t r a t i v e purposes, Table 7.1 contains comparative 1966 figures for a number of hospitals. Table 7.2 i s comprised of similar 1970 figures for the same hospitals. The reader i s referred to Table 5C.1 for the ICDA categories corresponding to each case number. Tables 7.1 and 7.2 require l i t t l e comment. Clearly there i s some 2 32 TABLE 7.1: 1966 CASE COSTS - SELECTED HOSPITALS (a l l costs are expressed in constant (1970) dollars) NC = no cases reported HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 1 534.54 551.28 429.38 432.22 411.73 2 621.46 609.22 506.99 571.60 403.57 3 471.15 541.10 478.30 386.99 219.13 4 242.56 262.03 250.11 222.80 155.12 5 308.67 301.94 321.39 254.02 191.18 6 677.18 584.42 791.40 562.51 874.72 7 607.83 633.02 515.36 1165.38 448.54 8 668.62 688.05 620.91 512.66 544.59 9 707.09 694.53 653.19 614.76 585.95 10 673.77 645.08 604.04 467.05 483.23 11 542.98 566.20 522.60 479.79 309.88 12 432.58 485.86 435.78 440.15 • 367.35 13 580.73 670.75 558.11 570.23 430.77 14 677.06 623.09 671.89 544.55 527.73 15 603.70 626.85 552.61 510.49 692.21 16 621.09 608.04 637.32 560.61 436.67 17 560.51 579.89 516.63 540.81 488.85 18 616.03 554.71 587.32 578.72 565.91 19 365.85 375.82 333.94 379.77 263.75 20 396.18 425.02 369.38 397.59 257.73 21 368.74 358.47 317.68 328.03 240.96 22 281.89 276.40 264.35 267.62 167.31 23 264.88 215.88 207.11 215.30 125.68 24 443.84 511.60 482.24 491.80 396.39 25 397.23 393.67 378.70 357.29 270.52 26 623.38 540.63 596.17 469.51 352.73 27 463.15 430.81 455.04 400.15 318.91 TABLE 7.1 (Cont'd) 3 HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 28 407.52 434.77 435.45 326.08 294.89 29 470.11 475.69 433.26 473.45 323.29 30 366.86 322.90 259.54 333.19 172.69 31 483.20 478.35 391.45 466.72 360.24 32 551.06 492.31 383.93 604.24 301.10 33 490.17 491.71 433.81 492.60 286.62 34 353.67 371.15 374.88 354.46 314.05 35 559.95 560.87 537.37 534.71 455.95 36 270.56 314.03 272.71 275.88 197.15 37 558.27 528.74 546.84 531.65 411.78 38 444.94 434.31 408.46 432.45 318.88 39 378.21 341.72 326.01 331.46 243.52 40 326.69 311.09 335.51 316.88 211.31 41 700.28 617.44 577.16 1058.83 484.71 42 374.31 360.38 349.18 333.54 271.75 43 304.22 323.51 301.72 294.07 203.24 44 357.78 355.18 366.82 317.89 201.66 45 343.99 311.70 291.61 244.21 136.06 46 160.63 198.56 151.88 166.02 60.35 47 187.40 238.91 167.17 179.43 88.84 48 282.83 273.82 230.89 244.29 123.19 49 205.41 226.97 207.10 183.98 90.83 50 219.73 244.39 209.49 220.88 124.23 51 393.18 388.41 344.60 360.26 270.93 52 251.67 244.68 203.78 212.02 126.82 53 392.57 385.10 393.34 350.21 261.37 54 208.37 230.20 221.90 210.16 102.17 55 273.23 284.90 261.03 283.55 173.78 56 321.00 352.06 301.04 290.82 207.76 57 352.68 373.47 339.82 337.91 266.98 TABLE 7.1 (Cont'd) 23k HOSPITA L SEQUENCE # CASE # 081 077 085 033 059 58 159.45 189.83 168.67 167.68 74.08 59 503.23 483.85 429.33 438.80 324.01 60 645.25 589.67 541.24 685.97 432.77 61 384.98 .376.35 333.26 327.70 266.53 62 323.48 326.41 309.38 297.49 200.39 63 778.69 821.80 832.93 843.77 612.57 64 269.27 287.27 240.42 254.40 131.43 65 383.55 408.97 372.37 377.78 257.28 66 405.90 431.98 404.24 407.36 289.11 67 585.70 625.18 631.48 569.07 489.67 68 251.83 272.71 244.34 246.48 151.28 69 272.81 305.24 257.16 290.28 186.87 70 481.47 480.40 447.05 471.76 343.11 71 229.33 258.25 226.16 255.71 142.32 72 286.14 307.69 274.59 292.50 .190.89 73 206.43 225.58 191.54 209.44 107.81 74 277.54 297.10 254.71 259.64 162.02 75 248.55 272.54 246.05 245.83 142.93 76 353.56 385.85 328.84 326.80 251.26 77 246.29 278.17 222.80 254.51 149.44 78 212.94 212.39 194.25 188.58 88.58 79 345.76 309.85 306.30 312.88 200.75 80 487.09 406.92 339.55 352.25 200.68 81 429.43 445.25 374.03 431.06 310.41 82 408.17 369.08 323.61 409.52 236.72 83 631.13 599.07 524.63 579.24 447.66 84 373.96 396.51 275.70 362.32 255.79 85 273.74 294.17 255.72 267.75 152.06 86 311.74 307.51 252.83 270.72 169.44 87 637.52 460.64 338.50 422.89 265.02 TABLE 7.1 (Cont'd) 2 3 5 HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 88 251.96 248.67 187.23 224.51 129.16 89 892.77 813.95 595.63 836.37 791.29 90 402.19 380.45 251.62 302.76 226.80 91 272.14 295.14 217.87 246.90 158.21 92 395.45 368.91 339.47 414.67 347.22 93 403.48 407.43 324.64 391.23 161.93 94 220.94 240.98 184.37 210.81 99.94 95 NC NC NC NC NC 96 266.85 290.58 267.28 256.50 152.41 97 414.97 442.99 425.33 330.00 365.03 98 343.53 359.69 332.37 388.50 306.28 TABLE 7.2: 1970 CASE COSTS - SELECTED HOSPITALS NC = no cases reported 236 HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 1 630.43 664.89 614.01 768.11 456.97 2 905.07 487.98 395.63 793.93 342.28 3 610.56 566.04 517.25 452.63 369.26 4 302.18 373.12 298.24 250.20 177.18 5 353.58 350.76 454.48 312.98 155.15 6 852.86 801.88 657.76 674.87 NC 7 781.20 800.53 609.82 624.67 1031.22 8 750.12 721.38 679.74 754.20 589.97 9 852.66 812.43 710.88 746.11 642.15 10 760.14 734.44 672.15 609.74 610.77 11 594.18 619.19 497.25 529.00 465.58 12 465.80 527.21 470.29 509.80 334.03 13 619.03 781.34 727.83 627.33 647.08 14 826.25 708.03 669.74 1010.75 674.23 15 662.16 759.43 585.11 563.32 469.53 16 660.68 684.32 674.94 654.98 451.62 17 716.85 693.32 666.23 832.70 557.93 18 692.27 648.26 680.69 659.96 570.82 19 430.24 457.52 405.21 394.39 315.15 20 418.97 388.36 343.57 385.83 239.96 21 449.45 453.08 396.31 435.96 258.66 22 366.51 366.60 299.77 300.67 195.07 23 415.91 367.92 374.95 323.80 292.65 24 536.20 499.70 450.20 454.84 408.43 25 536.98 468.67 441.58 368.12 271.05 26 595.33 690.08 505.91 501.87 NC 27 511.00 438.89 411.63 485.74 308.22 28 416.38 407.02 309.12 320.67 165.07 29 532.19 521.37 655.85 574.83 361.79 TABLE 7.2 (Cont'd) 237 HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 30 393.71 397.16 302.90 415.57 236.77 31 483.62 436.73 506.32 461.03 320.43 32 859.41 642.32 569.79 674.81 486.43 33 661.84 577.91 462.42 623.19 353.48 34 461.04 499.23 373.76 426.06 261.87 35 607.20 605.58 565.22 527.41 473.22 36 331.17 365.52 330.30 333.65 236.98 37 704.54 616.85 580.18 583.51 450.80 38 564.05 486.68 491.33 498.19 362.36 39 482.17 389.72 432.19 414.91 246.36 40 388.59 369.75 332.95 342.93 242.31 41 927.22 704.61 625.72 621.29 561.65 42 475.52 424.85 495.33 417.93 272.63 43 385.13 396.31 354.44 331.71 239.90 44 465.64 428.68 429.66 443.40 ,276.45 45 646.72 . 522.91 475.05 590.27 316.41 46 212.28 245.69 214.50 187.16 85.47 47 283.64 305.44 272.89 202.69 125.22 48 369.81 397.86 318.84 287.84 177.61 49 352.74 375.56 309.59 301.26 149.99 50 259.13 281.49 241.86 233.24 131.92 51 397.55 418.02 404.47 393.29 292.05 52 298.53 301.18 2.35.84 232.03 162.06 53 437.03 455.09 442.25 428.62 280.39 54 353.00 384.89 311.86 298.18 148.69 55 334.63 338.13 290.31 287.78 188.52 56 380.99 396.99 357.90 363.08 232.91 57 418.46 456.37 352.15 376.42 314.00 58 281.88 311.38 282.52 242.25 137.18 59 720.87 694.82 599.39 618.94 402.38 60 722.05 694.31 629.78 566.32 412.38 TABLE 7.2 (Cont'd) 2 3 8 HOSPl CTAL SEQUENCE # CASE # 081 077 085 033 059 61 429.98 449.93 399.93 375.01 285.90 62 375.03 392.24 379.39 357.95 234.24 63 1142.12 1296.52 1354.11 1042.76 1174.94 64 393.21 392.20 368.10 317.67 206.47 65 463.04 471.31 413.58 397.39 295.82 66 448.10 471.66 435.05 442.84 287.50 67 654.01 702.27 642.62 595.57 523.42 68 312.51 315.67 271.91 279.90 165.93 69 323.85 324.96 298.01 323.42 214.82 70 495.88 493.64 468.47 430.33 314.51 71 252.30 296.53 250.69 279.44 130.26 72 346.71 379.79 343.36 356.48 241.03 73 244.99 268.28 228.36 242.39 129.74 74 410.19 427.32 375.03 390.58 281.99 75 312.94 339.39 309.24 293.41 '183.11 76 422.98 466.68 407.22 374.19 298.88 77 300.38 321.42 281.37 264.65 159.12 78 339.70 318.93 294.34 260.33 144.90 79 436.87 424.06 450.39 336.69 238.73 80 640.06 528.13 425.48 523.80 324.33 81 488.86 553.03 418.82 548.42 383.52 82 457.88 442.51 389.93 457.72 291.20 83 647.76 630.56 546.58 560.28 419.23 84 528.15 607.19 486.30 420.24 357.75 85 328.41 362.66 302.77 314.48 235.08 86 436.41 397.14 312.85 382.33 178.53 87 749.44 637.73 475.37 595.66 344.30 88 337.50 337.94 295.09 276.25 142.23 89 1138.59 918.84 692.82 979.62 735.16 90 557.43 555.14 373.04 420.71 266.45 TABLE 7.2 (Cont'd) 239 HOSPITAL SEQUENCE # CASE # 081 077 085 033 059 91 340.31 373.27 316.36 404.77 208.01 92 533.88 450.04 461.21 495.36 388.68 93 619.05 549.07 451.33 349.31 237.24 94 320.37 326.61 280.75 267.36 155.44 95 NC NC NC NC NC 96 318.96 345.89 317.23 293.54 184.15 97 488.31 489.33 554.73 365.81 349.00 98 303.16 321.25 293.92 309.88 169.16 variation across hospitals i n case costs, as we would expect. In particular, a teaching hospital such as number 081 exhibits, on average, higher costs than a smaller c i t y hospital (059). The five hospitals for which these figures are presented are a l l of considerable size, each exceeding 200 bed capacity. A few points of interest may be derived through a close inspection of the underlying data for these tables. In particular, whereas those advocating length of stay differences as the driving force behind case cost variation might find support in the following 1966 figures, HOSP. SEQ.# CASE # # OF CASES TOTAL LENGTH OF STAY ALS CASE COST 085 1 13 163 12.54 429.38 033 1 9 114 12.67 432.22 they would be somewhat harder pressed to explain away these: HOSP. SEQ.# CASE # # OF CASES TOTAL LENGTH OF STAY ALS CASE COST 081 12 148 2732 6.54 432.58 085 12 42 369 8.79 435.78 This phenomenon i s not restricted to inter-hospital comparisons, however, as evidenced by the following intra-hospital s t a t i s t i c s : HOSP. SEQ.# CASE # # OF CASES TOTAL LENGTH OF STAY ALS CASE COST 081 6 70 1110 15.86 667.18 081 14 60 1234 20.57 677.06 Thus, complexity differences exert a considerable influence in determining marginal case cost variations. Two other figures which stand out in the 1966 table require comment. Hospital 033 reports abnormally high case costs for diagnostic categories #7 and #41, abnormality deriving not from absolute values, but from their position relative to costs of identical cases in the other four hospitals. In both cases, a small number of discharges, one or two of which may have involved very extensive lengths of stay, appear to be responsible. In CASE# # OF CASES . TLS ALS CASE COST 7 7 541 77.29 1165.38 7 89 2252 25.30 607.83 41 19 1131 59.53 1058.83 41 415 10506 25.32 700.28 particular, HOSP. SEQ.# 033 081 033 081 In addition, category #7 contains a l l cases of malignant stomach neoplasms. Hence, different admission - readmission practices of the two hospitals, or hospital transfer policies for these particular cases could easily generate the differentials derived here. Whereas one hospital may send cancer patients home any number of times during the duration of i l l n e s s , whence each readmission i s treated here as a new case, hospital 033 may have encountered one or two extremely lengthy cases where the patient was hospitalized for the entire elapsed time of i l l n e s s . Support for this i s offered by the 1970 s t a t i s t i c s for the same hospital and case type. In that particular year, 15 cases were discharged, generating an average length of stay of only 20.27 days, and a much lower case cost of 624.67. This type of small sample-induced bias leads to the use of relative case loads as weights in the aggregation procedures. The second phase of the case cost generation analysis involved aggregation across hospitals, for each year. Using our previously introduced notation, we calculate MC , for the t*^ year as: 3 1 MO = £ MC. . c. ,.. „ ^ ^ . . , i t . n t l i t (where C. = total provincial 1 c 3 t j t type j cases discharged in year t) Thus, each hospital's proportion of C^ t i s used as i t s particular weight in the aggregated figure. The results for each year comprise Table 7.3. TABLE 7.3: AGGREGATED YEARLY CASE COSTS (al l figures in 1970 dollars) NC = no cases YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 1 414.44 594.68 .491.97 586.61 567.18 378.70 387.38 335.40 2 503.15 645.05 575.24 754.58 511.45 383.83 428.19 500.89 3 329.38 482.29 356.35 426.16 438.27 311.30 290.27 241.01 4 160.23 262.91 227.98 208.18 196.27 160.30 192.98 148.45 5 212.31 280.17 236.63 184.11 220.61 173.42 192.70 159.01 6 616.14 798.21 653.17 1011.63 781.32 576.32 503.35 480.62 7 513.71 710.81 494.78 645.18 649.04 461.01 433.03 358.95 8 584.09 722.77 567.23 706.35 673.21 482.00 422.57 380.61 9 636.24 791.26 665.98 818.20 711.53 515.27 452.28 433.75 10 605.39 710.07 585.16 732.67 660.24 461.08 412.98 391.78 11 471.85 609.20 526.25 584.83 551.72 399.22 373.38 337.52 12 392.51 477.61 419.31 496.59 419.67 313.93 309.26 311.76 13 549.33 635.67 548.62 724.96 623.47 502.25 423.97 410.90 14 617.66 754.62 620.59 744.54 682.58 479.06 378.33 374.54 15 526.15 624.23 554.26 - 664.40 624.62 440.13 386.78 406.82 16 576.86 649.15 597.87 683.88 593.97 499.19 395.56 399.44 17 459.67 693.98 588.68 616.70 613.04 490.87 435.40 417.82 TABLE 7.3 (Cont'd) YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 18 533.46 614.04 567.33 640.68 616.28 461.62 398.51 382.67 19 287.56 343.89 324.91 363.00 329.78 267.84 279.75 248.39 20 322.76 408.60 318.75 325.37 298.12 247.62 248.32 230.84 21 282.27 344.80 325.21 362.16 342.99 269.46 284.93 268.24 22 185.89 253.95 232.20 231.71 234.72 193.51 221.88 180.14 23 136.91 242.67 171.13 292.77 302.04 229.18 251.41 208.90 24 429.86 513.59 485.46 475.23 428.79 296.08 316.56 309.19 25 309.28 389.21 329.50 400.75 352.53 275.94 304.75 256.03 26 477.74 692.21 565.94 590.89 482.15 383.74 356.65 337.55 27 367.00 480.20 396.00 361.68 368.08 279.43 276.69 252.82 28 349.33 420.85 355.97 278.70 251.81 211.81 233.81 195.92 29 417.47 495.30 525.41 570.13 512.17 413.80 377.37 344.76 30 246.50 327.90 273.85 301.12 305.93 242.63 261.21 227.83 31 410.50 455.90 435.64 467.84 430.02 325.30 330.25 292.24 32 419.92 578.00 526.99 703.53 666.45 526.83 515.23 467.57 33 417.06 524.04 477.63 533.85 554.60 434.99 434.30 365.03 34 298.67 434.55 365.25 415.38 372.42 296.03 286.87 260.28 35 509.66 547.86 534.47 613.51 517.71 397.63 357.11 377.21 36 237.18 313.79 301.72 333.46 282.61 229.05 241.02 212.77 37 472.54 570.90 560.92 647.49 591.69 442.18 378.42 386.43 TABLE 7.3 (Cont'd) YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 38 360.26 449.36 416.54 463.15 434.15 334.36 328.67 283.92 39 260.45 357.53 299.36 340.69 343.23 269.05 290.18 241.15 40 238.13 310.97 289.30 287.21 281.00 226.98 240.41 192.57 41 v 607.81 714.83 657.48 787.92 735.74 521.16 . 509.72 469.32 42 294.72 362.19 338.68 408.99 356.14 275.47 273.01 252.15 43 234.83 304.60 266.58 297.97 288.25 236.59 243.27 224.11 44 260.73 371.14 297.22 345.60 340.40 252.84 252.02 223.19 45 196.88 277.51 258.21 416.04 460.93 310.50 298.55 272.56 46 89.12 131.15 129.57 112.23 126.02 110.73 157.45 110.35 47 85.09 177.68 116.11 117.11 135.39 122.53 156.69 109.23 48 160.48 220.07 204.52 215.98 236.27 180.68 199.48 158.64 49 126.25 175.41 162.13 191.41 213.71 169.32 198.13 159.26 50 152.07 185.29 184.88 175.81 165.51 157.29 187.45 172.19 51 327.31 383.41 363.93 359.58 337.88 261.11 269.89 261.09 52 123.49 208.73 189.12 187.83 143.12 157.21 207.54 229.80 53 287.19 354.20 301.30 351.91 329.05 256.78 266.76 217.50 54 126.31 199.19 172.24 204.57 203.85 168.26 206.30 154.48 55 203.41 260.41 247.88 256.85 236.98 184.65 217.62 182.35 56 250.10 304.50 290.59 310.05 291.56 224.80 238.74 210.13 57 267.21 345.25 321.03 334.45 309.94 250.03 275.35 227.46 TABLE 7.3 (Cont'd) YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 58 89.90 155.79 146.69 171.50 182.18 144.47 184.63 141.34 59 388.96 473.92 423.69 589.87 548.36 397.19 370.59 333.46 60 518.32 603.41 519.84 618.72 554.98 410.97 366.01 320.65 61 280.48 352.20 316.04 351.72 327.42 252.74 260.85 226.42 62 235.83 305.69 272.74 291.07 286.65 233.19 255.34 214.62 63 772.97 974.43 1072.91 1377.85 1144.13 832.08 627.59 756.41 64 171.46 255.83 251.94 301.49 262.49 196.64 221.15 175.47 65 320.24 372.84 371.73 410.24 359.33 278.89 279.16 254.80 66 346.40 390.93 361.32 385.48 365.03 284.10 275.23 254.31 67 534.27 606.62 557.82 655.98 568.86 423.35 370.37 375.86 68 175.36 238.22 208.50 208.46 197.12 166.78 204.53 175.83 69 198.45 266.36 238.75 248.40 238.68 207.68 230.07 194.78 70 402.37 459.88 420.86 447.06 403.15 308.61 300.88 287.14 71 167.09 220.22 198.67 185.73 174.05 135.73 177.90 145.76 72 218.60 272.04 250.75 283.97 272.86 228.06 243.82 229.87 73 139.09 195.28 199.06 179.21 168.78 147.51 182.70 146.14 74 209.94 266.32 267.30 286.98 338.59 285.26 271.37 283.25 75 181.84 233.14 236.21 253.67 232.38 186.53 210.30 182.32 ro TABLE 7.3 (Cont'd) YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 76 286.78 336.78 310.94 355.18 334.12 254.20 251.97 221.77 77 173.60 283.37 239.74 236.16 222.71 160.01 188.38 176.15 78 110.08 168.15 155.68 193.55 205.12 159.32 205.94 152.12 79 239.04 298.98 290.85 278.34 297.30 224.80 252.66 218.55 80 294.55 342.92 342.70 436.92 438.20 315.96 321.11 293.07 81 345.48 436.63 390.43 451.38 408.34 322.42 298.41 260.31 82 302.93 372.87 368.51 370.14 354.13 280.77 279.95 253.95 83 543.44 602.59 569.89 626.46 547.83 412.28 373.01 364.55 84 240.96 374.06 295.58 447.80 411.39 299.86 277.21 249.17 85 206.01 237.45 235.24 242.56 235.89 192.20 217.20 178.17 86 218.44 275.92 265.70 264.05 263.05 209.84 233.50 195.45 87 366.10 480.57 397.14 464.61 456.69 336.43 349.31 284.38 88 155.16 215.32 211.66 202.70 205.74 174.19 205.53 168.64 89 788.45 932.55 819.53 1005.25 918.26 605.55 536.04 488.84 90 256.82 329.31 308.16 350.15 358.77 263.57 273.51 237.19 91 191.69 254.31 237.45 263.29 261.51 200.91 221.87 177.58 92 294.60 446.22 376.91 . 425.02 377.98 273.07 293.92 242.87 93 240.15 330.00 295.17 312.82 324.97 251.46 255.27 204.76 94 131.74 184.99 193.55 191.69 196.13 172.08 208.58 159.67 95 28.62* NC 289.55 NC NC NC NC NC TABLE 7.3 (Cont'd) YEAR CASE # 1966 1967 1968 1969 1970 1971 1972 1973 96 197.43 247.04 248.75 255.45 237.11 189.03 209.11 182.07 97 328.07 435.05 399.53 396.73 367.97 263.25 264.10 220.01 98 301.75 340.35 299.30 258.22 222.78 190.42 215.46 193.50 * Only 1 case reported in province. 21*3 The variation across years i l l u s t r a t e d in Table 7.3 i s not unexpected. Each year's figures were derived from a different equation, and as discussed in the last chapter, the parameters were anything but stable. In addition, case complexities were different for each year. While absolute magnitudes have shifted around over time, relative case costs have remained remarkably stable over the eight years, as ill u s t r a t e d previously i n Table 5.1. Further-more, i t is extremely d i f f i c u l t to hazard a guess as to which years' figures might be unrealistically high or low, insofar as there may have been inherent trends toward lower lengths of stay, less diagnostic work-up within hospitals etc. i n the later years. The f i n a l phase of this analysis attempts to 'aggregate out' such problems. The figures in Table 7.4 may be denoted by MC_. , where MC. = Z MC. . C. where C. = ZC. , t = 1966,1973. 3 - 3t _ l t 3 ]t C. 3 Thus, each year's contribution to a particular case cost i s determined by i t s proportion of the total type j cases discharged from a l l B.C. hospitals , being considered, during the eight years of analysis. One question which arises from the figures in Table 7.4 concerns the extent to which these relative prices are r e a l i s t i c ; i.e. has this analysis generated believable numbers? Reference to Table 5C.1 indicates an affirmative answer. As one would expect, the cost of treating an additional cancer patient (cases #6 - #18) i s considerably in excess of that for an influenza victim. In particular, whereas the malignancies averaged around $540 per case, an influenza case could be expected to generate marginal expenditures in the neighbourhood of $123.00. Again, the reader i s reminded that cases such as the malignant neoplasms are subject to potential downward bias i n our case cost figures due to readmissions or transfers between hospitals, and biased figures may also result for potentially f a t a l TABLE 7.4: MARGINAL COST BY DIAGNOSTIC (in 1970 dollars) CATEGORY CASE # M.C. CASE # M.C. CASE # M.C. CASE # M.C. 1 463.34 26 465.41 51 318.14 76 291;53 2 558.99 27 330.48 52 179.09 77 210.24 3 361.61 28 273.10 53 296.03 78 169.52 4 . 190.92 29 445.00 54 180.59 79 262.93 5 199.64 30 271.25 55 223.39 80 346.10 6 664.67 31 372.88 56 263.97 81 359.57 7 528.54 32 549.93 57 290.10 82 319.45 8 558.22 33 463.53 58 153.57 83 497.82 9 628.23 34 334.08 59 432.90 84 319.83 10 549.75 35 480.21 60 463.35 85 215.45 11 473.76 36 269.29 61 291.48 86 238.25 12 397.27 37 502.82 62 261.48 87 387.06 13 545.50 38 377.32 63 922.52 88 192.34 14 562.47 39 302.67 64 233.60 89 751.90 15 520.43 40 259.42 65 329.22 90 294.16 16 543.55 41 615.05 66 331.86 91 223.78 17 528.88 42 322.11 67 509.16 92 330.66 18 518.58 43 261.78 68 197.19 93 276.67 19 307.56 44 290.33 69 226.59 94 180.41 20 302.24 45 290.52 70 373.63 95 224.32 21 311.81 46 122.43 71 178.92 96 221.78 22 216.28 47 122.63 72 250.12 97 353.52 23 229.62 48 197.70 73 169.88 98 222.03 24 411.38 49 170.89 74 280.92 25 324.75 50 172.75 75 215.17 diseases i n which some patients suffer 'premature' death. The nephritis and nephrosis, and fracture of femur cases topped the case expense l i s t , while the extremely common acute upper respiratory infections and influenza cases vied for low cost honours. These are anything but surprising results, and lend credence to the methodology. Other relatively expensive case categories are malignant neoplasms of buccal cavity, pharynx and rectum; and diseases of the arteries. The other end of the scale i s comprised of (in addition to the two mentioned above) such diagnoses as gastroenteritis and c o l i t i s (non-ulcerative), complications of pregnancy, and skin and subcutaneous tissue infections. Considering the level of aggregation which produced these figures, the results are encouraging and suggest that further research based upon this, or a similar methodology could be f r u i t f u l . With regard to the absolute values, the 1970 B.C. Report on Hospital Statistics (1973) reported average gross expenditure per patient day, for 2 the entire province at $52.92. The inpatient share w i l l be somewhat lower than that figure but we can ascertain 'ball park' figures from i t . From the inpatient s t a t i s t i c s of Tables 12 and 13, same publication, we calculate an average length of stay of 8.66 days for public hospitals, based on a l l case types. 3 This yields an average gross per-case expenditure of $458.29. A cursory inspection of the figures i n Table 7.4 indicates that these marginal case costs are not drastically out of line with the above rough computation, although we might reasonably expect our marginal figures to be somewhat lower than the averages for equivalent case types. In particular, IPEXP/TOTEX was computed for a l l hospitals for 1970, the 4 average value being 0.858. Thus, the average per-case inpatient expenditure would be in the neighbourhood of $393.21. In conclusion, then, the analysis has yielded marginal case costs apparently not out of line with published average figures of a much more aggregative, non-case-specific, nature. In addition the relative costs appear to coincide with our exceedingly limited c l i n i c a l expertise as to which cases would occupy various rungs i n an ordinal scale. The following three chapters of this project i l l u s t r a t e one application of these figures - assessment of the potential a b i l i t y of alternative delivery systems to reduce hospital expenditures. As we now have what we consider to be f a i r l y reliable case costs, we w i l l be able to investigate the expenditure implications of decreasing case loads, using, for what we believe to be the f i r s t time, costs disaggregated on a case specific basis. Chapter 7 - Footnotes 2 5 2 1. The programs u t i l i z e d for this chapter are not included i n the thesis, but are available from the author.. In particular, various minor technical and data d i f f i c u l t i e s encountered i n u t i l i z i n g s t a t i s t i c s from different reports over time are often not documented in the text. 2. B.C. Department of Health (1973,21), Table 9. 3. Ibid., Table 12, pp. 26-27; and Table 13, pp. 29-31. The reported figures, and calculations from them are as follows: Adults and Children Newborn Total Discharges 1970 369118 36892 406010 ALS of Discharged Patients, 1970 8.84 6.87 8.66 Gross Expenditure Per Patient Day . — — 52.92 Average Gross Expenditure Per Discharged Case — — $458.29 4. Appendix 7A contains the hospital specific fractions. APPENDIX 7A: 197Q Inpatient Share of Hospital Gross Expenditures 2 5 3 C2) (l)/(2) HOSPITAL # IPEXP C $ ) TOTEX C $ ) 001 1247225 1423970 .876 002 456007 484885 .940 003 137412 144890 .948 004 336342 368745 .912 005 191860 201468 .952 006 168256 192727 .873 007 3405137 3762323 .905 008 1287061 1528688 .842 009 472154 532644 .886 010 1013275 1201037 .844 Oil 619872 776516 .798 012 347438 396878 .875 013 2168394 2332596 .930 014 1238947 1494914 .829 015 481839 612353 .787 016 422851 482241 .877 017 1180631 1376273 .858 018 1805924 2154117 .838 019 237869 300488 .792 020 498207 528476 .943 021 290057 385852 .752 022 341281 411388 .830 023 1111197 1275113 .871 024 262926 292919 .898 025 490749 565500 .868 026 306148 351534 .871 027 336561 416912 .807 028 2178975 2374785 .918 029 1524620 1815141 .840 030 420315 469015 .896 APPENDIX 7A (Cont'd) 25k C 1 ) (2) (D/(2) HOSPITAL # IPEXP ($) TOTEX ($) 031 353825 389748 .908 032 310164 363335 .854 033 4449924 5453051 .816 034 106494 110793 .961 035 2990136 3473523 .861 036 638030 712337 .896 037 1296323 1517634 .854 038 427586 494146 .865 039 300418 330538 .909 040 244768 253842 .964 041 166093 223575 .743 042 457789 524669 .873 043 179409 189938 .945 044 651841 834107 .781 045 1614502 1923945 .839 046 126131 138120 .913 047 3100251 3577772 .867 048 1273693 1415063 .900 049 100278 102085 .982 050 7838058 9817831 .798 051 3244369 3438877 .943 052 1895693 2091243 .906 053 6766545 7568598 .894 054 115660 129398 .894 055 486199 537000 .905 056 1897369 2118584 .896 057 1312963 1552895 .845 058 1590817 1842483 .863 059 3660019 4181205 .875 060 1374313 1522941 .902 061 252935 277179 .913 APPENDIX 7A (Cont'd) 2 5 5 CD * (2) (l)/(2) HOSPITAL # IPEXP C$) TOTEX ($) 062 179650 200354 .896 063 1166089 1338074 .871 064 418412 461790 .906 065 476647 528873 .901 066 750115 877394 .855 067 589496 653902 .902 068 716764 811843 .883 069 216089 272923 .792 070 65010 74566 .872 071 328985 406360 .810 072 1234403 1478709 .835 073 150548 178408 .844 074 2761807 3076680 .898 075 1710831 1790229 .956 076 1588348 1639462 .969 077 9824072 12239638 ' .803 078 2652299 2771957 .957 079 157320 157320 1.000 080 1408111 1623727 .867 081 32316168 38257424 .845 082 613128 678505 .904 083 2146257 2401462 .894 084 10325251 12244396 .843 085 7026515 8304077 .846 086 2074840 2462379 .843 087 992604 1165853 .851 TOTAL 156091794 181857148 .858 * IPEXP was calculated as described i n the Chapter 5 discussion on the formation of the CASEX variable. 2 5 6 Chapter 8: The Canadian Clinics The preceding four chapters of the thesis embodied, inter a l i a , the generation of hospital case-specific costs for ninety-eight diagnostic categories. This chapter applies those costs to the u t i l i z a t i o n s t a t i s t i c s from two of the Canadian-based studies reviewed in Chapter 3. It w i l l be recalled that i n that chapter we reviewed a number of matched population u t i l i z a t i o n studies i n which case-specific u t i l i z a t i o n patterns were reported. The potential savings realizable by alternative medical care delivery modes through decreased hospital admissions, i s estimated by combining those figures with the case cost s t a t i s t i c s derived in the previous chapter. In this chapter we confine ourselves to the two Canadian studies which are conducive to this application. The varying degrees of case-specificity in the u t i l i z a t i o n s t a t i s t i c s reported lead to numerous study-specific aggregation problems. The remainder of this chapter i s subdivided into two sections, each dealing with one of these studies. 8.1 Sault Ste. Marie C l i n i c (source of data: Hastings et a l . (1973a)). In order to apply our case costs, we must f i r s t derive the d i f f e r e n t i a l u t i l i z a t i o n figures between subscribers of the GHA and Prudential plans. This calculation i s shown in Table 8.1. It should be noted that while the figures displayed in Table 8.1 were for discharges other than newborns, our case costs are derived using a l l discharges and deaths. However, the induced error i s small and the direction of bias i s predictable. 1 The diagnosis-specific u t i l i z a t i o n s t a t i s t i c s provided in this study are reported only at the level of the thirteen broad ICDA categories. This necessitated an aggregation of our 98 diagnoses into the same thirteen categories. It i s obvious, and unavoidable, that we w i l l lose a certain TABLE 8.1: Comparative Utilization Experience of Dual Choice Population: GHA vs. Prudential -Diagnostic Category (1) Discharge Rate* per 1000 GHA Subcribers (2) Ratio: GHA/ Prudential (3) Estimated Discharge Rate per 1000 Prudential Subscribers (4) Discharge Rate Differential per 1000 Subscribers Neoplasms 5.8 0.88 6.6 0.8 Allergic, endocrine,metabolic 2.9 0.83 3.5 0.6 Mental 4.7 0.76 6.2 1.5 Nervous system 5.9 1.11 5.3 -0.6 Circulatory 7.9 1.18 6.7 -1.2 Respiratory 12.6 0.41 30.7 18.1 Digestive 14.5 0.90 16.1 1.6 Genitourinary 11.1 0.75 14.8 3.7 Deliveries, complications 20.9 0.80 26.1 5.2 Musculoskeletal 3.5 0.64 5.5 2.0 Symptoms, etc. 3.4 2.43 1.4 -2.0 Accident, poisoning, violence 8.6 1.09 7.9 -0.7 Balance of Cases 7.6 1.17 6.5 -1.1 SOURCE: Columns 1 and 2 are from Hastings et a l . (1973a), Table 2, p.94 Column 3 = (1) / (2) Column 4 = (3) - (1) * other than newborns N> 2 5 8 degree of detail through such a massive aggregation. However, the small sample size upon which that particular study was based precludes use of a finer breakdown, even i f one had been reported. In particular, the small number of discharges i n many of the diagnostic categories would have made any calculated u t i l i z a t i o n differentials suspect, at best. Since this study was based on 1967-68 data, i t was decided that the 1967 and 1968 B.C. provincial case mix would be used to establish weights for the aggregation procedure. 2 Thus, using the data contained i n Table 8.2, for the f i r s t category in the Hastings et a l . (1973a) study, neoplasms, we can compute the diagnostic category cost figure as, Z(C./C)-MC. j = 1,... # of case types in the neoplasms category; MCj = case cost for case type j ; C_. = # of neoplasm cases of type j ; C = tot a l number of neoplasm discharges in province. For neoplasms our cost figure i s determined to be $428.68 per case. 3 Since the discharge d i f f e r e n t i a l between subscriber populations i s reported to be 0.8 per 1000 subscribers, we derive a gross hospital expenditure saving of (428.68)• (0.8) = $342.95. A similar procedure was followed for the other twelve broad categories reported in the study. The results