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Standardizing the hospital’s case load for diagnostic mix and resource use : a comparison of the RNI… Hardwick, Jill Margaret 1982

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STANDARDIZING THE HOSPITAL'S CASE LOAD FOR DIAGNOSTIC MIX AND RESOURCE USE: A COMPARISON OF THE RNI AND INFORMATION THEORY INDICES by JILL MARGARET HARDWICK B.A., University of Sydney, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Health Care and Epidemiology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1982 Q J i l l Margaret Hardwick, 1982 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f HEALTH CARE AND EPIDEMIOLOGY T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 2 0 7 5 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V 6 T 1W5 Date A P r i l 2 4 ' 1 9 8 2 DE-6 (2/79} Abstract STANDARDIZING THE HOSPITAL'S CASE LOAD FOR DIAGNOSTIC MIX AND RESOURCE USE: A COMPARISON OF THE RNI AND INFORMATION THEORY INDICES JILL MARGARET HARDWICK The University of B r i t i s h Columbia Hospital cost containment i s a p r i o r i t y f or p r o v i n c i a l governments i n Canada and reimbursing agencies i n the United S t a t e s — a consequence of the dramatic r i s e i n the rate of h o s p i t a l cost increases. Studies have shown that t h i s increase i s mainly due to an increase i n resource use per patient day—more intensive labour; more laboratory t e s t s , drugs; more sophisticated technology. The l e v e l of resource use obviously v a r i e s for d i f f e r e n t cases, depending on the nature of the patient's i l l n e s s . The problems facing reimbursing agencies are that of reducing the rate of growth of h o s p i t a l expenditures and an equitable reimbursement of h o s p i t a l s , taking adequate account of t h e i r diverse case mix. Simple measures of h o s p i t a l output such as the number of cases or the number of patient days assume an homogeneous output. As a consequence, various standardization techniques have been developed to standardize for case mix v a r i a t i o n , i n i t i a l l y , output standardization was attempted using proxies for case mix such as the number of services and f a c i l i t i e s a v a i l -able i n a h o s p i t a l . Later, diagnosis i t s e l f was used and weighted i n a v a r i e t y of d i f f e r e n t ways. The purpose of t h i s study i s to compare two approaches to case mix s t a n d a r d i z a t i o n — i n f o r m a t i o n theory and the Resource Need Index. These approaches r e l y on d i f f e r e n t assumptions. Hence the i n t e n t i o n i s to c r i t i c a l l y examine t h e i r conceptual bases and compare t h e i r r e l a t i v e a b i l i t y to explain i n t e r - h o s p i t a l cost differences i n Alberta. The i i empirical r e s u l t s show that the information theory measure performs better than the Resource Need Index i n explaining h o s p i t a l costs. An i l l u s t r a t i v e example i s given to show how t h i s technique can be b u i l t into the budget s e t t i n g process i n Alberta to e f f e c t a more equitable d i s t r i b u t i o n of resources among h o s p i t a l s . Robert G. Evans, Ph.D. Thesis Supervisor i i i Table of Contents Page Chapter 1 Introduction. 1 1.1. Reasons for Hospital Cost Increases i n Canada.. 1 1.2. Government Concern 5 1.3. P o l i c y I n i t i a t i v e s . 6 1.4. Methods of Cost Containment 8 1.5. Scope of t h i s Thesis 9 1.6. Purpose of t h i s Study 11 Reference Notes 12 Chapter 2 Hospital Cost Studies: A C r i t i c a l Review of the L i t e r a t u r e with Special Attention to Output Standardization 13 2.1. Theoretical Assumptions 14 2.2. The Neoclassical Cost Theory of the Firm 15 2.3. P e c u l i a r i t i e s of the Hospital Industry 19 2.4. "Economies of Scale' Studies 25 2.5. Reimbursement Studies 36 2I5:i: Group Target C e i l i n g 37 2.5.2. I n d u s t r i a l Engineering 38 2.5.3. Departmental Budget Review 39 2.5.4. Prospective Reimbursement 40 2.6. Standardization of Output i n Terms of Case Mix. 42 2.6.1. Specialty Mix 42 2.6.2. Diagnostic Proportions 42 2.6.3. Diagnostic Proportions and A d d i t i o n a l Case Mix Measures 44 2.6.4. Information Theory 45 2.6.5. Other Applications of the Information Theory Measure i n Canada 47 2.6.6. App l i c a t i o n of the Information Theory Measure i n the U.S 51 2.6.7. Diagnosis Related Groups 53 2.6.8. Resource Need Index 59 2.6.9. Common Problems 63 2.7. Summary of Standardization of Output i n Terms of Case Mix 66 2.7.1. Diagnostic Factor Proportions 66 2.7.2. Information Theory 67 2.7.3. Diagnosis Related Groups 68 2.7.4. Resource Need Index. 70 Reference Notes. 72 i v Page Chapter 3 Methodology f o r the Comparison of Two Approaches to Case Mix Standardization: Information Theory and the Resource Need Index. 75 3.1. Form of the Hospital Equation. 76 3.2. Sources of Data. 80 3.2.1. Hospitals... 81 3.2.2. Time Period 81 3.3. Variables. 83 3.3.1. Dependent Variables 83 3.3.2. Independent Variables 85 3.4. Regression Analysis 94 Reference Notes 96 Appendix 98 Chapter 4 Empirical Results 103 4.1. An Evaluation of the RNI Compared to Information Theory Measures of Case Mix 104 4.2. Significance of the Regression C o e f f i c i e n t s . . . . . 112 4.3. Selection of the "Best" Equation 117 4.3.1. DAYEX or CASEX? 118 4.3.2. The equation of "best f i t " 119 4.3.3. Appl i c a t i o n of the estimated cost,., equation to the budgeting process 124 Reference Notes 133 Chapter 5 Summary and Conclusion 134 Reference Notes 142 Bibliography 143 v L i s t of Tables Page 1.1. Health Expenditures i n Canada, 1970-1978 2 1.2. Hospital Expenditures i n Canada, 1970-1978 3 2.1. "Economies of Scale 1 Studies: Summary of Findings 22 2.2. Quebec Approach - L i s t and Source of Output Variables 50 3.1. Hospital and Bed D i s t r i b u t i o n , Alberta, 1979 82 3.2. Eigenvalue of Age-Sex Factor Scores 90 3.3. Values for Most of the Independent Variables and the Two Dependent Variables (CASEX and DAYEX) Used i n the Regression Analysis 98 4.1. DAYEX Equations with A l t e r n a t i v e Case Complexity Variables... 105 4.2. CASEX Equations with A l t e r n a t i v e Case Complexity Variables... 1071 4.3. DAYEX Equations with Size, U t i l i z a t i o n , Wage, Indirect Expense, Case Complexity and S p e c i a l i z a t i o n Variables 109 4.4. CASEX Equations with Size, U t i l i z a t i o n , Wage, Indirect Expense, Case Complexity and S p e c i a l i z a t i o n Variables........ H I 4.5. DAYEX Equations with Information Theory Case Complexity and S p e c i a l i z a t i o n Variables 120 4.6. CASEX Equations with Information Theory Case Complexity and S p e c i a l i z a t i o n Variables 123 4.7. Actual and Predicted Cost per Case i n 112 Alberta Hospitals.. 126 v i L i s t of Figures Page 2.1. The Short Run Cost Structure i n the Neoclassical Theory of the Firm 17 2.2. The Long Run Cost Structure i n the Neoclassical Theory of the Firm 18 2.3. Summary of Lengths df Stay D i s t r i b u t i o n f or DRGs Formed i n p a r t i t i o n i n g process 55 2.4. Steps Involved i n Converting Average Charge Data to a Resource Need Index 61 v i i Acknowl ed gemen t s Special thanks go to my thesis committee: Dr. Robert Evans, thesis supervisor, Dr. Morris Barer, Mr. Francis Brunelle, Dr. Anne Crichton. Their combination of talents and t h e i r support have been e s s e n t i a l i n the development and completion of the t h e s i s . Robert Evans helped me develop the conceptual framework of the study and meticulously c r i t i q u e d every aspect of the work as i t proceeded. His perspective and understanding of the subject made working with him a valuable learning experience. Morris Barer provided e s s e n t i a l technical expertise and very useful c r i t i c a l comments on an e a r l i e r d r a f t . He provided access to computer programs, allowing the empirical sections of the thesis to proceed much more r a p i d l y than would have been otherwise possible. Fran Brunelle, as Director of I n s t i t u t i o n a l Operations, Alberta Hospitals and Medical Care, and preceptor f o r my summer clerkship i n 1979, i n s t i g a t e d the study. His support and enthusiasm for the project ensured funds for the purchase of necessary data and my summer employment. His i n t e r e s t enabled access to a l l relevant data within the Department of Hospitals and Medical Care, and h i s c r i t i c a l comments along the way were most u s e f u l . I am deeply indebted to Anne Crichton for her u n f a i l i n g support throughout my graduate studies including my i n i t i a l acceptance to the program. Her i n t e l l e c t u a l i n s i g h t and teaching s k i l l s have aroused my i n t e r e s t and increased my knowledge i n numerous areas of health p o l i c y and planning. v i i i Other people i n Alberta Hospitals and Medical Care deserve mention for t h e i r support and/or i n t e r e s t and assistance: Ted Wright, Ken Moore, Je f f Babb, Larry Charach, Mo Cheung, Don Graydon. Special thanks go to Sheri Game f o r providing computer expertise and f u l f i l l i n g a l l my data requests. L i s a Holtorf, Celine Hanlon and Ann McCall were responsible for a congenial work environment, as well as providing c l e r i c a l assistance and typing. To my classmates i n the Health Services Planning Program I am thankful for a stimulating learning environment and many deep frien d s h i p s . My family, despite t h e i r physical distance, offered encouragement through regular correspondence. Evan Jones not only provided continuing support but also offered astute comments and constructive c r i t i c i s m . G a i l Kuhry and L i z Stephenson did a f i r s t c lass job typing the f i n a l d r a f t . i x 1 Chapter 1. Introduction The rapid growth i n health expenditures i n Canada and i n t e r -n a t i o n a l l y has been a source of major concern i n the l a s t decade. This has prompted numerous studies on the magnitude and composition of the health b i l l and the reasons f o r the dramatic cost increases. Table 1.1 shows t o t a l health expenditures i n Canada during the l a s t decade. They have increased from 6,086.6 m i l l i o n d o l l a r s i n 1970 to 16,181.5 m i l l i o n d o l l a r s i n 1978 with an average annual rate o f increase of 13.1 percent. This r i s e i s s i g n i f i c a n t l y greater than the rate of increase of the Consumer Price Index (CPI), which has an average rate of growth over the same period of 7.7 percent. A s i g n i f i c a n t proportion of t o t a l health expenditures are h o s p i t a l expenditures. Within t h i s category, general and a l l i e d s p e c i a l h o s p i t a l s take the l a r g e s t share. The l a t t e r are the acute short term h o s p i t a l s and t h e i r expenditure i s approximately 40 percent of the t o t a l health budget. Table 1.2 shows that t h e i r expenditures rose from $2251.7 m i l l i o n i n 1970 to $6642.1 m i l l i o n i n 1978. The average annual rate of increase was 14.7 percent, even higher than the rate of increase for t o t a l health expenditures (13.1%) over the same period. 1.1 Reasons f o r Hospital Cost Increases i n Canada What are the reasons f o r t h i s rapid increase i n h o s p i t a l costs? The answer to t h i s question i s complex and i s re l a t e d to population growth, u t i l i z a t i o n patterns, p r i c e changes and changes i n the composit-ion of the h o s p i t a l workforce."'' Table 1.1. Health Expenditures i n Canada, 1970-1978 1970 1971 1972 1973 1974 1975 1976 1977 1978 Total health expenditures ($m) 6,086.7 6,935.8 7,542.9 8,429.6 9,906.0 11,888.0 13,551.2 14,702.7 16,181.5 Rate of increase 14.0 8.8 11.8 17.5 20.0 14.0 8.5 10.1 Rate of increase of CPI 2.9 4.8 7.5 10.9 10.8 7.5 8.0 9.0 Dolla r s per capita 285.44 •321.22 345.66 381.91 442.32 523.08 588.54 631.55 688.77 Percent of GNP 7.10 7.34 7.17 6.82 6.71 7.19 7.09 7.04 7.04 Source: National Health Expenditures i n Canada, 1970-1978, Health Information D i v i s i o n Information Systems Directorate, P o l i c y , Planning and Information Branch, Department of National Health and Welfare, August 1980. Table 1.2 Hospital Expenditures in.Canada, 1970-1978 1970 1971 1972 1973 1974 1975 1976 1977 1978 Total h o s p i t a l expenditures 2758.6 3078.5 3365.2 3783.2 4588.4 5679.0 6434.6 6768.5 7337.7 General and a l l i e d s p e c i a l h o s p i t a l s l Total expenditure 2251.7 2529.8 2785.7 3150.2 3877.7 4873.7 5673.0 6046.1 6642.1 Percent of t o t a l health exp 37.0 36.5 36.9 37.4 39.1 41.0 41.9 41.1 4i.o Rate of increase of t o t a l general & a l l i e d s p e c i a l h o s p i t a l expenditure 12.4 10.1 13.1 23.1 25.7 16.4 6.6 9.9 Rate of increase of CPI 2.9 4.8 7.5 10.9 10.8 7.5 8.0 9.0 Dollars per capita 105.60 117.16 127.66 142.72 173.15 214.45 246.38 259.71 282.72 Percent of GNP 2.63 2.68 2.65 2.55 2.63 2.95 2.97 2.90 2.89 2 Average cost per patient day 52.23 58.47 64.64 71.35 84.94 105.95 120.56 126.41 130.38 Rate of increase 11.9 10.6 10.4 19.0 24.7 13.8 4.9 3.1 Patient days per 100,000 pop. (M) 12.3 12.3 12.3 12.0 11.9 11.7 11.5 11.7 (F) 10.8 11.0 11.0 10.8 10.8 10.7 10.5 10.7 """Statistics Canada c l a s s i f i e s hospitals into three d i f f e r e n t categories: General^Allied S p e c i a l , Mental. General h o s p i t a l s provide for the diagnosis, treatment and care of a l l types of diseases to people of a l l age and sex groups. A l l i e d Special hospitals include p e d i a t r i c , maternity, r e h a b i l i t a t i o n , extended care and other h o s p i t a l s . 2 Mean cost per patient day (excluding educational programs and s p e c i a l research) f or t o t a l p u b l i c (excluding proprietary and federal) h o s p i t a l s . Sources: (1) Canada. Department of National Health and Welfare. National Health Expenditure i n Canada,1970-78. (2) Canada. S t a t i s t i c s Canada. Hospital i n d i c a t o r s , 1970-77. Catalogue 83-001. (3) Canada. S t a t i s t i c s Canada. Hospital Morbidity, 1970-77. Catalogue 82-206. CO 4 Evans (1975) and Soderstrom (1978) examine the recent h o s p i t a l cost increases i n Canada, as c r i b i n g these increases to two main sources. F i r s t , there has been increased u t i l i z a t i o n of h o s p i t a l services, measured in terms of population growth, admission rates and patient days per admission. Second, there has been an increased cost per patient d a y — the actual cost of the services received by the patient has increased for each day of h i s (her) h o s p i t a l stay. Their data reveal that u t i l i z a t i o n i s not the major source of t h i s high rate of increase i n h o s p i t a l costs. Evans (1975) reports an increase annually of only 2.1 percent i n population and 1.4 percent increase i n patient day u t i l i z a t i o n between 1953 and 1971. The major source of the h o s p i t a l cost increases i s the r i s e i n cost per patient day. This f i g u r e increased by 9.3 percent annually for the same time period. Table 1.2 shows cost per patient day for the period 1970-1978. Costs per patient day have increased for a v a r i e t y of reasons. Most s i g n i f i c a n t of these reasons i s the increase i n wages and s a l a r i e s . This i s p a r t l y due to general i n f l a t i o n i n the economy; but i t i s also due to a "catching up" of h o s p i t a l employees who had experienced r e l a t i v e l y lower wages than other sectors o f the economy—a hangover from the period when hospita l s were cha r i t a b l e i n s t i t u t i o n s . In addition, the composition of the h o s p i t a l workforce has changed. I t comprises more sp e c i a l i z e d and,therefore, more q u a l i f i e d personnel who a t t r a c t higher s a l a r i e s . Increased costs per patient day are also a function of increased resource use per patient day. Evans (1975) showed an increase i n r e a l resource use i n terms of medical supplies and drugs as well as labour input for the period 1953-1971. There i s no reason to suspect that t h i s 5 pattern has changed. If anything,real resource use may have increased further with the advent of increasingly s p e c i a l i z e d medical technology. The framework of conventional economic theory implies that cost increases may be due to changing forces of demand, changing forces of supply, or both. Those who claim that h o s p i t a l cost increases are due to demand forces argue t h i s p o s i t i o n i n terms of increased u t i l i z a t i o n . They argue that an increase i n admissions per capita forces up costs. The evidence c i t e d e a r l i e r , however, shows that there have been no s u b s t a n t i a l increases i n admissions per capita i n Canada. Demand side economists take t h i s argument further. They claim that even small increases i n demand push up o v e r a l l costs through p r i c e increases due to an i n e l a s t i c supply. If supply were i n e l a s t i c though, there should be a corresponding r i s e i n occupancy rates. This has not occurred. F i n a l l y , they believe that there has been an increas-ed demand f o r i n t e n s i t y , i . e . more services per case or per day. This assumes, however, that patients a c t u a l l y demand s p e c i f i c services when they are h o s p i t a l i z e d . This i s not the case. I t i s the doctors, or the providers of the s e r v i c e s , who determine the nature and amount of s e r v i c e s . Thus i t i s the factors determining the character of supply that are responsible for the cost increases - i t i s the doctors who determine resource use and the h o s p i t a l s , with t h e i r i n c r e a s i n g l y expensive labour force and technology, who influence the l e v e l of h o s p i t a l expenditure. 1.2. Government Concern Government concern for the rate of increase i n h o s p i t a l costs i n Canada f i r s t developed i n the l a t e s i x t i e s . Before t h i s time, the major p o l i c y concerns of the government were those of ensuring f i n a n c i a l access to health care and e s t a b l i s h i n g uniformity i n the 'quality' of c a r e — a l o g i c a l sequel to the introduction of n a t i o n a l h o s p i t a l and medical insurance. These p r i o r i t i e s i n e v i t a b l y l e d to increased, rather than decreased expenditures. 6 The period also coincided with s u b s t a n t i a l h o s p i t a l expansion through the National Health Grant Program (1948-1972). This program approved and pro-vided f i n a n c i a l assistance for more than 130,000 beds. Federal grants were also given for nurses' and i n t erns' residences, l a b o r a t o r i e s , diagnostic and treatment areas for inpatients and outpatients, community health centres and teaching f a c i l i t i e s (Le C l a i r , 1975, 14). This c a p i t a l expansion gener-ated necessary recurrent expenditures which f u e l l e d the r a p i d l y r i s i n g costs. By the l a t e s i x t i e s i t was becoming apparent that health care costs would continue to consume: a larger proportion of GNP unless there was some e f f o r t to contain costs. Task Forces on the Cost of Health Services i n Canada (1970) were established to examine factors r e l a t e d to health c o s t s — u t i l i z a t i o n , operational e f f i c i e n c y , s a l a r i e s and wages, beds and f a c i l i t i e s , methods of d e l i v e r i n g medical care, the p r i c e of medical care, the cost of public health services. The Task Forces produced a long s e r i e s of recomm-2 endations i n a l l these areas . The Community Health Centre Project (Hastings Report, 1972) was also established i n 1971 because of continuing concern over the increase i n health services costs. This report recommended the develop-ment "of a s i g n i f i c a n t number of community health centres ... as non-profit corporate bodies i n a f u l l y integrated health services system". This recomm-endation had deliberate cost implications because community health centres were seen by some as a cheaper a l t e r n a t i v e to some forms of h o s p i t a l care. 1.3. P o l i c y I n i t i a t i v e s The rapid increase i n costs p r e c i p i t a t e d a v a r i e t y of p o l i c y i n i t i a t i v e s . They included a p o l i c y to share f a c i l i t i e s which would increase e f f i c i e n c y and minimize d u p l i c a t i o n of s e r v i c e s . The r e s u l t was c e n t r a l laundries, bulk purchasing and planned d i s t r i b u t i o n of s p e c i a l i z e d c l i n i c a l and laboratory se r v i c e s . Regionalisation of planning and management of services was also 7 introduced to reduce competition and prevent d u p l i c a t i o n . The effectiveness of t h i s p o l i c y , however, was reduced by the reluctance of the c e n t r a l author-i t i e s to r e l i n q u i s h c o n t r o l . The D i s t r i c t Health Councils (DHCs) i n Ontario are an example of a f a i l e d attempt at d e c e n t r a l i z a t i o n . DHCs were proposed by Mustard (1974) to plan and manage health services at a d i s t r i c t l e v e l i n an attempt to increase community p a r t i c i p a t i o n and bring about cost r e s t r a i n t . However, the reluctance of the p r o v i n c i a l government to authorize budgetary authority to the DHCs reduced the DHCs power, rendering them incapable of a l t e r i n g the system and achieving t h e i r objectives. Global budgeting was another p o l i c y introduced to overcome i n f l e x i b i l i t y and i n e f f i c i e n c y i n the h o s p i t a l system. P r i o r to t h i s , budgets were a l l o c -ated on a " l i n e - b y - l i n e " b a s i s . Line-by-line budgeting requires d e t a i l e d estimation of a l l s a l a r i e s and supplies f o r each h o s p i t a l a c t i v i t y . Expen-diture must then keep within the a l l o c a t i o n for each a c t i v i t y and cannot be transferred between a c t i v i t i e s . Global budgeting was introduced to allow administrators more d i s c r e t i o n over t h e i r resources and to make them accountable for t h e i r decisions. One proven way of r e s t r a i n i n g costs was to reduce the supply of beds. This has been used e f f e c t i v e l y i n most provinces but i t has obvious l i m i t a t -ions. For p o l i t i c a l reasons, i t i s easier to slow down the rate of expansion than i t i s to a c t u a l l y close beds. Thus i t i s easier to reduce the bed supply i n provinces l i k e B r i t i s h Columbia, where the population i s growing r a p i d l y , than i t i s i n provinces with a stable or decreasing population. Moreover, bed reduction i s a crude approach.. I t i s based on the notion of a predetermined number of beds per thousand population which are supposed to r e f l e c t the "need" of the population. As there i s no defined c r i t e r i a to e s t a b l i s h "need", these numbers are usually a r b i t r a r y . Nevertheless, t h i s method has been e f f e c t i v e to a c e r t a i n extent i n containing costs. 8 Despite recognition of the problem of increasing h o s p i t a l costs, there was l i t t l e incentive f o r the p r o v i n c i a l governments to reduce costs. The f e d e r a l - p r o v i n c i a l cost sharing agreement discouraged t h i s because expendit-ures were shared on an equal b a s i s . I f the p r o v i n c i a l governments t r i e d to contain costs by reducing beds or providing cheaper a l t e r n a t i v e s to h o s p i t a l inpatient care, they would end up l o s i n g funds from the fed e r a l government under t h i s reimbursement system. Only as recently as 1977 was the arrange-ment changed. At t h i s time, the f e d e r a l government no longer guaranteed the p r o v i s i o n of f i f t y percent of h o s p i t a l expenditures. I t decided on a base l e v e l f o r each province with an annual increase equal to the change i n the CPI. As costs are r i s i n g f a s t e r than changes i n the CPI, the p r o v i n c i a l governments have to take greater f i n a n c i a l r e s p o n s i b i l i t y f o r h o s p i t a l expenditures. The onus i s i n c r e a s i n g l y on them to introduce r e s t r a i n t i n the system. 1.4. Methods of Cost Containment A cost containment strategy must proceed on a number of l e v e l s - hospitr-:. a l , regional, p r o v i n c i a l . Some approaches to improved e f f i c i e n c y at the h o s p i t a l and regional l e v e l have been discussed. These include p o l i c i e s of r e g i o n a l i s a t i o n of services and r e g i o n a l i s a t i o n of the planning and admin-i s t r a t i o n of s e r v i c e s ; global budgeting. Other approaches include u t i l i z a t -ion review and peer review—programs aimed to force doctors to be accountable to each other and to the system generally; departmental budgeting which attempts to create cost awareness at a department l e v e l and to delegate some of the f i s c a l r e s p o n s i b i l i t y from the chief administrator to a number of department heads; i n d u s t r i a l engineering experiments which are e s s e n t i a l l y time and motion studies aimed at improving operational e f f i c i e n c y . Cost containment at the p r o v i n c i a l l e v e l can be achieved by ' improving the current methods of reimbursement to h o s p i t a l s , reducing the 9 t o t a l bed supply, s u b s t i t u t i n g some forms of h o s p i t a l care for cheaper a l t e r -natives, and/or changing the method of payment of physicians from f e e - f o r -service to a s a l a r i e d or sessional payment. Some of these p o l i c i e s have been t r i e d , others are considered too d i f f i c u l t p o l i t i c a l l y . 1.5. Scope of t h i s Thesis The focus of t h i s thesis i s not an evaluation of these various approach-es to cost containment. I t i s not that these programs are unimportant. Rather, some l i m i t s have to be imposed on the scope of t h i s t h e s i s . The study ,A therefore, focusses on one of these strategies to contain costs — a t the p r o v i n c i a l , l e v e l . It examines ways of improving the current r e -imbursement system to allow informed decisions to be made about where cost savings can be made. More s p e c i f i c a l l y , i t examines ways of standardizing for the heterogeneous nature of the h o s p i t a l product and suggests a method of reimbursement that takes case mix v a r i a t i o n across h o s p i t a l s into consideration. Most commonly, output i s measured i n terms of t o t a l number of cases or patient days but t h i s measure assumes homogeneity across h o s p i t a l s both i n terms of the combination of h o s p i t a l a c t i v i t i e s and the types of patients treated. A l l o c a t i o n of budgets on t h i s basis i s inequitable because h o s p i t a l costs vary according to the mix of a c t i v i t i e s (inpatient, outpatient, teaching, etc.) and according to the types of patients and patient days. Berki (1972, 34) i l l u s t r a t e s the heterogeneity of patients and patient days by describing three d i s t i n c t and d i f f e r e n t types of services received by patients at d i f f e r e n t points i n h i s (her) stay: ( i ) admission-specific (chest x-ray, blood t e s t s , administration); ( i i ) s t a y - s p e c i f i c (routine nursing care, hotel-type s e r v i c e s ) ; ( i i i ) d i a g n o s i s - s p e c i f i c (laboratory, s u r g i c a l operations). Thus h o s p i t a l output must be standardized to account 10 for the a c t i v i t y mix and case mix i f the comparison of h o s p i t a l s f o r budget-ary purposes i s to be meaningful and i f funds are to be equitably d i s t r i b u t e d . Present methods of budgeting i n Canada do not take case mix v a r i a t i o n 3 into account. Budgets are developed on a l i n e - b y - l i n e basis for each of the major h o s p i t a l a c t i v i t i e s . Estimates of costs for personnel, equipment and supplies are calculated f o r each department—medical, nursing, radiology, pathology, etc. These estimates are then submitted to the p r o v i n c i a l govern-ment f o r approval. Some negotiation ensures, but t h i s i s not usually based on w e l l defined c r i t e r i a . The main c r i t e r i o n f o r s e t t i n g budgets i s l a s t year's costs with a factor added for i n f l a t i o n and new s e r v i c e s . There i s no attempt to account f o r the case mix of the h o s p i t a l except what i s i m p l i c i t i n l a s t year's costs. Hospital expenditure i s not systematically linked to output, standardized for case mix complexity. The focus i s on h o s p i t a l inputs, not outputs. Thus, there i s no way of comparing the performance of one h o s p i t a l with another and budget a l l o c a t i o n i s an a r b i t r a r y , ad hoc process based on incrementalism and rules of thumb (Evans, 1975, 152-3). There i s growing recognition of t h i s problem and t h i s study began i n response to a request by the government of Alberta which was seeking guidance on ways of improving the budget review process. The government had exper-ienced continuing d i f f i c u l t y i n i t s bargaining with h o s p i t a l s over prospect-ive budgets, possessing no data on the r e l a t i v e performance of h o s p i t a l s . The government needed a measure of h o s p i t a l output that r e f l e c t e d the cost of t r e a t i n g d i f f e r e n t types of patients. A systematic approach to reimburse-ment that takes account of case mix d i f f e r e n c e s , not only allows f o r better negotiations with h o s p i t a l s , but also has implications f o r reducing the rate of cost increases. 11 1.6. Purpose of t h i s Study The purpose of t h i s study i s to compare two a l t e r n a t i v e methods of standardizing h o s p i t a l output f o r use i n the budget s e t t i n g process. One method i s the information theory approach f i r s t used by Evans and Walker (1972) i n Ontario. The other approach i s the Resource Need Index, developed by the Commission on Professional and Hospital A c t i v i t i e s . Both methods d i f f e r e n t i a t e patients or patient days on the basis of discharge diagnosis. However, they d i f f e r i n the way they c l a s s i f y and assign weights to t h i s diagnosis information. Further d e t a i l s on both of these approaches w i l l be provided i n the following chapter. This study examines"the conceptual merit of the two methods and the extent to which they explain differences i n cost per case or cost per patient day across h o s p i t a l s . From t h i s process we can hopefully i n f e r which method, i f e i t h e r , can be an e f f e c t i v e instrument for budgetary purposes. 12 Reference Notes, Chapter 1 1. This chapter discusses reasons f o r h o s p i t a l cost increases i n Canada. References to a discussion of U.S. h o s p i t a l cost increases include F e l d s t e i n (1971), Salkever (1972), Baron (1974), J e f f e r s and Siebert (1974), Chassin (1978), Hughes, Baron, Dittman et a l . (1978), Zubkoff, Raskin, Hanft (1978). 2. Another study undertaken at t h i s time to look s p e c i f i c a l l y at h o s p i t a l costs i s Fraser (1971). 3. Budgets are developed on a l i n e - b y - l i n e basis for each of the major h o s p i t a l a c t i v i t i e s . However, once the t o t a l budget i s decided, i t i s given to the administrator as a " g l o b a l " budget f o r him (her) to use at h i s (her) d i s c r e t i o n . (S)He i s not t i e d to the l i n e - b y - l i n e estimate i n h i s (her) a l l o c a t i o n of the funds. 13 Chapter 2. Hospital Cost Studies: A C r i t i c a l Review of the L i t e r a t u r e  with Special Attention to Output Standardization This chapter i s a review of studies which examine the r e l a t i o n s h i p between h o s p i t a l cost and output. It i s not confined to Canada but includes the United States and B r i t a i n because s i m i l a r i t i e s between health care systems ( i f not i n terms of insurance, d e f i n i t e l y i n terms of organization and d e l i v e r y of services and medical technology) make compari-sons and generalizations possible. These studies are grouped according to the p o l i c y questions they were attempting to answer at the time. Two major groups have been i d e n t i f i e d : the 'economies of scale' studies and the 'reimbursement' studies. The 'economies of scale' studies were a response to the question, "What i s the optimal s i z e f or a h o s p i t a l ? " They were concerned with estimating the long run h o s p i t a l cost curve as a means to determining the h o s p i t a l s i z e at which unit costs were minimized. This i n t e r e s t was h i s t o r i c a l l y r e l a t e d to the massive h o s p i t a l construction programs that developed from the passage of the H i l l Burton Act (1946) i n the United States and the National Health Grant Program (1948) i n Canada. (Le C l a i r , 1975, 13-14) The 'reimbursement' studies, on the other hand, were a response to the r a p i d l y increasing cost of operating h o s p i t a l s , i n p a r t i c u l a r to the question, f i r s t posed at the end of the s i x t i e s and early seventies, "How do we contain/control h o s p i t a l costs?" Researchers undertaking these studies had s h i f t e d t h e i r focus to the short run average cost curve. They were attempting to estimate the cost-output r e l a t i o n s h i p i n order to improve e f f i c i e n c y i n the h o s p i t a l system through 14 the reimbursement process. The major issue confronted by the researchers conducting these studies was the problem of measuring output accurately. They devised a v a r i e t y of standardization methods which w i l l be discussed below. Before analysing these studies i n d e t a i l , the broad t h e o r e t i c a l assumpt-ions underlying the twomajor groups are examined, as t h i s o f f e r s perspective on the conceptual background from which the studies were derived, the r e l a t -ive usefulness of the studies, and t h e i r success i n answering the p o l i c y questions they were addressing. 2.1. T h e o r e t i c a l Assumptions The authors of the 'economies 1 of; scale' studies hypothesize that aver-age h o s p i t a l costs i n i t i a l l y decline as s i z e increases as a consequence of the s p e c i a l i z a t i o n of some factors of production and because of the i n d i v i s -i b l e nature of others ("lumpy" inputs). In other words they assume that with an increase i n the s i z e of the h o s p i t a l , there i s greater s p e c i a l i z a t i o n of tasks performed, with a r e s u l t i n g increase i n p r o d u c t i v i t y . Moreover, t with an increase in. h o s p i t a l s i z e , there are more patients and a presumed more e f f i c i e n t use of equipment and f a c i l i t i e s . They hypothesize further that beyond a c e r t a i n s i z e , costs (diseconomies) associated with the adminis-t r a t i o n of a large h o s p i t a l , outweigh the economies due to large scale operation. The authors undertaking the 'reimbursement' studies are s p l i t into two groups. One group assumes that i t can estimate the technical cost curve for a group of h o s p i t a l s , because i t believes c e r t a i n technical r e l a t i o n s h i p s hold. There e x i s t s the presumption that i t i s possible to introduce incen-t i v e s into the system, improve e f f i c i e n c y and contain costs. However, t h i s i s p a r a d o x i c a l — u n d e r l y i n g the assumption that a technical cost curve can be r e a d i l y estimated i s an assumption that i n b u i l t pressures towards e f f i c i e n c y already e x i s t . Perhaps h o s p i t a l s e x h i b i t i n g p o s i t i v e residuals from the 15 estimated cost function are assumed to display the i n e f f i c i e n c y which r e q u i r -es c o r r e c t i o n . The other group does not make an assumption, implying i n e v i t -able cost minimization. For t h i s l a t t e r group, i t may be possible i n p r i n -c i p l e to define a technical cost curve, but such a cost-output r e l a t i o n cannot be automatically:'inf erred from the observable operation of ' r e a l l i f e ' h o s p i t a l s . They are concerned with describing the behaviour of a group of h o s p i t a l s and i d e n t i f y i n g the r e l a t i v e l y e f f i c i e n t or r e l a t i v e l y i n e f f i c i e n t h o s p i t a l s . They hypothesize that they can improve r e l a t i v e e f f i c i e n c y through the reimbursement process and therefore, control h o s p i t a l cost i n -creases. However, they do not claim that absolute e f f i c i e n c y i s achievable because the motivation towards absolute e f f i c i e n c y does not e x i s t . The hypotheses postulated i n the 'economies of scale' studies and some of the 'reimbursement' studies are predicated on the basis of a conceptual framework drawn o r i g i n a l l y from the n e o c l a s s i c a l cost theory of the firm. This theory w i l l be b r i e f l y described here. Then i t w i l l be compared with the actual c h a r a c t e r i s t i c s of the h o s p i t a l industry to assess whether these assumptions represent useful abstractions f o r t h i s p a r t i c u l a r industry. 2 . 2 . The Neoclassical Cost Theory of the Firm The d e r i v a t i o n of the cost curve, according to t r a d i t i o n a l economic theory, rests on a major assumption—the r a t i o n a l pursuit of p r o f i t maximization. As a minimum p r e r e q u i s i t e , i t must be assumed that the t e c h n i c a l l y optimum output from any combination of productive factors i s achievable i n p r a c t i c e . D i f f e r e n t amounts of each of the three major inputs, or factors of production (land, labour, c a p i t a l ) w i l l produce a p a r t i c u l a r l e v e l of output.. However, the actual combination of inputs chosen by the f i r m w i l l depend on the r e l a t i v e p r i c e s of these factors of 16 production as well as the t e c h n i c a l e f f i c i e n c y of the firm to convert these inputs into a given l e v e l of output. T r a d i t i o n a l economic theory predicts that the f i r m w i l l consider, for any l e v e l of output, the minimum-cost combination of factors of production. The chosen l e v e l of output of the firm w i l l be that f o r which p r o f i t s are maximized, and requires the j u x t a p o s i t i o n of a demand or revenue curve with the cost curve. To accommodate r e a l i s t i c a l l y the time i t takes for a f i r m to a l t e r the combination of inputs so as to achieve the economically most e f f i c i e n t l e v e l of output, economists have adopted a time-period a n a l y s i s . In p a r t i c u l a r , the 'short run' i s assumed to be a time period during which the quantity of some inputs cannot be varied. Factors which cannot be varied i n the short run are c a l l e d fixed f a c t o r s ; those that can be varied are c a l l e d v a r i a b l e factors ( e s p e c i a l l y labour and m a t e r i a l s ) . The 'long run' loosely r e f e r s to the time period during which a l l factors of production may be varied ( i n p a r t i c u l a r , plant and equipment). The shape of the firm's cost curve i s dependent upon te c h n i c a l factors regarding the complementarity of v a r i a b l e amounts of factors of production. This t e c h n i c a l aspect i s embodied in the law of 'variable proportions' or 'diminishing returns'. There e x i s t s a p a r t i c u l a r l e v e l of v a r i a b l e factors (and a r e s u l t i n g l e v e l of output) which i s most compatible with the given l e v e l of 'fixed' f a c t o r s . This i s represented by the point at which the average product of the v a r i a b l e factors i s at a maximum. Any greater a p p l i c a t i o n of v a r i a b l e factors w i l l r e s u l t i n diminishing returns, lowering the average product of a l l v a r i a b l e factors employed. 17 The analysis i s t y p i c a l l y c a r r i e d out at the l e v e l of a s i n g l e -product firm, the nature of the product being assumed to be unchanged (or homogenous) for the period under consideration. Having defined these assumptions and conditions, we are now i n a p o s i t i o n to describe the shape of short run cost curves for the firm, which may be constructed from product curves. Output Output ( i ) T o t a l cost curve ( i i ) Marginal and average cost curve Figure 2.1. The Short Run Cost Structure i n the Neo c l a s s i c a l Theory of the Firm. It can be seen i n Figure 2.1 that the average v a r i a b l e cost curve reaches a minimum and then r i s e s . With fixed factor p r i c e s , when average product per worker i s maximized (assuming an appropriate u t i l i z a t i o n of mat e r i a l s ) , average v a r i a b l e cost i s at a minimum. When output per 18 worker Is r i s i n g with output, the v a r i a b l e cost per un i t of output i s f a l l i n g ; when output per worker i s f a l l i n g , the v a r i a b l e cost per unit of output i s r i s i n g . The law of diminishing returns implies eventually increasing average v a r i a b l e cost. The same phenomena can be represented by a r i s i n g marginal cost curve, showing the r i s i n g incremental cost of producing an a d d i t i o n a l l e v e l of output. D i f f e r e n t t e c h n i c a l considerations are relevant i n the long run. The long run average cost curve i s the l e a s t cost method of producing each possible l e v e l of output when a l l the factors are free to be varied. This curve i s determined by the a l t e r n a t i v e technologies presently con-ceivable to the industry and by the pr i c e s of the factors of production. Thus the long run average cost curve, i n graphic terms, divides the cost l e v e l s that are attainable with known technology and given factor p r i c e s , from those that are unattainable. (See Figure 2.2.) Figure 2.2. The Long Run Cost Structure i n the Neoc l a s s i c a l Theory of the Firm. 19 The actual behavior or performance of the firm also depends on the market structure or the c h a r a c t e r i s t i c s of market organization i n which the firm operates. There are many aspects of the market structure which a f f e c t the behaviour of the f i r m — t h e ease of entering the industry, the number of firms i n the industry, and the extent to which a p a r t i c u l a r firm can influence the demand for the product, e.g. through ad v e r t i s i n g . Economists have emphasised a few t h e o r e t i c a l market structures that are meant to represent the extreme cases of the types of markets that are said to e x i s t i n a market society, v i z . , perfect competition and monopoly. These t h e o r e t i c a l models d i f f e r predominantly with respect to the number of competitors i n the industry. However, i t i s necessary to emphasise that there are a number of assumptions about the behaviour of the firm that apply to a l l models. These include the assumptions of cost theory described h e r e — t e c h n i c a l e f f i c i e n c y (short run), diminishing returns and product homogeneity—as well as other assumptions rel a t e d to the demand and supply curves of the industry. One of the major assump-tions of demand and supply analysis i s the independence of the forces underlying these two curves, i . e . the l e v e l of demand i s exogenous and i s not determined by the l e v e l of supply. 2.3. P e c u l i a r i t i e s ' o f the Hospital Industry"^ The framework of conventional microeconomic theory needs to be compared with the actual c h a r a c t e r i s t i c s of the h o s p i t a l industry to determine whether the assumptions underlying t h i s theory are applicable to the h o s p i t a l industry. A cursory glance suggests that t h i s i s not the case. Most hospital s are n o t - f o r - p r o f i t , so the h o s p i t a l does not have p r o f i t maximization as i t s major goal. The aim of the h o s p i t a l i s probably 20 best represented as an i n t e n t i o n to break even, on average. Occasionally i t may incur a s h o r t f a l l or a surplus but neither of these options can p e r s i s t because a constant s h o r t f a l l would force the h o s p i t a l to close through bankruptcy and a surplus would eventually r e s u l t i n a reduction of funds from the reimbursing agency. As a c o r o l l a r y to the absence of the p r o f i t motive, we must question whether the h o s p i t a l makes a systematic attempt to minimize costs. Although i t may be s o c i a l l y desirable for h o s p i t a l s to minimize costs, i t i s d i f f i c u l t to ascertain whether they a c t u a l l y do. Hospital output i s not homogenous. It varies according to i t s range of a c t i v i t i e s — inpatient care, outpatient care, teaching, research, etc. and i t varies within each of these a c t i v i t y groups (e.g. d i f f e r e n t diagnoses among in p a t i e n t s ) . Thus the output of a h o s p i t a l must be standardized to take account of these product differences i f we are to begin to compare the e f f i c i e n c y of h o s p i t a l s . Moreover we suspect a. p r i o r i that the actual combination of services or inputs for a p a r t i c u l a r patient i s u n l i k e l y to be the l e a s t cost combination. This combination of services i s not determined by the f i n a n c i a l managers of the h o s p i t a l , but rather by the physician who uses the h o s p i t a l . (S)he i s not usually paid by the h o s p i t a l , h i s (her) l e v e l of income i s not dependent on the cost of t r e a t i n g h i s (her) patient so (s)he has no i n t e r e s t i n ensuring that the patient i s treated for a minimum cost. Thus the combination of procedures, t e s t s , drugs, etc., which (s)he orders for the patient, i s not n e c e s s a r i l y the l e a s t - c o s t combination. Furthermore, the l e a s t - c o s t combination i s r a r e l y known because the technology i t s e l f of the industry i s not f i x e d , but l e f t to 21 the i n d i v i d u a l d i s c r e t i o n of the medical p r a c t i t i o n e r . So there i s no a p r i o r i l e v e l of t e chnical e f f i c i e n c y f or a given diagnosis. This r e s u l t s i n the rather absurd s i t u a t i o n where h o s p i t a l administrators are expected to promote e f f i c i e n c y , but have l i t t l e c o n t r o l over the produc-t i o n (treatment) process of t h e i r 'output' (patients), which i s l e f t to the doctors. This peculiar organizational phenomenon has been referred to as the h o s p i t a l ' s two l i n e s of authority (Smith, 1955). The patient does not usually question the treatment recommended by the physician both because (s)he does not have complete information about the nature of h i s (her) i l l n e s s and because (s)he i s not usually responsible for payment of services received. In Canada and B r i t a i n , the population i s covered by na t i o n a l health insurance so that h o s p i t a l costs are borne almost s o l e l y by the government; i n the United States 2 about 90 percent of the population have some form of h o s p i t a l insurance through private or public (Medicare and Medicaid) sources. I t i s d i f f i -c u l t f or the reimbursing t h i r d p a r t i e s (be i t the government or p r i v a t e insurance companies) to monitor the i n d i v i d u a l costs of services because the heterogenous nature of the h o s p i t a l product makes i t d i f f i c u l t to estimate a cost-output r e l a t i o n s h i p and to derive a 'representative' cost for a p a r t i c u l a r diagnosis. The cost depends on the case mix complexity of the h o s p i t a l , severity of disease, h o s p i t a l s i z e and u t i l i z a t i o n rate and the range of h o s p i t a l a c t i v i t i e s (inpatient, outpatient, education, e t c . ) . These variables have to be c o n t r o l l e d systematically i n any attempt to compare costs across h o s p i t a l s . The lack of information a v a i l a b l e to patients about the quantity and type of services required means that the aggregate demand curve for the h o s p i t a l industry i s not exogenously determined. Patients express 22 t h e i r demand for services by seeking medical care but t h i s demand i s influenced by the supplier of services, the doctor, who manipulates the nature and l e v e l of u t i l i z a t i o n . In other words the physician responds to the demand for care by deciding what the p a r t i c u l a r service mix w i l l be for each patient. This n e c e s s a r i l y b r i e f d e s c r i p t i o n of the h o s p i t a l industry suggests that the assumptions of n e o c l a s s i c a l cost theory may not be r e a d i l y a p p l i c a b l e . The heterogenous, often i l l - d e f i n e d product mix, and the absence of a p r o f i t motive, make cost minimization an u n l i k e l y behaviour for the h o s p i t a l sector. Thus the attempted de r i v a t i o n of a long run average cost curve i n order to determine whether or not economies scale exist: i n the h o s p i t a l industry i s misdirected. It i s not s u r p r i s i n g .that ther.e!;has developed no consensus of the s i z e of the most e f f i c i e n t h o s p i t a l or on the shape of the long run average cost curve. Table 2.1. 'Economies of Scale' Studies: Summary of Findings Researcher Carr and F e l d s t e i n Berry Francisco Ingbar and Taylor Cohen M. F e l d s t e i n Lave and Lave Existence of Economies of Scale Yes Yes No No Yes, Strong Yes No Minimum Long Run Average Cost Point i n Terms of Beds  190 560 - 790 depending on measure of q u a l i t y 300 - 900 depending on equation s p e c i f i c a t i o n (U.K. data) Source: This i s a modified version of Table 5-1 i n Berki (1972) 23 Table 2.1 summarizes the findings of these researchers whose studies are discussed i n d e t a i l l a t e r i n t h i s chapter. Their c o n f l i c t i n g r e s u l t s beg the question, "Is i t at a l l appropriate or relevant to determine the optimal s i z e of a h o s p i t a l ? " Even i f i t were possible to do, i t i s not r e a l l y f e a s i b l e to b u i l d optimal sized h o s p i t a l s a l l over the country for at l e a s t two reasons: f i r s t , i n d i v i d u a l h o s p i t a l e f f i c i e n c y i s not the sole c r i t e r i o n for l o c a t i n g h o s p i t a l s . Other factors such as p o l i t i c s and a c c e s s i b i l i t y are also taken into considera-t i o n . Second, i t may not be an economically e f f i c i e n t s o l u t i o n anyway, when viewed i n terms of the t o t a l h o s p i t a l system, because the savings r e s u l t i n g .from economies of scale must be balanced against the a d d i t i o n a l transportation costs a r i s i n g from a smaller number of evenly d i s t r i b u t e d h o s p i t a l s . ^ The early incentive 'reimbursement' studies were s i m i l a r l y unsuccessful i n t h e i r attempts to i d e n t i f y e f f i c i e n c y . The reasons for t h e i r d i f f i c u l t i e s w i l l be discussed more f u l l y below. It i s s u f f i c i e n t to note that the underlying assumptions of t h e i r analysis led to misguided p o l i c y implications. By attempting to i d e n t i f y t e c h n i c a l e f f i c i e n c y , they assume a number of t e c h n i c a l r e l a t i o n s h i p s for the h o s p i t a l industry (cost minimization, product homogeneity) that do not hold. In f a c t the analysis i t s e l f i s paradoxical. On the one hand, they claim that h o s p i t a l s are i n e f f i c i e n t because of t h e i r odd incentive structure (lack of a p r o f i t motive). On the other hand they assume that, by looking at h o s p i t a l behaviour, one can i d e n t i f y t e c h n i c a l e f f i c i e n c y . Pauly (1970) examines and r e f l e c t s upon t h i s paradox. Evans (1971) and l a t e r Evans and Walker (1972) broke from the t r a d i t i o n of the e a r l i e r studies by not attempting to i n f e r that the 24 actual cost-output r e l a t i o n they were estimating represented the tech-n o l o g i c a l constraints under which any h o s p i t a l system has to operate. Rather the actual cost-output r e l a t i o n may be the r e s u l t of either technological constraints or of 'behavioural' patterns. There i s no ready means of i s o l a t i n g the technological f a c t o r s . So the most one can assume from f i t t i n g a cost-output r e l a t i o n for a group of hospit a l s i s that one can only describe the way those hospi t a l s "behave", i . e . t h e i r d i s t r i b u t i o n around the average l e v e l of e f f i c i e n c y . If some underlying, more e f f i c i e n t pattern of h o s p i t a l behaviour e x i s t s , i t w i l l not be discovered using t h i s methodology. Evans was the f i r s t researcher examining the h o s p i t a l cost-output r e l a t i o n who stated e x p l i c i t l y t h i s d i f f e r e n c e between defining h o s p i t a l technology and describing h o s p i t a l behaviour and the l i m i t a t i o n s of the methodology to achieve the former. Subsequent investigations i n the area, looking at ways to standardize h o s p i t a l output for reimbursement purposes, acknowledge that they can only hope to improve the r e l a t i v e e f f i c i e n c y of h o s p i t a l s . So they admit, by implication, that they are only describing behaviour for the group of hospit a l s being studied. It i s these researchers, beginning with Evans, whose work form the second group of reimbursement studies. Having provided both the p o l i c y content and the t h e o r e t i c a l frame-work within which these two groups of cost studies developed, we proceed to describe them i n more d e t a i l , i n p a r t i c u l a r the ways i n which they 4 have adjusted for the output heterogeneity of the h o s p i t a l . 25 2.4. 'Economies of Scale' Studies Carr and F e l d s t e i n (1967) estimated an aggregate long run t o t a l cost function using multiple regression analysis on a sample of 3147 voluntary, short term general h o s p i t a l s i n the United States. The dependent v a r i a b l e i n the multiple regression equation was t o t a l cost. The factors which were expected to a f f e c t costs were included as inde-pendent v a r i a b l e s . These variables were measures of s i z e (patient days, 2 (PD) and PD )) and measures of f a c i l i t i e s , services, and programs (number of f a c i l i t i e s and services, (S)), number of f a c i l i t i e s times the number of patient days (S x PD), number of outpatient v i s i t s (OPV), existence of a pr o f e s s i onal nursing school (NS), number of student nurses (N), number of types of internship and residency programs offered (IRP), number of interns and residents (IR), a f f i l i a t i o n with a medical school (MS). The major fin d i n g was consistent with the hypothesis that there e x i s t cost economies to s c a l e — a s h o s p i t a l s i z e increases, average cost declines u n t i l i t reaches a minimum l e v e l at about 190 patients and then i t begins to r i s e . There was, however, an unexpected r e s u l t . The c o e f f i c i e n t of the major v a r i a b l e (S x PD), which was intended to standardize for v a r i a t i o n i n h o s p i t a l patients or output, was s i g n i f i -cantly negative. This implied that costs were decreasing with increasing numbers of services and patient d a y s — t h e opposite to what Carr and F e l d s t e i n expected. They explained that t h i s unexpected r e s u l t was due 2 to a high c o r r e l a t i o n between the three v a r i a b l e s , S x PD, PD and PD . A second analysis was undertaken to control for t h i s e f f e c t . Hospitals were grouped according to the number of f a c i l i t i e s , services and programs they provide. A separate regression equation was calculated for each group of h o s p i t a l s . The r e s u l t s showed that economies of scale "appear 26 to e x i s t over a wide range of sizes i n each of the service c a p a b i l i t y groups" (Carr and Fe l d s t e i n , 1967, 61). However, the shape of the curves f o r each of these service c a p a b i l i t y groups are not very steep, and the di f f e r e n c e i n the average cost per patient day between the top and the bottom of the steepest curve i s only about $7—which may be s t a t i s t i c a l l y s i g n i f i c a n t but i s i n s i g n i f i c a n t i n p o l i c y terms. Berry (1967) was also concerned with i s o l a t i n g the e f f e c t s of hos p i t a l s i z e on cost. He categorized 5293 of the 5684 non-federal, short term general and other s p e c i a l h o s p i t a l registered i n 1963, into 40 groups, according to the a v a i l a b i l i t y or n o n a v a i l a b i l i t y of 28 f a c i l i t i e s and services. The r e l a t i o n s h i p between average cost and the l e v e l of output was measured f or the 40 groups of hospital s using multiple regression analysis with average cost per patient day as the dependent v a r i a b l e and t o t a l patient days as the independent v a r i a b l e . The average cost curve of hospitals with a given number of f a c i l i t i e s and services decreases as output increases i n 36 out of the 40 groups analysed. This i s s t a t i s t i c a l l y s i g n i f i c a n t f o r 26 of these 36 equations but not always s i g n i f i c a n t i n p o l i c y terms.^ In a l a t e r paper, Berry (1970, 69) discusses "ways to employ the av a i l a b l e data to make better adjustments f o r product mix than have heretofore been made." He groups the 6000 short term general h o s p i t a l s f o r 1965 by nature of co n t r o l (government, voluntary, proprietary, t o t a l ) and estimates a cost equation f o r each using multiple regression a n a l y s i s . The dependent v a r i a b l e i s cost per patient day. The l e v e l of output i s measured by the average d a i l y census. Product mix i s adjusted for by 40 independent v a r i a b l e s : 7 dummy vari a b l e s representing a c c r e d i t a t i o n and approval; 27 dummy variables representing the a v a i l a b i l i t y of f a c i l i t i e s and services; the average 27 length of stay; the proportion of outpatient a c t i v i t y ; the proportion of b i r t h s ; and the number of student nurses, medical students and other trainees per patient. Approximately 25 percent of the v a r i a t i o n i n cost per patient day for a l l short term general h o s p i t a l s are explained by the included v a r i a b l e s . Berry found a c e r t a i n amount of m u l t i c o l l i n e a r i t y among the 40 var i a b l e s and since they contributed s i g n i f i c a n t l y to the explanatory power of the cost equations, he decided they should be further analysed. Factor analysis was applied to the 40 variables i n an attempt to i d e n t i f y a few s i g n i f i c a n t common factors which would represent v a r i a t i o n s i n the product mix of h o s p i t a l s . Berry i d e n t i f i e d eight meaningful factors which he claims can be used to adjust for product mix i n any a n a l y s i s o f the r e l a t i o n s h i p between h o s p i t a l costs and output. Berry (1973) decided to examine whether there was a systematic pattern to the a v a i l a b i l i t y of f a c i l i t i e s and services i n short term general h o s p i t a l s . He developed a matrix to determine the most represen-t a t i v e combination of services and f a c i l i t i e s i n ho s p i t a l s of d i f f e r e n t sizes (measured i n terms of t o t a l number of f a c i l i t i e s ) . Five categories of h o s p i t a l s were defined: basic, q u a l i t y enhancing, complex, community, s p e c i a l . A basic h o s p i t a l has f a c i l i t i e s and services common to each other group on the scale. Thus the groups, from basic to s p e c i a l , are characterized by an increasing number and d i v e r s i t y of services. This categorization of hos p i t a l s was more systematic and comprehensive than Berry's i n i t i a l grouping (based on factor analysis) because i t i s a cumulative measure, thereby introducing an index of r e l a t i v i t y into the groups. Berry (1974) b u i l t t h i s complexity of scope of services into a more d e t a i l e d analysis of h o s p i t a l cost. He defined the cost function i n terms of l e v e l of output, q u a l i t y of services, product mix, factor 28 p r i c e s , e f f i c i e n c y . The e f f e c t of these factors on h o s p i t a l cost was analysed for approximately 6,000 h o s p i t a l s for the years 1965, 1966 and 1967. The analysis provides i n s i g h t into the various factors a f f e c t i n g h o s p i t a l cost. Berry concludes that h o s p i t a l s are subject to economies of scale but the absolute magnitudes are rather i n s i g n i f i c a n t . "A much more fundamental question i s what i s the optimal mix of complexities of scope of services or what i s the optimal mix of types of h o s p i t a l s " (Berry, 1974, 309). Francisco (1970) uses a s i m i l a r technique to Berry. He defines 25 homogenous h o s p i t a l groups, based on various combinations of the 16 f a c i l i t i e s / s e r v i c e s l i s t e d by the American Hospital Association. Regression analysis of average cost per patient day as a function of output ( t o t a l patient days) were undertaken for these 25 groups of hos p i t a l s . These r e s u l t s showed a negative but weak r e l a t i o n s h i p between unit costs and.output with only seven s i g n i f i c a n t regression c o e f f i c i e n t s out of twenty-five. This r e s u l t made Francisco reluctant to claim the existence of economies of scale. However, separating groups of large h o s p i t a l s and groups of small h o s p i t a l s , he found s i g n i f i c a n t economies of scale f o r the small h o s p i t a l s . The large h o s p i t a l s , on the other hand, exhibited constant returns to scale. The studies reviewed so far are s i m i l a r i n that they assume that h o s p i t a l s with i d e n t i c a l or s i m i l a r f a c i l i t i e s produce a r e l a t i v e l y homog-enous output. This same approach has also been adopted by other research-ers not j u s t interested i n the r e l a t i o n s h i p between h o s p i t a l costs and s i z e . It has been used to develop h o s p i t a l c l a s s i f i c a t i o n systems [see Edwards, et a l . (1972), Berry (1973), P h i l l i p and Iyer (1975), T r i v e d i (1978)] for the purpose of evaluating h o s p i t a l performance through 29 u t i l i z a t i o n review (e.g., comparisons of length of stay), peer review, qu a l i t y of care studies; to a s s i s t i n h o s p i t a l s t a f f i n g , or i n determining the optimal mix of types of h o s p i t a l s ; to f a c i l i t a t e sampling procedures when only a few h o s p i t a l s need to be studied. As a method of standardizing h o s p i t a l output, however, t h i s approach presents problems. The main problem stems from i t s basic assumption that the presence or absence of a f a c i l i t y or service i s a proxy for i d e n t i c a l numbers and types of patients. Hospitals are grouped according to the combination of f a c i l i t i e s and services a v a i l a b l e and the assumption i s that within each group each h o s p i t a l produces a homogeneous output. This.: suggests that h o s p i t a l s within each group have the same f a c i l i t i e s and services and these services are s i m i l a r i n terms of s i z e , u t i l i z a t i o n rates and type of patients treated. This assumption i s too s i m p l i s t i c as there i s l i k e l y to be a range i n the s i z e and u t i l i z a t i o n of f a c i l i t i e s or services for any p a r t i c u l a r group of h o s p i t a l s . S i m i l a r l y there w i l l be a range i n the amount of services consumed by the patients i n any given group of h o s p i t a l s . To t h e i r c r e d i t , Carr and F e l d s t e i n , Berry and Francisco acknowledged that t h e i r use of surrogates was far from s a t i s f a c t o r y as a method of s standardizing f o r h o s p i t a l product heterogeneity. However t h i s informa-t i o n on f a c i l i t i e s and services was the only data available to them. They recognized that standardization i n terms of diagnosis would have greater power i n explaining i n t e r - h o s p i t a l cost d i f f e r e n c e s . Another problem with these studies i s that they do not d i s t i n g u i s h adequately between the major a c t i v i t i e s of the h o s p i t a l — i n p a t i e n t care, outpatient care and teaching. In making i n t e r - h o s p i t a l cost comparisons i t i s n a t u r a l l y d e s i r a b l e to ensure that cost comparisons are of s i m i l a r 30 outputs. As inpatient care i s the predominant h o s p i t a l a c t i v i t y , a rigorous analysis requires the i s o l a t i o n of inpatient costs from these other a c t i v i t i e s . Thus output heterogeneity i s defined i n terms of differences among h o s p i t a l a c t i v i t i e s ( inpatient, outpatient, etc.) and product differences within these a c t i v i t i e s (the d i f f e r e n t types of in p a t i e n t s ) . V a l i d cost comparisons, therefore, require adjustments for the a c t i v i t y mix of the h o s p i t a l . This can be done i n one of two ways: (i) by placing, on the r i g h t hand side of the h o s p i t a l cost equation, v a r i a b l e s which indi c a t e the l e v e l of non-inpatient a c t i v i t y ; ( i i ) by sub-t r a c t i n g from the average cost per case or patient day on the l e f t hand side of the equation, the cost a t t r i b u t a b l e to these a c t i v i t i e s . Barer and Evans (1980, 14) present the advantages and disadvantages of each of these approaches and conclude that the l a t t e r approach i s usually d e s i r -able. Right hand side standardization requires a p o t e n t i a l l y long l i s t of independent variables i f i t i s to be done accurately which i s cumber-some and i s l i k e l y to r e s u l t i n c o l l i n e a r i t y among the many out-patient v a r i a b l e s . Carr and Fe l d s t e i n , Berry and Francisco, i n the studies noted above, adjust f o r these a c t i v i t i e s on the ri g h t hand side of the equation. To adjust for teaching, Berry and Francisco include a dummy v a r i a b l e to indica t e the presence or absence of a teaching program. Carr and Fel d -s t e i n weight the equation according to the actual number of teaching programs offered. In each case there i s no j u s t i f i c a t i o n given for the method adopted nor i s there any analysis that reveals the reason for cost increases. If teaching i s characterized by high f i x e d costs, a dummy va r i a b l e i s probably adequate. If the d i v e r s i t y of the teaching program 31 (medical, nursing, etc.) i s responsible for increasing costs, Carr and Feldstein's v a r i a b l e i s appropriate. However, costs may be r e l a t e d to the number of students i n the program, and f i x e d costs may be low. In t h i s case neither v a r i a b l e s u f f i c e s . Ingbar and Taylor (1968) took a s l i g h t l y d i f f e r e n t approach to the previous researchers. They did not categorize homogenous groups of h o s p i t a l s on the basis of a v a i l a b l e f a c i l i t i e s . Rather they attempted to standardize h o s p i t a l output according to the number of services performed for the patient. They developed an extensive l i s t of v a r i a b l e s (over 100) from which eleven major f a c t o r s or a c t i v i t i e s were derived using p r i n c i p a l components a n a l y s i s . These include ( i ) size-volume, ( i i ) u t i l i z a t i o n , ( i i i ) length of stay, (iv) laboratory a c t i v i t y , (v) radiology a c t i v i t y , (vi) s u r g i c a l a c t i v i t y , ( v i i ) maternity a c t i v i t y , ( v i i i ) p e d i a t r i c a c t i v i t y , (ix) ambulatory a c t i v i t y , (x) p r i v a t e services, (xi) ward services. The e f f e c t of these factors on measures of unit cost were tested using regression a n a l y s i s . A s i n g l e v a r i a b l e , r e l a t e d to the volume of the a c t i v i t y (e.g., number of inpatient weighted operations for (vi) s u r g i c a l a c t i v i t y ) was chosen to represent each f a c t o r . Two h o s p i t a l cost equations were estimated to e s t a b l i s h the r e l a t i o n s h i p between h o s p i t a l s i z e and capacity. Cost per a v a i l a b l e bed day and cost per patient day were the dependent v a r i a b l e s ; the eleven a c t i v i t y measures were the independent v a r i a b l e s . Their r e s u l t s were d i f f e r e n t from t h e i r expectations. They revealed an inverted U-shaped average cost function, with a cost maximum at 150 beds! This novel discovery suggested that cost economies were to be had at either small scale or very large scale opera-t i o n . However, the curve was so smooth that the authors concluded that cost i n t h i s sense was v i r t u a l l y constant with respect to s i z e . 32 Cohen (1967) (1970) also adopted a weighted service approach as h i s method of output standardization. Instead of using type and quantity of services performed (e.g., Ingbar and Taylor, 1968), he weighted each service^ by i t s estimated average cost. Cohen defined output of a h o s p i t a l as the sum of the products of the weights and units of any service per-formed i n that h o s p i t a l : S, = W. Q.. k l xk where i s service output i n the kth h o s p i t a l . W i s the weight of the i t h service. Q^k 1 S the quantity of the i t h service i n the kth h o s p i t a l . The weight of the i t h service (VL) was determined by d i v i d i n g the service u n i t ' s average cost by the average cost of a patient day. Average cost of each service unit was determined by summing t o t a l cost of that service unit across the 23 h o s p i t a l s i n the sample and d i v i d i n g by the t o t a l number of service u n i t s . Cohen (1970) adds another factor to take account of differences i n q u a l i t y of care between h o s p i t a l s . This i s done i n two steps: f i r s t , by the addition of a dummy va r i a b l e i n d i c a t i n g whether a h o s p i t a l i s either a f f i l i a t e d or not a f f i l i a t e d with a medical school; second, by using a v a r i a b l e that r e f l e c t s the degree of a f f i l i a t i o n with the medical school, i . e . an a f f i l i a t e d h o s p i t a l was c l a s s i f i e d as providing 10, 20 or 30 percent "more care" than a n o n - a f f i l i a t e d h o s p i t a l . Cohen's r e s u l t s , unlike Ingbar and Taylor, revealed the existence of economies of scale with the optimal sized h o s p i t a l being somewhere i n the range of 560-790 beds depending on the q u a l i t y v a r i a b l e used. Several c r i t i c i s m s have been made of the weighting methods used by both Ingbar and Taylor and Cohen. Berki (1972, 93) notes that Ingbar and 33, Taylor's v a r i a b l e s were randomly selected, lacking a t h e o r e t i c a l frame-work. Consequently the r e s u l t i n g a c t i v i t i e s or factors do not have "independent a n a l y t i c meaning." Also i n the f i n a l equation, they estimate cost per bed day as the dependent v a r i a b l e and service expenses or departmental expenses (e.g., r a d i o l o g i c a l a c t i v i t y ) as the independent v a r i a b l e s — i n e f f e c t they are " c o r r e l a t i n g d i f f e r e n t d e f i n i t i o n s of out-put" (Berki, 1972, 94). Cohen's method of weighting by average costs was also c r i t i c i s e d by Berki (1972) and P. F e l d s t e i n (1970). Cohen weighted the services or independent variables by t h e i r average cost, then assumed that the sum of these same costs equalled t o t a l h o s p i t a l costs, or the dependent v a r i a b l e . S t a t i s t i c a l l y he i s not explaining costs but describing them. As Berki (1972, 37) comments, " s t a t i s t i c a l l y one would expect a high degree of autocorrelation between output weighted by cost and cost i t s e l f . " Also Cohen weighted these service units by the aggregate average cost f i g u r e derived from summing costs across a l l h o s p i t a l s i n the sample. This assumes there are no e f f i c i e n c y differences among h o s p i t a l s . P. F e l d s t e i n (1970, 295) questioned the measures used for estimating q u a l i t y . He f e l t that a f f i l i a t i o n with a medical school i s "not a s u f f i c i e n t l y discriminating measure for a l l q u a l i t y differences among large h o s p i t a l s i n an urban area." ' F i n a l l y both Ingbar and Taylor's study and Cohen's studies can be c r i t i c i s e d f o r not adequately adjusting for the range of h o s p i t a l a c t i v i t i e s — i n p a t i e n t , outpatient, teaching, etc. A p a r t i a l r i g h t hand standardization was attempted by Ingbar and Taylor and Cohen with the i n c l u s i o n of a v a r i a b l e for outpatient v i s i t s but there was no account for outpatient radiology and laboratory a c t i v i t y i n the adjustment process. 34 g In the studies mentioned to date, researchers have used two s i m i l a r methods of standardizing h o s p i t a l output. In both cases they standardize output for service mix differences among h o s p i t a l s . The f i r s t method controls f o r the range of f a c i l i t i e s and services a v a i l a b l e at the hos-p i t a l and assumes s i m i l a r u t i l i z a t i o n patterns across h o s p i t a l s [Carr and F e l d s t e i n (1967), Berry (1967, 1970, 1974), Francisco (1970)]. The second method controls for differences i n the number of services a c t u a l l y performed for the patient [Ingbar and Taylor (1968), Cohen (1967 and 1970)]. Both groups of authors assume that the range of services and f a c i l i t i e s a v a i l a b l e i s a reasonable proxy for the range of diagnoses that a h o s p i t a l i s capable of t r e a t i n g and therefore, i s an adequate means of adjusting for h o s p i t a l product d i f f e r e n t i a t i o n . However, a more d i r e c t approach i s to standardize output i n terms of the patient rather than i n terms of the services a v a i l a b l e or services received. This i s also a more accurate approach, according to Lave and Lave (1971) who showed a low c o r r e l a t i o n between case mix measures and measures of service c a p a b i l i t y . The f i r s t attempt at standardizing output i n terms of the patient was undertaken by M. F e l d s t e i n (1965, 1967) using s p e c i a l t y groupings. 9 F e l d s t e i n (1967) c l a s s i f i e d the patients of 177 B r i t i s h non-teaching h o s p i t a l s for: the year 1960 into e i g h t ^ ' s p e c i a l t y ' categories: general medicine, p a e d i a t r i c s , general surgery, ear nose and throat, traumatic and orthopaedic surgery, gynaecology, o b s t e t r i c s and other. He expressed the number of cases treated i n each of the categories as a proportion of t o t a l cases and used l i n e a r regression analysis to estimate the extent to which i n t e r - h o s p i t a l v a r i a t i o n s i n costs per case and costs per patient week were explained by differences i n case mix. He found that case mix differences explained 27.5 percent of the v a r i a t i o n s i n 35 o v e r a l l ward costs per case. Using t h i s method of standardization of output, F e l d s t e i n (1967) examined the r e l a t i o n s h i p between h o s p i t a l cost and s i z e and concluded that cost i s unaffected by s i z e . However he further hypothesized that t h i s apparent absence of any influence on s i z e may be the r e s u l t of two counteracting f a c t o r s : the "pure scale e f f e c t " and the "case flow e f f e c t " , i . e . , the number of beds and the cases treated per bed per year. When he incorporated a caseflow v a r i a b l e into the equations estimating 2 long run average cost, R was increased, and a U-shaped curve was observed, with a minimum point at around 900 beds. F e l d s t e i n concluded he had detected a scale economies e f f e c t , with the optimal s i z e somewhere between 310 and 900 beds depending on the equation s p e c i f i c a t i o n . While F e l d s t e i n was able to explain a s i g n i f i c a n t proportion of i n t e r - h o s p i t a l cost differences using h i s method of standardizing output, his eight s p e c i a l t i e s categories were s t i l l very broad. Heterogeneity within these categories, e s p e c i a l l y the l a r g e r , more diverse ones such as general medicine, surgery, must be seen as a c r i t i c i s m of t h i s method of grouping. F i n a l l y to complete t h i s review of h o s p i t a l cost studies concerned with the question of economies of scale we should consider Lave and Lave (1970a and 1970b). They eliminated case mix or product mix from t h e i r average cost function, because they assumed that "while the output mix d i f f e r s among h o s p i t a l s , i t i s constant within a h o s p i t a l (over a short time period)" (Lave and Lave, 1970a, 380). Thus they assumed a l l h o s p i t a l s have a constant case mix i n the short run. Lave and Lave (1970a) applied t h e i r techniques to 74 western Pennsylvania hospi t a l s for the period 1961-1967. The f i r s t analysis was 36 a time series analysis expressing average cost as a function of time, u t i l i z a t i o n and s i z e . The second was a pooled (cross section, time series) estimate which took account of other parameters such as the h o s p i t a l ' s teaching status, l o c a t i o n (urban or r u r a l ) and the i n i t i a l values of s i z e , u t i l i z a t i o n and cost. The r e s u l t s of both methods were remarkably s i m i l a r , and Lave and Lave concluded that t h e i r method had been successful i n accounting f o r the multi-product nature of the h o s p i t a l . They noted "our r e s u l t s i n d i c a t e that i f economies of scale e x i s t i n the h o s p i t a l industry, they are not very strong" (Lave and Lave, 1970a, 394). As t h i s d e s c r i p t i o n of the 'economies of scale' studies reveals, there was no consensus on whether there e x i s t s an optimal s i z e for a h o s p i t a l . As stated e a r l i e r the assumptions upon which the analysis r e s t s are inappropriate to the h o s p i t a l industry, so t h i s lack of agree-ment among researchers i s no surprise. However, recognition by the economics profession of t h i s f a u l t i n t h e i r analysis has not been f o r t h -coming—hence the development of t h i s s u bstantial body of l i t e r a t u r e with misguided p o l i c y implications. 2.5. Reimbursement Studies Rapidly r i s i n g h o s p i t a l costs i n both Canada and the United States i n the l a t e s i x t i e s led to recognition of the need for some systematic attempt at h o s p i t a l cost containment. This gave r i s e to a second genera-t i o n of h o s p i t a l cost studies whose aim was to develop reimbursement procedures that would be e f f e c t i v e i n c o n t r o l l i n g costs. These studies were d i f f e r e n t from the 'economies of scale' studies which focused on long run average costs. Instead they were concerned with short run 37 average costs. In addition case mix differences among hospital s became a c r i t i c a l issue as h o s p i t a l costs are c l e a r l y affected by the types of patients they treat. Reimbursing agencies need to be able to standardize for these v a r i a t i o n s i n output i f they are to gauge r e l a t i v e e f f i c i e n c y among hos p i t a l s and achieve an equitable a l l o c a t i o n of resources. A number of reimbursement schemes have been proposed, a l l of which have been reviewed from time to time by a number of a u t h o r s T h e y include the group target c e i l i n g approach, i n d u s t r i a l engineering, departmental budget review and prospective reimbursement. Experiments with reimbursement schemes, p a r t i c u l a r l y incentive reimbursement schemes, based on the group target c e i l i n g approach, i n d u s t r i a l engineering and departmental budget review, have been under-taken i n the United States. These are described here to allow examination of the methods used to account for case mix differences among h o s p i t a l s . 2.5.1. Group Target C e i l i n g Approach The e a r l i e s t attempts at incentive reimbursement, using the group target c e i l i n g approach, were undertaken by Blue Cross of Western Pennsylvania i n 1966. Nine groups of h o s p i t a l s were established based on the hos p i t a l ' s l o c a t i o n (metropolitan, urban, r u r a l ) and the extent of i t s teaching program (advanced teaching, teaching and non-teaching) . Hospitals were reimbursed r e t r o s p e c t i v e l y on the basis of incurred costs, but i f a hos p i t a l ' s average cost per patient day was above i t s group's c e i l i n g (10 percent above the average cost per patient day for the group), the h o s p i t a l would only be reimbursed at the c e i l i n g rate. This method of reimbursement assumes that h o s p i t a l s within each group had an homogenous output, measured on the basis of l o c a t i o n and teaching programs. The complexity of a h o s p i t a l ' s case load was not considered. 38 Thus the reimbursement scheme penalizes or places under un f a i r pressure the administrator whose ho s p i t a l ' s case mix becomes more expensive. S i m i l a r l y the h o s p i t a l whose case mix becomes les s expensive i s rewarded, for reasons unrelated to the r e l a t i v e e f f i c i e n c y of the h o s p i t a l (Lave, Lave and Silverman, 1973, 8 4 ) . Shuman, Wolfe arid Hardwick (1972) attempted to improve on t h i s approach by b u i l d i n g a case mix factor into the proposed reimbursement scheme. However, lack of data meant they had to resort to measuring case mix as a function of medical s t a f f a t t r i b u t e s . They included t h i s v a r i a b l e i n a model with indices representing services, education, l o c a t i o n , out-patient a c t i v i t y and s i z e c l a s s e s . Each h o s p i t a l was c l a s s i f i e d i n d i -v i d u a l l y according to the e f f e c t of these factors on t o t a l cost. Future costs were predicted and c o n t r o l bands established which were used to determine incentives, penalties and maximum reimbursement to the providers. Although t h i s method was a s l i g h t improvement over the a r b i t r a r y c l a s s i f i -c a tion of the Western Pennsylvania scheme where teaching and l o c a t i o n determined the h o s p i t a l c l a s s and hence the rate, medical s t a f f a t t r i b u t e s i s s t i l l an i n d i r e c t measure of case mix and, therefore, a poor surrogate. 2.5.2. I n d u s t r i a l Engineering Another approach to incentive reimbursement i s based on 12 i n d u s t r i a l engineering techniques. These techniques aim at improving the e f f i c i e n c y of h o s p i t a l a c t i v i t i e s by reducing labour requirements, maximizing labour performance, increasing output per unit of labour, reducing the use of materials or supplies. Incentives are paid to the hospita l s on the basis of savings r e s u l t i n g from the introduction of these e f f i c i e n c y programs. This approach focuses on the e f f i c i e n t combination of h o s p i t a l inputs and i s not concerned with h o s p i t a l outputs. It r e l i e s 39 on d e t a i l e d time and motion studies i n each department of each h o s p i t a l . Rewards are made on the basis of improved e f f i c i e n c y within h o s p i t a l s — there are no comparisons of r e l a t i v e e f f i c i e n c y between h o s p i t a l s — s o a r e l a t i v e l y i n e f f i c i e n t h o s p i t a l stands to make large savings and i s rewarded while a r e l a t i v e l y e f f i c i e n t h o s p i t a l stands to gain very l i t t l e . 2.5.3. Departmental Budget Review Departmental budget review was used by the Connecticut 13 Hospital Association and SSA i n a program of incentive reimbursement. Target budgets were set for i n d i v i d u a l h o s p i t a l departments by a committee comprising representatives from equivalent departments i n other h o s p i t a l s i n the state. This was a form of peer review with the understanding that members of s i m i l a r departments could set r e a l i s t i c targets f o r each other. At the end of the year, the hospi t a l ' s actual costs were reviewed against i t s target. Connecticut Blue Cross and SSA had agreed i n advance to pay the higher c o s t s — e i t h e r the actual departmental costs or the targeted costs. As a consequence the h o s p i t a l had nothing to lose, but i t did have an incentive to operate below i t s target. Again standardization of f i n a l h o s p i t a l output was not considered. Targets were set for intermediate services, not f i n a l s ervices. Case mix i n a h o s p i t a l was assumed constant, so the r e a l incentive f o r the h o s p i t a l was not to become more e f f i c i e n t but to reduce the number of complex cases they treated. These early incentive reimbursement schemes were not successful i n containing h o s p i t a l costs. There were three main reasons for t h i s : f i r s t , payment to the hospital s was made r e t r o s p e c t i v e l y and the onus was not on the h o s p i t a l to keep within i t s targeted budget because the reimbursing agency usually paid e i t h e r the actual costs incurred by the 40 h o s p i t a l or the targeted costs, whichever were the highest. Second, the incentives for the h o s p i t a l to operate below i t s expected c o s t s — i t was allowed to r e t a i n the d i f f e r e n c e between the actual and the expected c o s t s — d i d not have cost containment implications. The surpluses, i f 14 any, were spent on expanding services and f a c i l i t i e s , which, i n turn, increase operating costs. More fundamental was the nature of the incentive structure which was inappropriate to the h o s p i t a l industry. In the absence of a p r o f i t motive and cost minimizing behaviour, there was l i t t l e point i n o f f e r i n g t r a d i t i o n a l incentives. Third, the lack of a systematic comparison of h o s p i t a l performance (with no accurate method of standardizing h o s p i t a l output) meant that i t was impossible to measure r e l a t i v e e f f i c i e n c y among ho s p i t a l s and to set budgets which r e f l e c t e d the case complexity of the h o s p i t a l . 2.5.4. Prospective Reimbursement Under prospective reimbursement, h o s p i t a l budgets are set i n advance for the year i n the form of a block budget or on the basis of a per day or per case rate and h o s p i t a l s are required to stay within these predetermined l i m i t s . Unlike retrospective reimbursement, pro-spective reimbursement s h i f t s some of the r i s k of cost onto the ho s p i t a l s by motivating them to be more cost conscious, to a n t i c i p a t e and j u s t i f y future expenditures. Moreover they are motivated to monitor the quantity and q u a l i t y of t h e i r services to ensure they are keeping within t h e i r budget and to keep costs down to avoid losses or to achieve surpluses (Dowling, 1974). Unlike some of the retrospective reimbursement schemes described e a r l i e r , prospective reimbursement does have the p o t e n t i a l for rewarding the r e l a t i v e l y e f f i c i e n t h o s p i t a l s and penalizing the i n e f f i c i e n t ones. 41 However, the effectiveness of t h i s approach depends l a r g e l y on the a b i l i t y of the reimbursing agency to i d e n t i f y the r e l a t i v e l y e f f i c i e n t v i s - a - v i s i n e f f i c i e n t h o s p i t a l s and set r e a l i s t i c budgets or rates for the h o s p i t a l s . Success depends upon meaningful i n t e r - h o s p i t a l cost comparisons which can only be achieved by accurate standardization for product d i f f e r e n c e s . Canada experimented very b r i e f l y with incentive reimbursement schemes and prospective budgeting has been the predominant form of h o s p i t a l reimbursement since the l a t e f i f t i e s . However, only recently, with a change i n the f e d e r a l - p r o v i n c i a l cost sharing agreement (1977), has the major part of the h o s p i t a l financing burden been placed on the p r o v i n c i a l government. This i s f o r c i n g them to review t h e i r budget set t i n g procedures to ensure that ( i ) they are equitable i n t h e i r a l l o c a -t i o n of resources to h o s p i t a l s and ( i i ) they encourage e f f i c i e n c y within h o s p i t a l s . They r e a l i z e that the improvements in,budgetary practices that they are seeking depend on f i n d i n g an accurate way of standardizing for differences i n h o s p i t a l output. In the United States reimbursing agencies are looking to prospective reimbursement as the l a t e s t and p o t e n t i a l l y most e f f e c t i v e means of c o n t r o l l i n g h o s p i t a l costs. However they also r e a l i z e that the p o t e n t i a l success of t h i s approach rests on solving the output standardization problem so that accurate comparisons of h o s p i t a l performance can be made. Consequently there has been a concentration of a c t i v i t y aimed at developing these methods of standardization of output for use i n reim-bursement. Most of the work undertaken for t h i s purpose has focused on standardization i n terms of case mix rather than service mix (the approach taken i n the 'economies of scale' s t u d i e s ) . 42 2.6. Standardization of Output i n Terms of Case Mix 2.6.1. Specialty Mix (Feldstein, 1967) Fe l d s t e i n (1965 and 1967)^ was the f i r s t to standardize h o s p i t a l output i n terms of the types of cases treated by the h o s p i t a l . He c l a s s i f i e d patients according to 'spe c i a l t y ' mix but t h i s approach had the problem of heterogeneity within the larger s p e c i a l t y categories such as general medicine and surgery. Development of the International C l a s s i f i c a t i o n of Diseases Adapted (ICDA) provided the base for a much more de t a i l e d c l a s s i f i c a t i o n of patients according to diagnosis. It enabled case mix to be defined d i r e c t l y which seemed i n t u i t i v e l y to be a better approach than d e f i n i t i o n on the basis of surrogates such as the number of f a c i l i t i e s and services. Lave and Lave (1971) provided empirical support f o r t h i s approach when they found that i n s t i t u t i o n a l c h a r a c t e r i s t i c s ( s i z e , teaching status, number of advanced services) explained only about 25 percent of v a r i a t i o n 16 i n case mix defined i n terms of diagnosis. 2.6.2. Diagnostic Proportions (Evans, 1971) Evans (1971) grouped the discharge diagnoses of a l l patients i n 185 acute h o s p i t a l s i n Ontario i n 1967 into 41 roughly homogenous ICDA categories and the age-sex data f o r the same patients were grouped into 40 categories. The proportion of patients and patient days i n each of these categories were calculated f o r a l l h o s p i t a l s . Then v a r i a b l e s , together with scale and a c t i v i t y v a r i a b l e s , represented, the independent variables of two regression equations: one with average inpatient expense per inpatient day (DAYEX) as the dependent v a r i a b l e , the other with average cost per case (CASEX) as the dependent v a r i a b l e . The r e s u l t s 43 showed that diagnostic mix "'explained' about 80 percent of the i n t e r -h o s p i t a l variance i n cost per case and about 50 percent of the variance i n cost per day" (Evans, 1971, 202). However, c o l l i n e a r i t y among the diagnostic and age-sex proportions suggested some attempt should be made to aggregate these categories. Factor analysis was used and the 41 diagnostic proportions were reduced to 10; the 40 age-sex categories were reduced to 6. These factors were included i n the regression equations with the other independent v a r i a b l e s and were shown to account for "85 percent of i n t e r - h o s p i t a l variance i n cost per case" (Evans, 1971, 206). Evans contrasts t h i s to M. Feldstein's (1967) f i n d i n g of 27.5 percent f o r U.K. data, arguing that the fineness of d e t a i l of the diagnostic data and the age-sex proportions enhanced h i s r e s u l t . He concludes that the diagnostic mix of a h o s p i t a l ' s inpatient load i s a c r i t i c a l determinant of h o s p i t a l inpatient costs. Other investigators have subsequently standardized h o s p i t a l output using ICDA groupings and factor analysis (or more p r e c i s e l y , p r i n c i p a l components a n a l y s i s ) . They are Lave, Lave and Silverman (1972, 1973), F e l d s t e i n and Shuttinga (1977), Zaretskey (1977), Goodisman and Trompeter (1979). Lave, Lave and Silverman (1972) take the 17 broad ICDA codes and compare three possible ways to deal with the c o l l i n e a r i t y problems inherent i n these groupings. They are ( i ) factor a n a l y s i s , ( i i ) c l u s t e r a n a l y s i s , ( i i i ) the reduction of explanatory v a r i a b l e s by aggregating v a r i a b l e s with s i m i l a r estimated marginal costs. They found the t h i r d method of aggregation was superior to the other two i n that i t was responsible for explaining a greater proportion of v a r i a t i o n i n actual 17 costs. F e l d s t e i n and Shuttinga (1977) began with 152 diagnostic groups, 44 51 s u r g i c a l groups and 10 age-sex groups. They used p r i n c i p a l components analysis to aggregate t h i s information into 10 diagnosis components and 10 s u r g i c a l components. S i m i l a r l y Zaretsky (1977) reduces 45 diagnostic categories to 12 factors and Goodisman and Trompeter (1979) reduced 44 primary diagnostic categories to 13 f a c t o r s . 2.6.3. Diagnostic Proportions and Ad d i t i o n a l Case Mix Measures  (Lave and Lave, 1972, 1973) Lave and Lave (1972, 1973) and F e l d s t e i n and Shuttinga (1977) include other measures of case mix, i n addition to diagnostic f a c t o r v a r i a b l e s , i n t h e i r regression equations developed to explain v a r i a t i o n s i n h o s p i t a l costs. F e l d s t e i n and Shuttinga (1977) include one other measure—the proportion of patients r e c e i v i n g 51 s u r g i c a l pro-cedures ( l a t e r reduced to 10 f a c t o r s ) . Lave and Lave (1972, 1973) include a v a r i e t y of other case mix measures: a measure of the incidence of surgery ( f r a c t i o n of patients who have surgery); two measures of disease "commonality"—the proportion of patients with a common diagnosis (must occur i n at least 0.5% of a l l p a t i e n t s ) , the proportion of non-s u r g i c a l patients with a common diagnosis; two measures of s u r g i c a l complexity based on the Blue Shield index of r e l a t i v e values for s u r g i c a l procedures—the proportion of patients with s u r g i c a l index d i f f i c u l t y K. 20 (easy surgery), the proportion of patients with s u r g i c a l d i f f i c u l t y index 5*70 (hard surgery). They hypothesized that h o s p i t a l s with a high proportion of s u r g i c a l patients would have higher costs; h o s p i t a l s with a high proportion of patients with "common" diagnoses would have lower costs; and hospital s with more complex surgery would have higher costs. A l l these hypotheses were confirmed i n the regression a n a l y s i s . Their approach and t h e i r 45 r e s u l t s supported t h e i r argument that there are many dimensions to the case mix measure and that a single measure based on diagnosis does not nece s s a r i l y reveal t h i s . 2.6.4. Information Theory (Evans and Walker, 1972) Evans and Walker (1972) took an innovative step i n t h e i r study of 97 B r i t i s h Columbia hospit a l s f or the year 1967. They increased the diagnostic breakdown which had been used i n Ontario (Evans, 1971) from 41 categories to 98 categories. They also proposed an a l t e r n a t i v e measure for adjusting for case mix v a r i a t i o n which i s an information measure based on the diagnostic proportions. They hypothesized "that complex cases tend to be handled i n a few hos p i t a l s with more extensive f a c i l i t i e s and more sp e c i a l i z e d s t a f f , while r e l a t i v e l y straightforward cases tend to be d i s t r i b u t e d more evenly over the h o s p i t a l system" (Evans and Walker, 1977, 399). Thus a measure of the degree of concentration of a case type i s a measure of i t s complexity. This measure of degree of concentration was provided by the expected information measure developed by T h e i l (1967). An index of the r e l a t i v e complexity of the h o s p i t a l s ' caseload was derived by f i r s t developing a set of diagnostic complexity values for the 98 diagnostic categories. Diagnostic categories which were concen-trated into a few hospital s were accorded the highest values; diagnoses which were d i s t r i b u t e d i n many hospital s were accorded the lowest values. The average value was 1. The proportion of cases i n each diagnostic category was then determined for each h o s p i t a l , m u l t i p l i e d by i t s r e l a t i v e weight and summed to give an index for each h o s p i t a l which represented 18 the r e l a t i v e complexity of i t s caseload. Two measures of h o s p i t a l complexity were derived: CMPXC1 indicates the r e l a t i v e complexity of the h o s p i t a l ' s caseload; CMPXC2 indicates the r e l a t i v e complexity of a 46 hospital's caseload a f t e r account has already been taken of differences i n h o s p i t a l s i z e . Evans and Walker included one of t h e i r a l t e r n a t i v e measures of case mix i n a number of regression equations along with a number of other independent v a r i a b l e s (number of rated beds, average length of stay, occupancy rate, d i r e c t educational expenses, outpatient expense, non-departmental expense (depreciation, r e n t a l and i n t e r e s t charges, i . e . c a p i t a l input), the presence or absence of a nursing school or medical 19 school a f f i l i a t i o n , one of three measures of s p e c i a l i a t i o n ). The dependent va r i a b l e s were cost per case (CASEX) and inpatient expense per inpatient day (DAYEX). They discovered that the complexity v a r i a b l e CMPXC1 explained nearly as much of i n t e r - h o s p i t a l cost v a r i a t i o n as did the previous eleven diagnostic f a c t o r scores used i n the Evans 1971 study. This indicates the s u p e r i o r i t y of t h i s s i n g l e measure over the factor score approach because i t reduces the number of v a r i a b l e s i n the regres-sion equation used to estimate average costs per case and per day, without a s u b s t a n t i a l l o s s of explanatory power. It i s also a more d i r e c t measure of case mix because i t captures the information i n the diagnosis matrix d i r e c t l y and avoids the a r b i t r a r y aggregation of diagnosis categories through factor analysis necessary to reduce c o l l i n e a r i t y among the o r i g i n a l 41 diagnostic categories. Horn and Schumacher (1979) draw the reader's attention to c e r t a i n diagnoses which do not f i t the assumption that a concentrated diagnosis i s complex, e.g. myocardial i n f a r c t i o n , emergencies. These may be common and widely d i s t r i b u t e d , but very complex. S i m i l a r l y , they claim there are a number of conditions that have low c l i n i c a l complexity/low death rate and are highly concentrated, e.g., conditions associated with l i m i t e d 47. f a c i l i t i e s , rare conditions, inappropriate admissions, or inappropriate coding or grouping. However, by d e f i n i t i o n , these anomalies could not have a very s i g n i f i c a n e f f e c t because t h e i r r e l a t i v e l y small numbers i n r e l a t i o n to the t o t a l caseload should minimize the e f f e c t on the h o s p i t a l ' s o v e r a l l complexity value. 2.6.5. Other Applications of the Information Theory  Measure i n Canada Barer (1977) used information theory to standardize for case mix differences between h o s p i t a l s i n B r i t i s h Columbia. The purpose of his study was to develop and test e m p i r i c a l l y a methodological basis f or determining marginal h o s p i t a l case costs. He derived these case costs using B.C. h o s p i t a l data and used them to compare the h o s p i t a l expenditure implications for a number of a l t e r n a t i v e forms of primary care. He found that community health c l i n i c s and physician group practices had the p o t e n t i a l f or reducing h o s p i t a l expenditures through reduced admission patterns. The major a n a l y t i c a l portion of the work involved the s p e c i f i c a t i o n , estimation and a p p l i c a t i o n of behavioural average cost equations. The equations were estimated from a time s e r i e s , c r o s s - s e c t i o n a l analysis of 87 B.C. h o s p i t a l s over an eight year period (1966-1973). Information theory was used to obtain case complexity variables to standardize for case mix v a r i a t i o n among h o s p i t a l s . Barer's time seri e s analysis revealed the s t a b i l i t y of these case mix weights over time. Despite Evans and Walker's (1972) and more recently Barer's (1977) success i n using the information measure of case mix complexity to explain i n t e r - h o s p i t a l cost differences i n Ontario and B r i t i s h Columbia, i t has not been applied to the h o s p i t a l budget review system i n either of these provinces. 48 However, i t i s being used i n Quebec as part of t h e i r three-stage process of c l a s s i f y i n g h o s p i t a l s f or budgetary purposes. Lance, Contandriopoulos, Thuy Nguyen (1979, 2) describe t h i s process which was developed to "correct the i n e q u i t i e s created by the financing methods founded on h i s t o r i c a l data." Quebec had adopted a global budget system i n 1972 i n which ho s p i t a l s were a l l o c a t e d budgets on the basis of 1970 expenditures, with an increase for p r i c e increases. As t h i s base represented actual costs i n 1970 with no account taken for the r e l a t i v e e f f i c i e n c y or i n e f f i c i e n c y of the i n d i v i d u a l h o s p i t a l s , the r e s u l t was that some hos p i t a l s were r e l a t i v e l y over-financed and others were r e l a t i v e l y under-financed. The review process of budgetary bases was developed to correct t h i s s i t u a t i o n . The f i r s t step i n t h i s process involves the formation of homogenous groups of h o s p i t a l s , measured i n terms of the s i m i l a r i t y of t h e i r output. The h o s p i t a l s are grouped using an index of s i m i l a r i t y derived from the a p p l i c a t i o n of information theory. The number of patient days for each of the 98 diagnostic categories (ICDA8) are computed as a proportion of t o t a l patient days for each i n d i v i d u a l h o s p i t a l . The d i s t r i b u t i o n of patient days across a l l Quebec hospita l s i s calculated for these same 98 diagnostic categories. A measure i s determined for each h o s p i t a l , using information theory, which qua n t i f i e s the extent to which the i n d i v i d u a l h o s p i t a l ' s d i s t r i b u t i o n of patient days d i f f e r s r e l a t i v e l y from the general d i s t r i b u t i o n f o r a l l Quebec h o s p i t a l s . An index of s i m i l a r i t y , which i s an extension of the information measure, compares the d i s t r i b u -t i o n between two h o s p i t a l s , measuring the difference between them, and the loss of information r e s u l t i n g from t h e i r fusion. The two most s i m i l a r 49 h o s p i t a l s are combined and t h i s process i s continued u n t i l the desired number of groups i s reached. The decision to stop the grouping process i s u sually made on a r b i t r a r y grounds but i s guided by the los s of i n f o r -mation at each stage. Various s t a t i s t i c a l t e s t s can be applied to the groups to test the within-group and between-group heterogeneity (Lance, Contandriopoulos, Thuy Nguyen, 1979, 11-13) and thereby derive the most d i s t i n c t i v e and the most homogenous groups. A second measure i s also used to group h o s p i t a l s — t h e Euclidean distance index. This i s used when other output v a r i a b l e s (related to teaching, research, outpatient care and other environmental factors) are included to characterize h o s p i t a l s , in addition to the diagnosis v a r i a b l e s (defined i n terms of ICDA). The index of s i m i l a r i t y based on information theory i s no longer applicable because of the d i v e r s i t y of v a r i a b l e s involved. These output v a r i a b l e s are presented i n Table 2.2. The number of diagnostic categories has been reduced from 98 to 18 to save on com-puter time and memory space. Lance et a l . f e l t the "diagnosis" v a r i a b l e ( d i s t r i b u t i o n of patient days by 18 ICDA codes) was the "most representative of h o s p i t a l output" and i t was given an a r b i t r a r y weight of 0.50; the other 12 v a r i a b l e s share an equal weight of .041667 (0.50-r 12). Euclidean distance indices were computed i n order to determine the optimal grouping of h o s p i t a l s , i . e . that grouping of hospit a l s which maximizes the between-group distance and minimizes the within-group distance. Of the 142 acute care h o s p i t a l s i n Quebec, 18 s p e c i a l h o s p i t a l s were excluded from the analysis and the remaining 124 h o s p i t a l s were grouped into 8 groups on the basis of the 2 indices of s i m i l a r i t y . Table 2.2. Quebec Approach - L i s t and Source of Output Variables (Lance, Contandriopoulas, Thuy Nguyen, 1979 1. Variables related to the TREATMENT OF INPATIENTS II . Variable related to the TREATMENT OF OUTPATIENTS - Dis t r i b u t i o n of patient-days by diagnosis (ICDA, 8th, two-digit c l a s s i f i c a t i o n ) . 1 - Average length of s t a y . 1 - Number of physicians by spe c i a l t y . ^ - general practioners - su r g i c a l s p e c i a l i s t s - medical s p e c i a l i s t s - laboratory s p e c i a l i s t s - r a d i o l o g i c a l s p e c i a l i s t s - D i s t r i b u t i o n of medical services.^ - hospital v i s i t s - external c l i n i c s v i s i t s - consultations - diagnostic and therapeutic procedures - su r g i c a l procedures r- other procedures - Age-sex d i s t r i b u t i o n of inpatients.^ - male, newborn - male, less than 1 year old - male, from 1 to 14 years old - male, from 15 to 44 years old - male, from 45 to 64 years old - male, from 65 years old and over - female, newborn - female, less than 1 year old - female, from 1 to 14 years old - female, from 15 to 44 years old - female, from 45 to 64 years old - female, from 65 years old and over - Cost of medical services i n external c l i n i c s . ^ I I I . Variable related to the TEACHING ROLE of hospitals - Number of interns and residents by s p e c i a l t y . ^ - interns - residents c l i n i c a l monitors - residents i n s u r g i c a l s p e c i a l t i e s - residents i n medical s p e c i a l t i e s - residents i n laboratory s p e c i a l t i e s - residents i n r a d i o l o g i c a l s p e c i a l t i e s - residents i n family medicine IV. Variable related to the RESEARCH ACTIVITIES of hospitals - % of research budget to admissible expenditures. 1 V. Variables related to ORGANIZATION FACTORS i n hospitals - Turnover rate of nursing personnel. 1 - Rate of occupancy. 1 - Number of separations per bed. 1 - Number of beds by s t a t u s . 1 - physical care short-term - physical care long-term ( r e h a b i l i t a t i o n ) - physical care long-term (convalescence) , - p s y c h i a t r i c care short-term - p s y c h i a t r i c care long-term - nursing home care - Index of distance from urban centres.^ 1 - Source: Ministry of Soci a l A f f a i r s , Financing Branch (according to forms DGF-1, or AH-101 f i l l e d i n by hospitals) 2 - Source: Quebec Professional Corporation of Physicians 3 - Source: Quebed Health Insurance Board 4 - Valued 0 i f the h o s p i t a l i s located in a town of 15,000 inhabitants or more; 1 i f i t i s 12 miles or less distance from a town of 15,000 or more; 2, i f i t i s 12 to 24 miles distance from such a town; 3, i f i t i s 24 to 36 miles distance from such a town; and 4, i f i t i s 36 miles and over distance from such a town. 51. Once the hospit a l s have been c l a s s i f i e d into groups the review process of budgetary bases proceeds to the next two stages: f i r s t , each h o s p i t a l within each group i s compared on a number of performance i n d i -cators to the average for the group, to determine whether i t i s i n a p o s i t i o n of r e l a t i v e excess or economy of resources; second, a p o l i c y i s developed for more equitable d i s t r i b u t i o n of t o t a l resources. 2.6.6. Ap p l i c a t i o n of the Information Theory Measure i n the U.S. Appl i c a t i o n of the information theory approach to the analysis of case mix complexity has not been confined to Canada. More recently the f i r s t studies have been undertaken i n the United States, t e s t i n g i t s a b i l i t y to predict h o s p i t a l costs i n a system that i s quite d i f f e r e n t from the Canadian system because i t i s neither regionalized nor v e r t i c a l l y integrated (Horn and Schumacher, 1979). Nevertheless, the researchers have demonstrated i t s a p p l i c a b i l i t y to the American health system [Horn and Schumacher (1979); Schumacher, Horn, Solnick, Cook and Atkinson (1980) ]. The f i r s t study applying the information theory measure of case mix complexity to U.S. data was undertaken by Horn and Schumacher (1979). They did not attempt to b u i l d t h i s measure of case mix complexity into a regression analysis i n order to predict h o s p i t a l costs. Rather t h e i r purpose was to compare t h i s measure with a c l i n i c a l measure of case mix complexity. The c l i n i c a l measure of case mix complexity was developed by Thompson, Fetter and others at Yale U n i v e r s i t y and Yale New Haven Hosp i t a l . More d e t a i l e d discussion of t h i s method occurs i n the next section. B r i e f l y , the method i s a way of c l a s s i f y i n g patients into 383 Diagnosis Related Groups (DRGs) which are mutually exclusive and 52 exhaustive categories with s i m i l a r c l i n i c a l a t t r i b u t e s i n terms of primary diagnosis, secondary diagnosis, s u r g i c a l procedures, age and sex and c l i n i c a l service. They also have s i m i l a r patterns of output u t i l i z a -t i o n as measured by length of stay. This scheme d i f f e r s from the most frequently applied d e f i n i t i o n of case mix, which i s based on the patient's primary diagnosis coded according to the International C l a s s i f i c a t i o n of Diseases Adapted (ICDA), i n the sense that i t not only s p e c i f i e s a diagnosis but r e l a t e s t h i s diagnostic information (and other demographic and therapeutic information) to output u t i l i z a t i o n , thus providing a measure of i t s r e l a t i v e complexity. Horn and Schumacher (1979) assumed that the degree of concentration (provided by T h e i l ' s expected information measure) of the 383 DRGs for a l l l i v e h o s p i t a l discharges from 45 Maryland h o s p i t a l s for the period October 1976 to March 1977, represented the r e l a t i v e complexity of each of these 383 DRGs. They then examined the index of complexity of the DRGs to see whether, i n t u i t i v e l y , i t provided a good measure of the complexity of diagnoses. They found 167 DRGs where i n t u i t i v e disagree-ments occurred—e.g. a DRG for a disease with surgery had a lower informa-t i o n theory complexity value than another DRG for the same disease without surgery. They revised the c l a s s i f i c a t i o n of DRGs from 383 to 272 and recalculated the r e l a t i v e complexity values. They then compared the information theory complexity numbers with "one author's (DNS) judgements as to whether the DRG was associated with high or low mortality and/or c l i n i c a l complexity" (Horn and Schumacher, 1979, 387). They found a s t a t i s t i c a l l y s i g n i f i c a n t agreement between the two measures of case mix complexity, which led them to conclude that "information theory has the po t e n t i a l to be useful i n quantifying case mix complexity" (388). 53 A l a t e r study by Schumacher, Horn, Solnick, Atkinson and Cook (1980) used t h i s information theoretic approach to obtain a measure of case mix complexity to analyse h o s p i t a l cost per case i n 216 acute hospit a l s i n Maryland. They used the 383 DRGs to define case mix rather than the 98 diagnostic categories from the ICDA which Evans and Walker (1972) had used. Regression equations were developed which predicted up to 88 percent of the variance i n i n t e r - h o s p i t a l cost per case, with the complexity v a r i a b l e being one of the most highly s i g n i f i c a n t p redictors. The r e s u l t s allowed for the i d e n t i f i c a t i o n of a number of high cost hospit a l s i l l u s t r a t i n g the p o t e n t i a l a p p l i c a t i o n of t h i s approach to a system of prospective cost per case reimbursement. 2.6.7. Diagnosis Related Groups (Fetter et a l . , 1980) The purpose of developing the patient c l a s s i f i c a t i o n scheme 20 known as the Diagnosis Related Groups (DRGs) was to define cases, not only i n terms of t h e i r c l i n i c a l a t t r i b u t e s but also i n terms of t h e i r u t i l i z a t i o n of h o s p i t a l f a c i l i t i e s . Each diagnostic category then represents "a c l a s s of patients with s i m i l a r processes of care and a predictable package of services (or product) from an i n s t i t u t i o n " (Fetter et a l . , 1980, 3). Thus the scheme of DRGs defines the t o t a l h o s p i t a l product with each patient cl a s s representing a p a r t i c u l a r pattern of 21 resource consumption (an 1isoresource' category i n Lave and Lave's [1971] terms). By est a b l i s h i n g t h i s r e l a t i o n s h i p between the case mix of the h o s p i t a l and the resources i t consumes, t h i s c l a s s i f i c a t i o n scheme i s p o t e n t i a l l y u s e f u l i n patient care monitoring, budgeting, cost c o n t r o l , reimbursement and planning (Fetter et a l . , . 1980, 2). The DRGs were constructed using three d i f f e r e n t types of inputs: physician judgment was required to ensure patient groups were medically 54 meaningful; data from acute h o s p i t a l s were examined to determine character-i s t i c s and frequency of actual discharges; a s t a t i s t i c a l algorithm was employ-ed to a s s i s t the formation of homogeneous patient classes defined i n terms of a s p e c i f i e d u t i l i z a t i o n measure. Length of stay (LOS) was chosen as the i n d i c a t o r of output u t i l i z a t i o n . They argue that "while i t may not be as accurate an i n d i c a t o r of the l e v e l of output as actual costs, i t i s s t i l l an important i n d i c a t o r of u t i l i z a t i o n as well as being e a s i l y a v a i l a b l e , well standardized and r e l i a b l e " (Fetter et a l . , 1971, 5). Lave and Leinhardt (1976) make a s i m i l a r claim about the importance of length of stay as an i n d i c a t o r of performance. The appropriateness of length of stay as an out-put i n d i c a t o r i s discussed l a t e r i n t h i s chapter. A l l diagnoses were i n i t i a l l y divided into 83 mutually exclusive and c o l l e c t i v e l y exhaustive Major Diagnostic Categories. This was performed by a committee of c l i n i c i a n s who developed these categories from the 1CDA8 and HICDA versions of the International C l a s s i f i c a t i o n of Diseases Adapted. The Major Diagnostic Categories were consistent i n terms of t h e i r anatomic and p h y s i o l o g i c a l c l a s s i f i c a t i o n as w e l l as patterns of c l i n i c a l management; they covered a l l codes with no overlap; there was a s i g n i f i c a n t number of patients i n each category. A consistent process was followed to p a r t i t i o n the 83 Major. Diagnostic Categories into 383 DRGs. F i r s t , a new computer system was developed that could handle large data bases e f f i c i e n t l y and operate on an i n t e r a c t i v e basis to accommodate c l i n i c a l input from physicians. This new system was c a l l e d AUTOGRP ( M i l l s , F etter, Riedel, A v e r i l l , 1976). It had the c a p a b i l i t y to draw on an algorithm that subdivides the 83 Major Diagnostic Groups into subgroups based on a number of p r e - s p e c i f i e d v a r i a b l e s that "maximize variance reduction or minimize the p r e d i c t i v e 22 error of the dependent v a r i a b l e " (Fetter et a l . , 1980, 6). The 55 Al Urinary Calculus Pafi»oti No S u r g e r y « 6 12 16 CO 2* 29 J2 length of stay [dcys) Pt««nc« of S4Cor*5aty Nonsurgical Group 0 « 8 12 16 20 24 28 32 length of stoy (days) DRG 239 Urinary CotcJu* >itr>our iUfQ#<T O 4 e 12 16 20 24 28 32 • length of stay ( d a y s ) Minor S u r g e r i e s i i2 '6 20 24 29 32 ler-jth of stay (days) ORG 24i 0 4 B 12 i6 20 24 28 32 length of stay (days) DRG 2 4 0 Lfciftof, Cotcul«j .(houl luigiry Mojor Surgeries n • 2 8 6 m « o n = 14 9 9 s d = 7 3 9 0 4-8 12 '6 20 2« 28 32 lervg,th 0f stay (daj») DRG 242 Urinary CoiCulul »ih n^ffi,orCKTIy_ CylTO«omj, u'«1«tolC"Tij, otn»f Figure 2.3. Summary o f l e n g t h s of stay d i s t r i b u t i o n for DRGs formed i n partxtionmg process. Source: Fetter et a l . (1980, 19, figu r e 2). 56 pre s p e c i f i e d independent variables were diagnoses, s u r g i c a l procedures, age, sex and c l i n i c a l service. The dependent v a r i a b l e , as stated e a r l i e r , was length of stay. The independent variables that yielded the highest percentage reduction i n variance of length of stay were the variables employed to divide the data set. Other factors were also considered: the groups had to be homogenous from a c l i n i c a l point of view; the number of groups had to be manageable; the means of the groups had to be s i g n i f i -cantly d i f f e r e n t from one another. Thus the r e s u l t i n g 383 DRGs were defined by some set of: the following patient a t t r i b u t e s : primary diagnosis, secondary diagnosis, primary s u r g i c a l procedure, secondary s u r g i c a l procedure, age, and ( i n one case) c l i n i c a l service area. Sex was included as an independent v a r i a b l e but i t was found not to be s i g n i f i c a n t i n reducing variance i n length of stay (see Figure 2.3). The structure of the DRGs varied considerably. Some Major Diagnostic Categories were not subdivided at a l l because p a r t i t i o n i n g on the basis of the defining variables did not produce sub-groups which were s i g n i f i c a n t l y d i f f e r e n t i n terms of the measure of output u t i l i z a t i o n (length of stay). On the other hand one Major Diagnostic Category 76, Fractures, was p a r t i t i o n e d into 13 subgroups or DRGs. The DRG scheme was constructed from a data base of 500,000 h o s p i t a l records from 118 ho s p i t a l s i n New Jersey, 150,000 records from one Connecticut h o s p i t a l and 52,000 records of f e d e r a l l y funded patients from 50 i n s t i t u t i o n s i n a PSRO region. Young, Swinkola and Hutton (1980) tested i t s external v a l i d i t y by applying the same method to the patient population of Western Pennsylvania. The 383 DRGs that were derived f o r the patient population i n New Jersey did not re-occur when the same 57 AUTOGRP c l a s s i f i c a t i o n algorithm was applied to Western Pennsylvania population data. They concluded that the patient c l a s s i f i c a t i o n scheme i s not independent of the population observed. These same researchers also tested the i n t e r n a l homogeneity of the 383 Diagnosis Related Groups to see i f they were comprised of patients who had a s i m i l a r pattern of resource consumption. They c l a s s i f i e d the Western Pennsylvania patients into the 383 DRGs as defined by Fetter et a l . They then applied the AUTOGRP c l a s s i f y algorithm to see i f the patients i n these classes could be p a r t i t i o n e d into other groups. In other words they took the actual length of stay of Pennsylvania patients i n these 383 DRGs and tested to see whether v a r i a t i o n i n the length of stay within a DRG could be s i g n i f i c a n t l y reduced i f the patients were divided on the basis of the same independent v a r i a b l e s (diagnoses, age, sex, s u r g i c a l operations, c l i n i c a l service) as Fetter et a l . (1980) had used. They also included some ad d i t i o n a l ; d e f i n i n g v a r i a b l e s . Their analysis revealed that s i g n i f i c a n t reduction i n v a r i a t i o n of length of stay could be achieved i n some DRGs by p a r t i t i o n i n g the patients into d i f f e r e n t groups on the basis of these independent v a r i a b l e s . They con-cluded that cases which were assumed to be s i m i l a r by Fetter et a l . were ei t h e r d i s s i m i l a r or else they were managed d i f f e r e n t l y i n d i f f e r e n t h o s p i t a l s . Another problem with the DRG c l a s s i f i c a t i o n scheme i s that i t assumes that the e f f e c t s of the defining v a r i a b l e s (age, surgery, etc.) are stable over time. This problem can be best explained by looking at an example. V a r i a t i o n i n length of stay for every urinary calculus patient (see Figure 2.3) i s reduced by the v a r i a b l e s , surgery and secondary diagnosis, to obtain 4 d i f f e r e n t DRGs. This occurred because 58 none of the other d e f i n i n g v a r i a bles (age, sex) had a s i g n i f i c a n t e f f e c t on v a r i a t i o n i n length of stay. It may have been that the patient sample from which t h i s scheme was developed had urinary calculus patients i n the same age-sex group. (This i s not a c r i t i c i s m of the sample as i t may represent the true pattern of urinary calculus among the population). However, i f over time, the incidence of urinary calculus changes so that i t a f f e c t s a d i f f e r s ent age-sex group, these variables may become s i g n i f i c a n t defining v ariables r e s u l t i n g i n d i f f e r e n t DRGs. The c r i t i c i s m i s that the DRG scheme i s a r e f -l e c t i o n of the age-sex structure and patterns of medical p r a c t i c e (both i n terms of therapeutic intervention and length of stay) that existed i n the o r i g i n a l patient population. This bias i s b u i l t into the scheme and cannot be adapted without a r e - d e f i n i t i o n of the t o t a l c l a s s i f i c a t i o n scheme. F i n a l l y , a minor c r i t i c i s m r e l a t e s to the exclusion of deaths from the data base i n the development of the DRGs. Fetter et a l . (1980, 8) remove them on the basis that t h e i r "lengths of stay were probably a t y p i c a l of the disease or problem under consideration". This i s the c a s e — t h e lengths of stay associated with deaths are unpredictable. They can be"either higher or lower than the average for the p a r t i c u l a r disease category to which they belong. However, i n the f i n a l a n a l y s i s , they are s t i l l a part of t o t a l costs and therefore should not be assumed away for the sake of s t a t i s t i c a l elegance. The general conclusion from t h i s c r i t i q u e of the DRGs i s that length of stay• i s not a good i n d i c a t o r of output u t i l i z a t i o n . It i s endogenous i n the sense that i t can be manipulated by the h o s p i t a l ; i t can vary s i g n i f i c a n t l y depending on medical pr a c t i c e patterns. Furthermore, i t does not c o r r e l a t e w e l l with actual costs because i t does not discriminate s u f f i c i e n t l y among d i f f e r e n t case types. For instance, t h e . r e l a t i v e complexity of a DRG i n terms of length of stay i s only a v a i l a b l e for DRGs within each of the 83 59 Major Diagnostic Groups. I t i s not possible to assume the cost of a case belonging to one Major Diagnostic Category i s the same as the cost of a case belonging to another Major Diagnostic Category simply because i t has the same length of stay. { The scheme i s already being applied to prospective cost per case reim-23 bursement i n the state of New Jersey. In t h i s state, a d i f f e r e n t i a l reim-bursement rate i s set for each DRG i n each h o s p i t a l . This rate i s established on the basis of a proportion of the actual cost of t r e a t i n g patients i n that DRG i n that h o s p i t a l and a proportion of the average cost of t r e a t i n g patients i n that DRG i n the state generally. These costs are obtained by a d e t a i l e d cost accounting approach described by Thompson, A v e r i l l and Fetter (1979) and the U.S. Department of Health Education and Welfare (1979). 2.6.8. Resource Need Index The Resource Need Index (RNI) has been developed by the Commission on Professional and Hospital A c t i v i t i e s (CPHA). I t i s an index-of the r e l a t i v e complexity of a h o s p i t a l ' s caseload defined i n terms of diagnosis and measured on the basis of average charge data. I t i s based on the assumption that charges are a proxy f o r actual costs and therefore, the index r e f l e c t s the r e l a t i v e costs or r e l a t i v e resource consumption of the h o s p i t a l . I t enables cost comparison among ho s p i t a l s and i s a t o o l to a s s i s t i n h o s p i t a l reimbursement. The Resource Need Index i s calculated from two f a c t o r s : case mix and Resource Need Units (RNUs). Case mix i s defined i n terms of the number of patients c l a s s i f i e d by diagnosis, age and whether or not surgery was performed. Cases are grouped into 349 categories which are reasonably homogeneous i n terms of diagnosis, patterns of care and length of stay. These groups are based on the Hospital Adaption of ICDA (H-ICDA) (Second E d i t i o n , CPHA) and 60 compatible with the f i r s t e d i t i o n of H-ICDA and ICDA-8. These diagnosis categories are subdivided into f i v e age groups (0-19, 20-34, 35-49, 50-64, 65 and over) and whether the patient received surgery or not. This gives a matrix of 3490 c e l l s into which a l l patients are c l a s s i f i e d . Charge information f or each c e l l i s obtained from CPHA's Study of Patient Charges (SPC). An average patient charge for each c e l l i s calculated from a data base con s i s t i n g of 2.8 m i l l i o n cases. It includes a l l patients (except deaths, patients transferred to another h o s p i t a l and patients staying over 70 days) from the 120 h o s p i t a l s p a r t i c i p a t i n g i n SPC f o r a l l or part of the three year period, 1974-77. These h o s p i t a l s vary i n the extent of t h e i r teaching program, i n s i z e from under 2,500 to over 25,000 discharges per year and represent a l l four census regions (Ament, 1976). A l l charge data 24 for the three years i s deflated to the 1971-72 d o l l a r value. The average charge for each c e l l i n the matrix i s the base upon which the Resource Need Index i s constructed. The r e l a t i o n s h i p between the average charge for a l l patients and the average charge i n each c e l l gives the r e l a t e ive value for that c e l l . This value i s known as the Resource Need Units (RNUs) for that c e l l . Average charge for a c e l l = RNUs (number of Resource Need Average charge for a l l patients Units f or that c e l l ) The RNUs are used to quantify the resources needed for a given mix of types of patients. This value i s known as the Resource Need Index (RNI). A RNI can be calculated f o r the h o s p i t a l as a whole or for i n d i v i d u a l services within the h o s p i t a l . If the RNI for the whole h o s p i t a l i s required, i t can be obtained by multi p l y i n g the RNUs i n each c e l l by the number of patients i n each c e l l and d i v i d i n g by the t o t a l number of patients i n the h o s p i t a l : 61 3490 RNI = (RNU. : P. . ) /P . i = l where P i s the number of patients i n h o s p i t a l j , c e l l i Pj i s the t o t a l number of patients i n h o s p i t a l j . See Figure 2.4. If h o s p i t a l j has an RNI of 2.00 and h o s p i t a l k has an RNI of 1.00, i t i s assumed h o s p i t a l j uses twice as many resources per case as h o s p i t a l k. The main c r i t i c i s m of the RNI i s i t s basic assumption that h o s p i t a l charge data i s a proxy f o r resource consumption. Goodisman and Trompeter (1979) examined the extent to which case mix (the proportion of patients f a l l -ing into 44 diagnostic categories and reduced by fac t o r analysis to 13 factors) explained average h o s p i t a l charges per case. They found that these case mix factors only explained about 58 percent of i n t e r - h o s p i t a l v a r i a t i o n i n average t o t a l charge per case. This was lower than the 72 percent of the v a r i a t i o n :" i n cost per case accounted f o r by Evans' (1971) diagnostic f a c t o r s . Goodisman and Trompeter (1979) concluded that t h i s weaker r e l a t i o n s h i p between case mix and charges v i s - a - v i s case mix and costs was explained by " i n t r a h o s p i t a l c ross-subsidization f or d i f f e r e n t treatments" (Goodisman and Trompeter, 1979, 54). Whatever the cause, t h i s lack of systematic c o v a r i a t i o n between per patient costs and per patient charges suggests that charges are not a good proxy for costs. Idea l l y the best way of assessing whether charges i n t h i s instance are a good proxy f o r costs would be to compare the average charge i n each diagnostic/ age/surgery category of the RNI matrix with the actual cost f i g u r e . CPHA has not done t h i s comparison because they do not have the equivalent cost data. However, we can assume from Goodisman and Trompeter's r e s u l t s that the r e l a t -ionship between case mix and charges i s not as strong as the r e l a t i o n s h i p 62 Average Charge Table from SPC M.L 0-4 9 :o-u 35-49 •i: ' *5 op op •» i"„"P" up OP Diagnosi  | ! Di»s,,„.i, ! I 1 1 Cholt-rjMili* t Diaen.^  346 1 Di^nusu 347 I 1 DtnRn>j%t% J4J 1 ! Diaenmi* 349 1 1 S5W* rt-f*'!*"1' ^ IO' * .11* J4W types of patients . . . the relationship between the average charge for all patients and the cell average gives the relative value for that cell Average charge for a cell Average charge for all patients = RNL's (the number of Resource Need Units for that cell) RNU Table DipncKi A(. l . 0~tt AUL 2"-U A M : .!?-«• 9 .1. ...... Croups op *>P op •P •P vp op •p •P •P Diagnosi  | Cholto&iti 1.5 Di«Enirii 346 Diagnosi  347 D i a g n o s i s 348 DUenfni* 349 1 Oeral A % nxzr from SPC Ps™ , , „ £» _ 1 |_SfOl> S500 "" J 3-190 t.vpes of patients RNI=Average number of RNUs per patient in any group of patients con-sidered. RNI~ S u m o f RNUs'  Total Number of Patients Figure 2.4. Steps involved i n converting average charge data to a Resource Need Index. Source: CPHA, What i s RNI? Ann Arbor: CPHA, 1978. 63 between case mix and costs. Another c r i t i c i s m of the RNI i s r e l a t e d to the method used to d e f l a t e charges to 1971-72 d o l l a r s . This adjustment method i s described i n footnote 24 of t h i s chapter. The d e f l a t i o n method i s not s e n s i t i v e enough to the d i f f -e r e n t i a l rates of p r i c e increase of f a c t o r inputs, i . e . wages and s a l a r i e s , supplies, drugs, food etc. Barer and Evans (1980) have shown that there i s quite s i g n i f i c a n t differences i n the rate of increase i n wages (115 percent growth over 7 years) compared to drugs ( f l a t p r i c e index _of 10.7 percent i n 7 years). These data indi c a t e the importance of d e f l a t i n g each factor p r i c e at a d i f f e r e n t rate. This i s not done i n the d e f l a t i o n of RNI charges which are a l l deflated at the same rate. Another p o t e n t i a l problem i s the c e l l r e l i a b i l i t y of the RNI matrix. The RNI matrix i s so large—3490 c e l l s — t h a t the small sample s i z e i n some c e l l s must reduce the r e l i a b i l i t y of the average charge f i g u r e . 2.6.9. Common Problems Two approaches discussed here define the complexity of case mix i n a h o s p i t a l i n terms of a sin g l e valued ( i . e . scalar) index which i s intended to capture the r e l a t i v e differences i n h o s p i t a l output. Evans and Walker, and l a t e r Barer, used information theory to define complexity values for 98 diag-n o s t i c categories. The case mix index for each h o s p i t a l i s the weighted sum of these values. Each diagnostic category has a r e l a t i v e weight and each hos-p i t a l has a r e l a t i v e index that i s d i r e c t l y r e l a t e d to these individual/weights The Resource Need Index i s constructed i n a s i m i l a r manner: each diagnostic c e l l i s assigned a Resource Need Unit value, which i s a r a t i o obtained by d i v -i d i n g the average charge for that c e l l by the average charge for a l l patients and the Resource Need Index f o r the h o s p i t a l i s derived by summing the Resource Need Units f or each patient and d i v i d i n g by the t o t a l number of pat i e n t s . Again there i s a d i r e c t r e l a t i o n s h i p between the values of the case mix weight assigned to the diagnostic category and the index derived f o r the h o s p i t a l . K l a s t o r i n and Watts (1980) c r i t i c i z e these approaches that reduce diag-n o s t i c c l a s s i f i c a t i o n data into a single-valued case mix index. They suggest-, as an a l t e r n a t i v e , a normative weighting process that i s divorced from actual p r a c t i c e . For example, "the appropriate indexing weights might be established by a panel of representative members of society without regard to differences i n the empirical c h a r a c t e r i s t i c s of case types (e.g. length of stay, cost, e t c . ) " ( K l a s t o r i n and Watts, 1980, 678). This suggestion appears fraught with i t s own problems. F i r s t , such an approach i s u n l i k e l y to produce a consensus i n the l i g h t of current evidence which indicates medical p r a c t i c e patterns are not uniform. Second, i t ra i s e s questions about how a "representative member of soc i e t y " i s defined. Surely a p o l i t i c i a n f i t s t h i s d e s c r i p t i o n p e r f e c t l y but how p r a c t i c a l and useful would i t be to have p o l i t i c i a n s performing t h i s task? They are u n l i k e l y to have the time to devote to such an exercise and they are u n l i k e l y to have the c l i n i c a l expertise to d i s t i n g u i s h between case types on the grounds of t h e i r r e l a t i v e complexity, e s p e c i a l l y without the assistance of empirical data such as length of stay and cost. I t seems that the only persons capable of performing t h i s task would be c l i n i c i a n s , who are not representative members of society and who would not be able to divorce themselves from t h e i r current p r a c t i c e patterns. A rather s i g n i f i c a n t problem common to these case mix standardizat-ion techniques discussed i n t h i s chapter i s t h e i r i n a b i l i t y to account f o r the se v e r i t y of a diagnosis. Patients are c l a s s i f i e d according to the r e l a t i v e complexity of t h e i r diagnosis v i s - a - v i s other diagnoses 65 but not according to the l e v e l s of s e v e r i t y or stages of t h e i r p a r t i c u l a r diagnosis. Gonnella and Goran (1975) i d e n t i f i e d three l e v e l s of s e v e r i t y : Stage I - disease with no complications or problem of minimal s e v e r i t y ; Stage II - disease with l o c a l complications or problem of moderate severity; Stage III - disease with systemic complications or a problem of a serious nature. Just as complexity of diagnosis has implications for resource usage,so does the severity of diagnosis. Garg et a l . (1978) used the staging mechanism developed by Gonnella and Goran to examine u t i l i z a t i o n of services for 24 diagnoses. They presented the r e s u l t s f or eight of these diagnoses and, as hypothesized, they found that patients with a more severe disease stage generated s u b s t a n t i a l l y higher t o t a l charges, a n c i l l a r y charges and had longer lengths of stay. Thus the severity of diagnosis does have implications for costs and should, i d e a l l y , be considered i n h o s p i t a l cost a n a l y s i s . However, the technique used to define the stages requires a s u b s t a n t i a l amount of physician input and so to define stages across a l l diagnostic categories would be a monumental task. The d e f i n i t i o n of stages also r e f l e c t s the p a r t i c u l a r medical p r a c t i c e patterns of the physicians providing the input which may not be uniform. If staging were included i n the standardization process, i t would add another dimension to the diagnosis matrix, which may make i t d i f f i c u l t or impossible to handle i n some approaches to case mix standardization. To date c l a s s i f i c a t i o n of severity has been used p r i -25 marily for u t i l i z a t i o n review and q u a l i t y review. Severity of diagnosis i s not to be confused with yet another dimension of case m i x — i n t e n s i t y , which r e f e r s to the quantity of resources required to treat a given type of case per day of stay 66 (Luke, 1979). This has implications for reimbursement schemes i f payment i s made on a per day basis. Restuccia and Murphy (1980) have used t h i s i n t e n s i t y measure i n t h e i r study of h o s p i t a l use and cost i n nine h o s p i t a l s i n Michigan. A t h i r d problem common to Lave and Lave (1971, 1972, 1973), the DRG scheme and the Resource Need Index i s the standardization of case mix i n terms of diagnosis, and whether or not surgery was performed. This standardization technique has a mixture of both input and output aspects: diagnosis i s a c h a r a c t e r i s t i c of the case and i s determined exogenously (not by the h o s p i t a l ) while surgery i s a c h a r a c t e r i s t i c of the way the case i s treated (and i s determined by the doctors at the h o s p i t a l ) . Thus, by including surgery i n the adjustment process, the measure of caseload i s contaminated by decisions the h o s p i t a l makes about t r e a t i n g that caseload. 2.7. Summary of Standardization of Output i n Terms of Case Mix E a r l i e r i n t h i s chapter i t was stated that prospective reimburse-ment w i l l only be e f f e c t i v e i n c o n t r o l l i n g costs i f the r e l a t i v e per-formance of the h o s p i t a l s can be evaluated i n order to set budgets r e a l i s t i c a l l y and a l l o c a t e resources equitably. This requires accurate standardization for case mix differences among h o s p i t a l s . This section summarizes the advantages and disadvantages of the various approaches to output standardization i n terms of case mix, from the point of view of 26 t h e i r usefulness i n s t r u c t u r i n g the h o s p i t a l reimbursement system. 2.7.1. Diagnostic Factor Proportions Evans (1971) showed that using diagnostic f a c t o r propor-tions to standardize for case mix differences was a dramatic improvement over previous attempts to standardize h o s p i t a l output on the basis of the 67 a v a i l a b i l i t y of services and f a c i l i t i e s i n the h o s p i t a l . This approach also explained more i n t e r - h o s p i t a l cost v a r i a t i o n than Feldstein's (1967) method of def i n i n g case mix i n terms of s p e c i a l t i e s . The main disadvan-tage of .this approach was the number of v a r i a b l e s required to represent case mix. 2.7.2. Information Theory Evans and Walker (1972) found the information theory approach to case mix standardization has a number of advantages: ( i ) case mix i s defined i n terms of a si n g l e v a r i a b l e which explains almost the same amount of i n t e r - h o s p i t a l cost v a r i a t i o n as the 10 diagnostic factor proportions; ( i i ) t h i s s i n g l e v a r i a b l e i s i n the form of an index which ranks ho s p i t a l s on a r e l a t i v e scale. Thus the r e l a t i v e complexity of a hos p i t a l ' s case mix can be e a s i l y q uantified; ( i i i ) i t can be used as an independent v a r i a b l e i n a regression equation (with average cost per case or per day as the dependent variable) to determine the r e l a t i v e e f f i c i e n c y of h o s p i t a l s . I t i s independent of average cost and there-fore, average cost does not appear on both sides of the equation; 27 (iv) the measure appears to be stable over time ; (v) a reimbursement scheme based on t h i s approach i s not e a s i l y manipulated by h o s p i t a l administrators. Even i f h o s p i t a l administrators could f i n d out which diagnostic categories are most l u c r a t i v e and they could sode patients accordingly, i t would not prove b e n e f i c i a l for very long. As more hospita l s became involved i n t h i s a c t i v i t y i t would ultimately a l t e r 68 the r e l a t i v e concentration of cases and a l t e r the r e l a t i v e diagnostic values. The disadvantages of the information theory approach are: (i) i t does not account for the sev e r i t y of a p a r t i c u l a r diagnosis — only i t s complexity i n r e l a t i o n to other diagnoses. ( i i ) there are some diagnostic c l a s s i f i c a t i o n s that are anomalous and do not f i t the assumption that increased concentration means greater case complexity. The rare cases occur i n small numbers and therefore should not a f f e c t the r e l a t i v e weighting of case values. The common but complex cases (myocardial i n f a r c t i o n ) s t i l l remain a problem. Despite i t s apparent advantages the information theory approach has not been incorporated into any reimbursement scheme i n eit h e r Canada or the United States. 2.7.3. Diagnosis Related Groups The major advantage of t h i s approach to case mix d e f i n i t i o n i s i t s purported a b i l i t y to r e f l e c t the resource use patterns of each diagnosis group. However, the test to see whether i t predicts h o s p i t a l costs better than a c l a s s i f i c a t i o n of patients using the ICDA has not been undertaken. Schumacher et "al. (1980) used the DRG scheme with information theory and found that i t was a good predictor of h o s p i t a l costs. However, they did not compare i t s p r e d i c t i v e a b i l i t y with the same measure of complexity based on the ICDA c l a s s i f i c a t i o n scheme. Young, Swinkola and Hutton (1980) tested the extenal v a l i d i t y of the DRGs by attempting to reproduce them using a d i f f e r e n t patient population. The 383 DRGs that were derived for the patient population of New Jersey did not re-occur, leading them to conclude that the patient 69 scheme i s not independent of the population observed. Another disadvantage of the DRG scheme i s that i t does not provide a simple rank or index of the r e l a t i v e complexity of each DRG. The r e l a t i v e complexity of a DRG i s only a v a i l a b l e for the DRGs within each of the 83 Major Diagnostic Groups and i s indicated by length of stay. Consequently i t i s not possible to compute an index f o r the h o s p i t a l simply on the basis of the length of stay value of the DRG. The scheme has to be used i n conjunction with another measure of complexity, e.g. information theory or cost information to determine the r e l a t i v e com-p l e x i t y of a ho s p i t a l ' s caseload. I f cost information i s used to quantify the r e l a t i v e complexity value of the DRG, and then values are used to construct an index for the ho s p i t a l s which i s then used as an independent v a r i a b l e i n a regression equation to explain i n t e r - h o s p i t a l cost d i f f e r e n c e s , the case mix values are not independent o f average cost (per case) and average cost appears on both sides of the equation. The DRG scheme has been applied to the reimbursement process i n the state of New Jersey. This was done i n i t i a l l y on the basis of a per day rate, f i x e d f o r each diagnostic category. However, t h i s approach had the disadvantage of encouraging longer lengths of stay. More recently, there has been a movement towards a cost per case reimbursement system. A rate per DRG was set i n advance f or each h o s p i t a l , based on the actual cost of t r e a t i n g patients i n that DRG i n that h o s p i t a l and the actual cost of t r e a t i n g patients i n that DRG for the state generally. This scheme runs the r i s k of another problem—hospitals . manipulating the l a b e l l i n g process of patients and c l a s s i f y i n g them inappropriately into more l u c r a t i v e DRGs. One way of overcoming t h i s problem would be to use information theory with the DRG c l a s s i f i c a t i o n 70 scheme to measure case mix complexity. This approach was applied i n Maryland by Schumacher et a l . (1980). In t h i s way h o s p i t a l case mix weights are determined exogenously by information theory and do not pro-vide the temptation for manipulation by h o s p i t a l administrators. More-over the case mix weights are not calculated on the basis of average costs. Consequently the case mix weight can be used as an independent var i a b l e i n a regression equation (with average cost per case as the dependent variable) and average cost per case does not appear on both sides of the equation. 2.7.4. Resource Need Index The advantages of the RNI as a method of standardizing h o s p i t a l output are: (i) i t i s not e a s i l y manipulated by h o s p i t a l administrators as they do not have access to the matrix of charges so they do not know the r e l a t i v e value of each diagnosis category, ( i i ) i t can be used as an independent v a r i a b l e i n a regression equation with average cost per case as the dependent v a r i a b l e , ( i i i ) i t ranks h o s p i t a l s on a r e l a t i v e scale so the difference between hospita l s can be quantified. The disadvantages of the RNI include: (i ) i t s assumption that average charge data i s a proxy for actual h o s p i t a l costs. ( i i ) i t s inadequate method of adjusting the charge data to constant d o l l a r s . These comments on the r e l a t i v e merits of each approach are based on a p r i o r i reasoning and a v a i l a b l e empirical evidence. Most of the empirical work, however, i s not a d i r e c t comparison of approaches to 71 case mix standardization. They are usually tests of the extent to which a p a r t i c u l a r approach explains case mix v a r i a t i o n . The purpose of t h i s study i s to compare two d i f f e r e n t approaches—the information theory approach and the Resource Need Index—by examining the extent to which they explain i n t e r - h o s p i t a l cost differences f o r hospit a l s i n Alberta. 72 Reference Notes, Chapter 2 1. For the o r i g i n a l discussions of the p e c u l i a r i t i e s of the health industry see Klarman (1965), Arrow (1973), Culyer (1973). 2. This estimate was made by the U.S. Congressional Budget O f f i c e (1979). There i s no si n g l e data source which provides a l l the information on the type and extent of health insurance coverage. However, more than 80 percent of people with private coverage are members of group health plans. The majority of workers with group health plans are covered for h o s p i t a l inpatient and outpatient care. Therefore we can assume that a l l people with private and public insurance coverage are covered for h o s p i t a l care. 3. In fa c t i t may be much more appropriate and r e a l i s t i c to determine economies of scale f or p a r t i c u l a r services within h o s p i t a l s . This has been considered by Lee and Wallace (1973), Jenkins (1979) and a more s p e c i f i c study of emergency service has been done by P h i l l i p (1969). 4. Useful reviews of the l i t e r a t u r e concerned with measuring h o s p i t a l output have been undertaken by Berki (1972), Migue and Belanger (1974), T a t c h e l l (1980). 5. For instance equation 16, Table 2 (Berry, 1967, 137) has a PD (patient days) c o e f f i c i e n t of .001. This suggests that the actual d i f f e r e n c e i n average cost between a h o s p i t a l with 15,000 patient days and a h o s p i t a l with 30,000 patient days i s only $1.50. This i s not very meaningful i n p o l i c y terms despite the fact that the coef-f i c i e n t i s s t a t i s t i c a l l y s i g n i f i c a n t . 6. Among the most important factors were medical education, basic services, complex services, length of stay, outpatient a c t i v i t i e s . 7. The 13 i d e n t i f i e d services are: operations (weighted), d e l i v e r i e s , diagnostic x-rays, laboratory examinations, phy s i c a l therapy t r e a t -ments, electrocardiograms, therapeutic x-ray treatment, blood trans-fusions, newborn days, outpatient v i s i t s , electroencephalograms, emergency room treatments, and adult and p a e d i a t r i c days (Cohen, 1967, 360). 8. Reviews of these early cost studies have been undertaken by Mann and Yett (1968), Hefty (1969) and Lave (1966). 9. A review of t h i s book has been written by Lave and Lave (1970c). 10. F e l d s t e i n started with 28 s p e c i a l t y categories but he was not able to handle t h i s number with the computer f a c i l i t i e s a v a i l a b l e . 11. Reimbursement schemes have been reviewed by Bauer and Densen (1974), Dowling (1974), and Chassin (1978). 73 12. Blue Cross of Western Pennsylvania conducted some of the early experiments with i n d u s t r i a l engineering. See Hardwick and Wolfe (1970), Hardwick and Wolfe (1972), and McCarthy (1975). 13. This i s described by E l n i c k i (1975). 14. May (1972) questioned whether ho s p i t a l s were responsive to the p o t e n t i a l for achieving surpluses. 15. Feldstein's work was discussed i n the 'economies of scale' section, e a r l i e r i n t h i s chapter. 16. Comparative studies of patient c l a s s i f i c a t i o n schemes were under-taken subsequently by Lee and Wallace (1972) and Rafferty (1972). Lee and Wallace (1972) compared f i v e d i f f e r e n t c l a s s i f i c a t i o n schemes based on (1) duration and extent of d i s a b i l i t y , (2) r i s k of dying, (3) c e l l u l a r processes within the body, (4) 17 broad ICDA codes, and (5) medical s p e c i a l t i e s . Rafferty (1972) also compared f i v e d i f f e r e n t ways of c l a s s i f y i n g patients according to 50 leading diagnoses, 44 diagnostic categories, 17 c l i n i c a l service departments, 3 age groups and 2 broad categories—-medical and s u r g i c a l . These researchers showed that the c l a s s i f i c a t i o n based on s p e c i f i c diagnoses and medical s p e c i a l t i e s explained more of the v a r i a t i o n i n case mix than the a l t e r n a t i v e schemes to which they were compared. 17. The authors believed a p r i o r i that t h i s t h i r d approach would be better because i t was 'purposive' i n that " i t embodies whatever p r i o r know-ledge and best a v a i l a b l e estimates one has of the marginal costs of the various case mix variables to c l u s t e r them" (Lave, Lave and Silverman, 1972, 172). 18. See Evans and Walker (1972) or Walker (1976) or Barer (1977) or Horn and Schumacher (1979) for the mathematical d e r i v a t i o n of t h i s index. 19. In addition to the two a l t e r n a t i v e measures of h o s p i t a l complexity, information theory can be used to y i e l d three a l t e r n a t i v e measures of s p e c i a l i z a t i o n : SPCLC1 i s a v a r i a b l e which measures the v a r i a t i o n i n the proportion of each h o s p i t a l ' s caseload f a l l i n g into p a r t i c u l a r diagnostic categories r e l a t i v e to the proportions of d i f f e r e n t diagnoses i n the t o t a l caseload of the province; SPCLC2 i s the same as SPCLC1 only the base measure i s not the proportions of t o t a l caseload but the mix of the average h o s p i t a l ; SPCLC3 i s derived using -jjj- as a " p r i o r " d i s t r i b u t i o n , beginning from the assumption that there are equal numbers of cases i n each diagnostic c l a s s . 20. This was f i r s t described by Thompson, Fetter and Mross (1975) and most recently by Fe t t e r , Shin, Freeman, A v e r i l l and Thompson (1980). 21. Lave and Lave (1971) coined t h i s phrase to describe case mix defined i n terms of the amount and type of resources necessary to treat d i f f e r e n t types of patients. 74 22. This s t a t i s t i c a l methodology i s a v a r i a t i o n of the Automated Inter-action Detector (AID) method of Sonquist and Morgan (1964). 23. For a more de t a i l e d d e s c r i p t i o n of t h i s a p p l i c a t i o n i n New Jersey, see U.S. Department of Health, Education and Welfare (1979) and Fetter et a l . (1980). Also see Smedja (1977). 24. This d e f l a t i o n method i s described by Ament and Loup (1974, note 1). To summarize: data on the f i r s t h a l f year's patients were used to bu i l d a preliminary base table giving charges norms (average gross charges) for each c e l l i n the matrix. Then for each half-year's data for each h o s p i t a l , a cor r e c t i o n factor was obtained as follows: "For each patient i n the h o s p i t a l the appropriate c e l l was i d e n t i f i e d and the corresponding charges norm looked up i n the preliminary base table. The sum of these charges norms across the h o s p i t a l was divided by the sum of the actual gross charges to give the c o r r e c t i o n f a c t o r . F i n a l l y , before accumulating the charges figure for b u i l d i n g the current base table, each patient's gross charge was m u l t i p l i e d by his h o s p i t a l ' s c o r r e c t i o n factor for the relevant h a l f year" (Ament and Loup, 1975, 5). 25. A discussion of severity index development i s presented by Krischer (1976), Krischer (1979), O ' N e i l l , Zador, Baker (1979). These indexes have a va r i e t y of purposes from p r e d i c t i n g mortality (Cumulative I l l n e s s Rating Scale) to the t r i a g e of trauma patients (Trauma Index). 26. Bentley and Butler (1979) provide a useful summary of some case mix measures and t h e i r reimbursement ap p l i c a t i o n s . 27. This was shown i n Barer's (1977) time series analysis of B.C. h o s p i t a l s . 75 Chapter 3. Methodology for the Comparison of Two Approaches to Case Mix Standardization; Information Theory  and the Resource Need Index A major problem facing p r o v i n c i a l governments i n Canada, and reimbursing agencies generally, i n t h e i r e f f o r t s to contain h o s p i t a l costs, i s that of the d i s t r i b u t i o n of funds between hospita l s i n an equitable and e f f i c i e n t manner, taking adequate account of differences i n h o s p i t a l output. Chapter 2 reviewed various methods of h o s p i t a l reimbursement. F i r s t , i t described why the assumptions of n e o c l a s s i c a l economic theory do not hold f or the h o s p i t a l i n d u s t r y — i n h e r e n t p e c u l i a r i t i e s make i t meaningless to t a l k i n terms of a technologically e f f i c i e n t cost curve i n the t r a d i t i o n a l sense. A cost-output r e l a t i o n can be estimated that describes the way i n which hospit a l s operate. The r e l a t i v e l y e f f i c i e n t or i n e f f i c i e n t h o s p i t a l s can be i d e n t i f i e d but i t i s not possible to determine whether the average cost-output behaviour i s the t e c h n i c a l l y most e f f i c i e n t . However, accurate estimation of t h i s cost-output equation depends upon standardizing f or the heterogeneous nature of the h o s p i t a l output. So Chapter 2 also examines the various methods used to standardize h o s p i t a l output. These ranged from standardization i n terms of ( i ) services and f a c i l i t i e s a v a i l a b l e , ( i i ) services performed, ( i i i ) case mix. Output standardization defined i n terms of case mix was the most accurate approach, contributing more to the explanation of i n t e r - h o s p i t a l 76 cost v a r i a t i o n than the other approaches. A v a r i e t y of techniques have been used to achieve t h i s form of output standardization. They include (i ) factor proportions, ( i i ) information theory, ( i i i ) Diagnosis Related Groups, (iv) Resource Need Index. A p p l i c a t i o n of these approaches to the reimbursement process has been described i n d e t a i l i n Chapter 2. The empirical section of t h i s thesis aims to compare the (extent to which two of these approaches explain i n t e r - h o s p i t a l cost differences i n Alberta. The two approaches are information theory and the Resource Need Index (RNI). By comparing the explanatory power of these two approaches to case mix standardization, i t i s hoped that we can determine which, i f e i t h e r , could be used to improve the reimbursement process i n the province of Alberta. 3.1. Form of the Hospital Equation The methodology involves developing a behavioural (as opposed to a technological) cost equation. The form of the h o s p i t a l cost equation i s derived from the work of Evans and Walker (1972) and Barer (1977)."'" The r e p l i c a t i o n of t h e i r model here i s quite deliberate as they have shown i t to consist of a s e r i e s of p l a u s i b l e variables that f i t well elsewhere. As the purpose of t h i s thesis i s to assess the r e l a t i v e merits of the two measures of case mix (RNI and information theory measures of case mix complexity) i t seems appropriate to do t h i s evalua-t i o n i n the context of a model whose variables and o v e r a l l explanatory power have been tested and shown to f i t w e l l i n another s e t t i n g . The focus thus remains on the explanatory power of the two major case mix variables and not on the j u s t i f i c a t i o n f o r the other variables used. 77 "We proceed from an i n i t i a l assumption—that h o s p i t a l inpatient costs are comprised of a fixed (per bed) and a va r i a b l e (per case) component. In addition, we allow for possible n o n - l i n e a r i t y i n the capacity v a r i a b l e by entering beds i n quadratic form. S p e c i f i c a l l y , we are assuming that 2 TC = p 1B + P 2 B + P 3 (other variables) C where TC = t o t a l inpatient costs B = rated bed capacity C = cases (separations i n year)" (Barer, 1977,' 111). p^,P2 = parameters expressing the influence of bed s i z e on t o t a l cost (marginal cost being measured by [p'^ + 2p^]) • p^ = a function which r e f l e c t s the influence of cases on t o t a l costs, constructed below. Case here r e f e r s to a l l separations, i . e . discharges, deaths and transfers of a l l patients (including newborns). 'Total costs' r e f e r s to inpa t i e n t a c t i v i t y costs only and excludes costs associated with out-patient and emergency services, teaching, research, and non-departmental expenses (including i n t e r e s t on loans, depreciation on land improvement, depreciation on buildings and service equipment, depreciation on major 2 equipment and r e n t a l expenses). Case mix for each h o s p i t a l i s represented by the information theory complexity measure, CMPXC1, and s p e c i a l i z a t i o n measure, SPCLC1 (to be defined below), or by the Resource Need Index (RNI). In addition a set of v a r i a b l e s , F^ to F^, i s included to adjust for the influence of the age-sex d i s t r i b u t i o n . (No separate age-sex variables are included i n the equations with the RNI because age i s included i n the construction of the RNI.) It i s also hypothesized that the cost of a s p e c i f i c case i s a function of average length of stay, wage l e v e l s within a h o s p i t a l , and of the s k i l l mix of non-medical s t a f f personnel attending to the patients. 78 Three a d d i t i o n a l variables ALS, WAGEL and WAGE2, are included to 3 represent these f a c t o r s . Furthermore, there are some non-inpatient costs which may have an e f f e c t on inpatient a c t i v i t y . For example, education i s not a d i r e c t inpatient expense but there can be no doubt that teaching must a f f e c t the nature of inpatient care. Thus two v a r i a b l e s , EDRAT and OUTXPD, f o r 4 education and outpatient expenses, are included here. Their purpose i s two-fold: " ( 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 s p e c i f i c a l l y delineated as being comprised of expenditures only for those functions, and ( i i ) they provide a check on the success of our non-inpatient expenditure elimination." (Barer, 1977, 116-117) The standardization procedure y i e l d s a function, p^, which can be expressed as follows: 9 P 3 = a Q + a^CMPXCl + a 2SPCLCl + £ a ± + 2 F ± i = l a,„ EDRAT + a,o0UTXPD + a..WAGE1 + a,„WAGE2 + a.,ALS 12 13 14 15 16 and, a l t e r n a t i v e l y , p„ = an + a,RNI + a_EDRAT + ao0UTXPD + a.WAGE1 3 0 1 2 3 4 + arWAGE2 + a,ALS 5 6 The v a r i a b l e s here can be described as follows: "CMPXC1 - . . . t h i s v a r i a b l e i s intended to capture differences across h o s p i t a l s i n case-mix proportions and i s a measure of the complexity of h o s p i t a l case load; SPCLC1 - a measure of h o s p i t a l s p e c i a l i z a t i o n i . e . an i n d i c a t i o n of the degree to which a h o s p i t a l i s l i m i t e d i n i t s capacity to handle a wide range of case types. " . . . i n general we expect small h o s p i t a l s to be more sp e c i a l i z e d as they are geared up to handle only a smaller range of cases.' (Evans & Walker, 1972, 402) 79 F -F 1 9 the factor scores from a factor analysis of the inpatient age-sex d i s t r i b u t i o n of cases across h o s p i t a l s . WAGE1 - a r e l a t i v e measure of the degree to which a h o s p i t a l u t i l i z e s a s k i l l - i n t e n s i v e non-medical s t a f f labour force. WAGE2 - a r e l a t i v e measure of the wage l e v e l of non-medical s t a f f personnel." (Barer, 1977, 117) EDRAT - r e f l e c t s the share of h o s p i t a l expenditure devoted to educational a c t i v i e s . OUTXPD - r e f l e c t s the share of h o s p i t a l expenditure devoted to outpatient a c t i v i t i e s . RNI - Resource Need Index - index r e f l e c t i n g the complexity of the ho s p i t a l ' s caseload defined i n terms of diagnosis, age and whether the patient received an operation, and measured on the basis of American average charge data. ALS - i s the average length of stay for a l l patients i n the ho s p i t a l . A more d e t a i l e d d e s c r i p t i o n of these v a r i a b l e s w i l l be provided i n a l a t e r section. Having defined t h i s p^ function i t i s possible to derive an average cost per case equation, CASEX, by d i v i d i n g the t o t a l cost equation by the t o t a l number of cases. o TC = p 1B + p 2B + P 3 (other variables) C now becomes 9 TC 2 _ -CASEX = = a + p B + P B + a CMPXC1 + a SPCLC1 + ^ a F. —— —-— 1=1 .+ a. „EDRAT + a, .OUTXPD + a. ,WAGE1 + a. _WAGE2 12 13 14 15 and + a,.ALS 16 TC ? CASEX = - ± = a + p B + p„B^ + a RNI + a EDRAT L» U X Z X Z. + a^OUTXPD + a,WAGE1 + a WAGE2 + a^ALS 3 4 5 6 80 In a s i m i l a r fashion i t i s possible to derive an average cost per inpatient day equation, DAYEX, by d i v i d i n g t o t a l inpatient costs by t o t a l days. Thus we derive DAYEX i n the following manner: DAYEX = = b Q + q LB + q 2B + b^MPXCl ~~D~ ~D 9 + b.SPCLCl + * b.. , 0 F. 2 i = l i+2 l + b,-EDRAT + b l o0UTXPD + b-.WAGEl + b.,CWAGE2 12 13 14 15 + b.-ALS 16 and TC ? DAYEX = — = b Q + q B + q B + bjRNI + b2EDRAT D ~D + b„0UTXPD + b.WAGEl + brWAGE2 + b rALS 3 4 5 6 3.2. Sources of Data 3.2.1. Hospitals The data f o r t h i s study are taken from 112 acute care h o s p i t a l s i n Alberta. Table 3.1 shows the t o t a l number of hos p i t a l s i n Alberta i n each s i z e category. This table shows there i s a large number of h o s p i t a l s i n the 25-99 bed size range. In fac t 68 percent of a l l h o s p i t a l s are i n t h i s category. The seven i n s t i t u t i o n s i n the two largest bed s i z e categories are a l l located i n the two major c i t i e s , Calgary and Edmonton. Table 3.1 reveals a t o t a l of 124 h o s p i t a l s . For the purpose of t h i s study only 112 hos p i t a l s were included. Seven ho s p i t a l s were excluded because data e i t h e r on t h e i r expenditures or case mix were 81 unavailable. A further f i v e h o s p i t a l s were excluded because they were a t y p i c a l and may have u n f a i r l y biased the r e s u l t s . The data for two hosp i t a l s i n Calgary were combined and are counted as one i n s t i t u t i o n as they submit a j o i n t Annual Return. The expenditures, f a c i l i t i e s and patient case mix data for these ho s p i t a l s are derived from two major sources: (i ) The h o s p i t a l annual return. Each h o s p i t a l i s required to submit an annual return to S t a t i s t i c s Canada, which consists of two parts, known as the HS-1 and the HS-2 forms. They contain a record of the f a c i l i t i e s and services of the h o s p i t a l as well as the f i n a n c i a l state-ments . ( i i ) The PAS abstract. Nearly a l l Alberta h o s p i t a l s subscribe to the Patient A c t i v i t y Study (PAS), a service offered by CPHA i n Ann Arbor, Michigan. This abstract records patient morbidity information and d e t a i l s of other patient c h a r a c t e r i s t i c s such as age and sex. Diagnosis i s coded according to the International C l a s s i f i c a t i o n of Diseases Adapted (ICDA) and grouped into 188 broad diagnostic categories for the purpose of i n t e r - h o s p i t a l comparisons. The raw data required for the development of both the information theory case mix complexity variables (CMPXC1 and SPCLC1) and the RNI come from t h i s PAS abstract. 3.2.2. Time Period This study i s a cross s e c t i o n a l analysis of h o s p i t a l costs for the period A p r i l 1978 to March 1979 using information from the annual returns. Unfortunately morbidity data from the PAS abstracts are not a v a i l a b l e for the same time period. Although these data are compiled on an annual basis, the yearly time period i s from January to December and not from A p r i l to March. So the case mix complexity variables are 82 Table 3.1. Hospital and Bed D i s t r i b u t i o n , Alberta, 1979 HOSPITAL BEDS Size Category No. Percent No. Percent 1000 - up 1 .81 1236 10.00 500 - 999 6 2 4.88 4529 36.63 300 - 499 3 2.44 1074 8.69 100 - 299 10 8.13 1583 12.80 50 - 99 28 22.76 1749 14.15 25 - 49 56 45.53 1869 15.12 1 - 24 19 15.45 324 2.62 TOTAL 1232 100.00 12364 100.00 1 - Beds i n Public and Federal General Hospitals. 2 - Includes Calgary Holy Cross and Calgary Rockyview as one i n s t i t u t i o n because t h e i r h o s p i t a l cost reporting i s combined. Source: Alberta Hospitals and Medical Care, Hospital Care In Alberta, S t a t i s t i c a l Supplement, for the year ended March 31, 1979, Edmonton: Health Economics and S t a t i s t i c s Branch, June 1980. 83' developed from data for the period, January to December, 1978; the expenditure data i s for the period A p r i l 1978 to March 1979. Barer (1977) provides evidence which suggests that case mix complexity, as estimated using information theory, i s extremely stable over periods of much longer than three months. Thus we are making two assumptions i n t h i s a n a l y s i s : ( i ) that case complexities do not vary s i g n i f i c a n t l y over a period of three months, ( i i ) that an i n d i v i d u a l h o s p i t a l ' s case mix over two twelve month periods, staggered by three months but with nine months overlapping, w i l l be equivalent. 3.3. Variables In t h i s section each of the variables i n the equation i s described i n d e t a i l . This d e s c r i p t i o n i s borrowed, for the most part, from Barer (1977). S i m i l a r l y the computer programs used to derive these variables were developed by Barer (1977) with only minor modifications needed to make them adaptable to 1978-79 data. 3.3.1. Dependent Variables (1) Average cost per case (CASEX) To quote d i r e c t l y from Barer (1977): "CASEX i s formally defined as inpatient cost per h o s p i t a l separa-t i o n . Thus i t i s t o t a l expenditure on inpatient care divided by number of separations. From t o t a l h o s p i t a l expenditure (TOTEX) as reported i n the HS-2 form, the following items were subtracted to a r r i v e at an estimate of in-patient expenditure (IPEXP): (i ) expenditure on nursing and medical education;" ( i i ) non-departmental expenses, which include rent on land and buildings?, and depreciation and i n t e r e s t on long term loans^. " ( i i i ) expenditure on s p e c i a l research projects; (iv) share of administration expenses a l l o c a t a b l e to non-inpatient care (see below); (v) estimated d i r e c t outpatient expenses which includes expenditure on the organized outpatient department, outpatient portion of radiology and laboratory depart-ment expenses, outpatient share of emergency department expenses, a l l ambulance service expenses, outpatient share of operating room expenditure, and outpatient physiotherapy expenses . With regard to item (iv) t o t a l administrative expenses were i n i t i a l l y subtracted, a f t e r which the following adjustment was undertaken to add back the inpatient share of administration services: Let IP = TOTEX - (items ( i ) , ( i i ) , ( i i i ) & (v) above, plus t o t a l administration expenses (ADMIN)). Thus, the i n i t i a l d e l e t i o n of non-inpatient expenses includes the e n t i r e administrative expenditure component. Now, i f we denote the inpatient share of administration by IPADMIN, and items ( i ) , ( i i ) , ( i i i ) and (v) together, by NONIP, i t follows that ADMIN = TOTEX - IP - NONIP. If we then,presume'that administrative a c t i v i t y i s a l l o c a t e d according IPADMIN = ADMIN • IP IP+NONIP = ADMIN • IP (TOTEX-ADMIN) Adding t h i s back to IP, we a r r i v e at IPEXP = IP + IP ADMIN,. = t o t a l inpatient expenditure. Thus, the inpatient share of t o t a l non-administrative expenses was used as the inpatient weight on administration expenses. Then, CASEX = IPEXP/SEPNS (SEPNS = number of separations)" (Barer, 1977, 129-131) 85 (2) Average cost per day (DAYEX) DAYEX i s formally defined as inpatient cost per h o s p i t a l day. Thus i t i s t o t a l expenditure on inpatient care divided by the t o t a l number of patient days."^ (See previous discussion of CASEX for an explanation of the method of estimating inpatient expenditure.) 3.3.2. Independent Variables (i ) Size/Capacity (INVCFR, BDCFR, INVDFR, BDDFR) In the o r i g i n a l Evans-Walker (1972) equation the v a r i a b l e CFR (case flow rate) i s used as a measure f or the number of cases per bed Q per year (cases divided by beds, —) . CFR = f In the CASEX equation, defined e a r l i e r i n t h i s chapter, there are two v a r i a b l e s which express t h i s same size r e l a t i o n s h i p — b e d s divided B B 2 by cases ( — ) and beds squared divided by cases ( — ). The v a r i a b l e , B 1 — , i s the CFR v a r i a b l e inverted, ( — )• This v a r i a b l e i s given the C „ CrR notation, INVCFR. S i m i l a r l y , — i s B*INVCFR, and i s given the notation, BDCFR. B B 2 In the DAYEX equation, the variables — and — are given the notation INVDFR, BDDFR res p e c t i v e l y , ( i i ) Case mix complexity CMPXC1 The v a r i a b l e , CMPXC1, i s derived from information theory and i s the same v a r i a b l e used by Evans and Walker (1972) and Barer (1977). The mathematical formulation of th i s measure i s described i n d e t a i l by Evans and Walker (1972), Walker (1976), Barer (1977) and Horn and Schumacher (1979), so i t w i l l not be repeated here. " B a s i c a l l y , h o s p i t a l complexity (CMPXC1) i s a weighted sum of the (standardized) complexities 86 of cases treated i n the h o s p i t a l , the weights being the proportion of t o t a l case load f a l l i n g within each case category" (Barer, 1977, 132). The value for each case type i s derived from the a p p l i c a t i o n of informa-t i o n theory and i s a function of the r e l a t i v e concentration of each case type throughout the h o s p i t a l system. The case type c l a s s i f i c a t i o n i s the 188 diagnostic category matrix of the Canadian Hospital Morbidity L i s t . The i n d i v i d u a l h o s p i t a l values can be seen i n Appendix 3.1, Table 3.3. SPCLC1 Information theory can be used to develop a measure of the s p e c i a l i z a t i o n of the h o s p i t a l . This r e f e r s to the range of d i f f e r e n t case types treated by the h o s p i t a l . Thus a small h o s p i t a l , with a r e l a t i v e l y small caseload, w i l l probably be highly s p e c i a l i z e d because the v a r i e t y of i t s case types w i l l not be very great. On the other hand, a large h o s p i t a l , which admits many complex case types w i l l not be as sp e c i a l i z e d because the range of d i f f e r e n t types of cases w i l l be much greater. The base for developing t h i s measure i s the p r o v i n c i a l case d i s t r i b u t i o n . The degree to which each h o s p i t a l ' s case mix proportions deviates from the p r o v i n c i a l proportions, the larger the information gain and the greater the value of the ho s p i t a l ' s s p e c i a l i z a t i o n measure. The i n d i v i d u a l h o s p i t a l s p e c i a l i z a t i o n values, SPCLC1, are contained i n Appendix 3.1, Table 3.3.^ RNI The development of the Resource Need Index has been described i n d e t a i l i n Chapter 2. B r i e f l y the index i s a measure of the complexity of the hosp i t a l ' s caseload. Complexity i s defined as the r e l a t i v e "expensiveness" of each case type, measured i n terms of the average 87 charges for those case types i n U.S. h o s p i t a l s . An index i s produced for each h o s p i t a l by assigning a r e l a t i v e value to each case category, then determining the proportion of the hos p i t a l ' s caseload i n each category and summing across a l l categories. The value of the index for each h o s p i t a l i s provided i n Appendix 3.1, Table 3.3. ( i i i ) Age-sex factor scores (F , F^, F^, F^, F , F ^ F^, F g , F g) Both diagnosis and age of-patient are accounted for i n the construc-t i o n of the RNI. However, the information theory measure of case complexity i s based on diagnosis information only. Since i t i s i n t u i t i v e l y p l a u s i b l e that both' age and sex could influence v a r i a t i o n i n cost per case, age-sex factor scores are developed to be used as a d d i t i o n a l v a r i a b l e s in.the equation using CMPXC1 as the measure of case mix. The d e s c r i p t i o n of the construction of these variables i s taken almost d i r e c t l y from Barer (1977): "The f i r s t stage i n constructing age/sex standardization v a r i -ables involved disaggregating the inpatient separations into an age-sex g r i d based on age at the date of admission. This matrix contained 40 columns (one row per hospital) as follows .,,12 Column 1 male newborn 2 " under 1 year 3 " 1-4 years 4 " 5-9 years 5 " 10-14 years Column 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 male 15-19 years " 20-24 years " 25-29 years " 30-34 years " 35-39 years " 40-44 years " 45-49 years " 50-54 years " 55-59 years " 60-64 years " 65-69 years " 70-74 years " 75-79 years " 80-84 years " 85+ years female newborn " under 1 year " 1- 4 years " 5- 9 years " 10-14 years " 15-19 years " 20-24 years " 25-29 years " 30-34 years " 35-39 years » 40-44 years " 45-49 years Column 33 female 50-54 years 34 " 55-59 years 35 11 60-64 years 36 " 65-69 years 37 " 70-74 years 38 " 75-79 years 39 " 80-84 years 40 " 85+ years The age-sex matrix was then standardized, by row, through con-version of the actual numbers to proportions of the t o t a l caseload for each h o s p i t a l , so that each row summed to one. "A factor analysis of the 40 standardized case proportion vectors was then employed to derive age/sex factor scores. In p a r t i c u l a r , factors were derived . . . by the p r i n c i p a l component method. The factors were then rotated using the varimax procedure and factor scores were computed through regression analysis. It i s these factor scores which were then employed as independent variables i n our a n a l y s i s " (Barer, 1977, 142-143). P r i n c i p a l components analysis i s used i n t h i s s i t u a t i o n because the aim i s to reduce the f o r t y age-sex variables into a reduced set, while s t i l l maintaining most of the o r i g i n a l variance that e x i s t s i n the raw data. P r i n c i p a l components analysis does t h i s by capturing the underlying r e l a t i o n s h i p s within the data and reducing them to a smaller set of factors or components that are orthogonal (uncorrelated) to each other. The actual number of components depends upon the degree of c o r r e l a t i o n among the o r i g i n a l v a r i a b l e s — t h e higher the c o r r e l a t i o n , the smaller the number of factors required to represent the o r i g i n a l data. Each component i s a l i n e a r composite of the f o r t y o r i g i n a l v a r i a b l e s , with the f i r s t p r i n c i p a l component accounting for more of the variance 90 i n the data as a whole than any other l i n e a r combination of variables (Nie et a l . , 1975, 470). The importance of a given factor can be assessed by determining the amount of t o t a l variance i n the data that i s accounted for by t h i s f a c t o r . This requires examining the eigenvalue of the factor and i t s corresponding proportion of the sum of eigenvalues. The SPSS package program for factor analysis was the one used here. Table 3.2 shows the eigenvalues of the factors and percent of variance explained by these fa c t o r s . A de c i s i o n was made to use 9 factors as they comprised approximately 80 percent of the t o t a l accumulated eigenvalues. This cut-off point of 80 percent was chosen on the basis of Barer's r a t i o n a l e — t h a t these nine factors accounted for 80 percent of the variance and an a d d i t i o n a l three factors would only add a small amount 13 (5 percent) to t h i s variance t o t a l (Barer, 1977, 146). Table 3.2. Eigenvalue of Age-Sex Factor Scores Cumulative Percent Factor Eigenvalue' " " of Variance 1 11.28764 28.2 2 7.16529 46.1 3 3.68176 55.3 4 2.85209 62.5 5 2.26936 68.1 6 1.57585 72.1 7 1.19693 75.1 8 1.15347 78.0 9 0.98663 80.4 10 0.71369 82.2 11 0.64812 83.8 12 0.57442 85.3 (iv) Education expenses (EDRAT) and outpatient expenses (OUTXPD). Each v a r i a b l e i s a measure of the proportion of t o t a l costs (TOTEX) al l o c a t e d to t h i s function. EDRAT includes a l l expenditures on nursing and medical education. OUTXPD includes expenditure on the organized outpatient department, outpatient portion of radiology and laboratory department expenses, outpatient share of emergency department expenses, a l l ambulance service expenses, outpatient share of operating room expenditure, and outpatient physiotherapy expenses. These two variables are included i n the regression equation p r i m a r i l y to test f o r i n d i r e c t e f f e c t s of education and outpatient expenses on inpatients costs. (v) Wage l e v e l s (WAGE1, WAGE2) Barer (1977) extended the o r i g i n a l Evans-Walker (1972) model to include two var i a b l e s that r e f l e c t e d h o s p i t a l wage l e v e l s : " ( i ) WAGE1 - an in d i c a t o r of the extent to which a h o s p i t a l has a r e l a t i v e l y c o s t l y service, or s k i l l , mix. A value greater than 1 would indic a t e that the h o s p i t a l i n question employs personnel i n a more co s t l y combination than the p r o v i n c i a l average. ( i i ) WAGE2 - an i n d i c a t o r of the extent to which h o s p i t a l j i s a r e l a t i v e l y high wage hospital.'. 1 (Barer, 1977, 148) The method of deriving these v a r i a b l e s i s also taken d i r e c t l y from Barer (1977). The relevant section i s reproduced as follows: "Hospital support (non-medical s t a f f ) personnel were p a r t i t i o n e d into eight sectors: 92 (1 (2 (3 (4 (5 (6 (7 (8 nursing administration short-term & long-term units f o r adults & chi l d r e n other nursing care l i b r a r y administration general administration laboratory diagnostic and therapeutic radiology other s p e c i a l services Data pertaining to t o t a l hours of work for each sector, and t o t a l wage b i l l a l l o c a t e d to each sector were obtained from the HS-1 and HS-2 tapes. The following notation i s used i n the construction of these two va r i a b l e s . W = average wage i n sector i ( i = 1, . . . .8, above), and h o s p i t a l j (j = 1 87) [for Alberta, h o s p i t a l j (j = 1, . . . .112)] H_ = no. of labour hours i n sector i , h o s p i t a l j . This basic notation gives r i s e to the following d e r i v a t i v e v a r i a b l e s : B. = £;W.. H.. = h o s p i t a l i wage b i l l 3 i i j i j B. = £.W. . H. . 3 i i ] H. = •S.H. . i 3 i j H =«.H.. W. = B./H. l i i W. = B./H. 3 .3 3 t o t a l p r o v i n c i a l sector i wage b i l l t o t a l h o s p i t a l j hours t o t a l p r o v i n c i a l sector i hours t o t a l p r o v i n c i a l hours p r o v i n c i a l average sector i wage rate average wage rate, h o s p i t a l j (continued) 93 IL = H^/H = sector i proportion of t o t a l p r o v i n c i a l hours IL = * * T / H = h o s p i t a l j proportion of t o t a l p r o v i n c i a l hours PTP..= H../H. = h o s p i t a l j proportion of t o t a l p r o v i n c i a l sector x hours PTH..= H../H. = sector i proportion of t o t a l h o s p i t a l j hours i j 13 3 The construction of each i s d e t a i l e d below. I f h o s p i t a l j has a r e l a t i v e l y c o s t l y s k i l l mix as defined above, we would a n t i c i p a t e a wage b i l l , f o r that h o s p i t a l , greater than a wage b i l l constructed by using h o s p i t a l j wage rates, but p r o v i n c i a l s k i l l mix proportions. Thus, WAGE1. = B./H. • S.W..H. = W./ ^  W..H. 3 3 3 1 1 3 1 j x 13 1 This measure w i l l be upward biased f o r any h o s p i t a l having one or more sectors i n which i t employs no one, as the denominator i s con-structed from p r o v i n c i a l s k i l l proportions, but i n d i v i d u a l h o s p i t a l sector wage rates. By computing H_^ , f or each h o s p i t a l , as H. = H. T.,_ x x • IND. < i 1 i i where IND. = ( 1 i f W.. ± 0 0 i f W.. - 0 13 we circumvented introduction of t h i s bias. Thus i f W_ = 0, the i th sector hours were excluded i n computing p r o v i n c i a l proportions. If h o s p i t a l j has a r e l a t i v e l y high wage l e v e l , t h i s would become apparent through a measure constructed from a numerator of h o s p i t a l j's wage b i l l , and a denominator of p r o v i n c i a l sector wage l e v e l s weighted by h o s p i t a l j 's s k i l l mix. Thus WAGE 2. = B./2.W.H.. = W./*W. • PTH.. 3 J u l ] 3 1 1 13 94-In t h i s case, there are no zero-value d i f f i c u l t i e s , as p r o v i n c i a l wage le v e l s are employed i n the denominator." (Barer, 1977, 147-9) Appendix 3.1, Table 3.3 provides values for these variables for a l l h o s p i t a l s . (vi) Average length of stay (ALS) The ALS va r i a b l e measures the average length of stay of a l l patients separated i n the given year. From the HS-1 form, data on t o t a l h o s p i t a l days of a l l cases (adults, children) separated from the h o s p i t a l were aggregated to form a t o t a l separated days stay f i g u r e . This was divided by t o t a l inpatient separations (for adults, children) to a r r i v e at an average length of stay figure for each h o s p i t a l . See Appendix 3.2, Table 3.3 for h o s p i t a l average length of stay. 3.4. Regression Analysis Having outlined the t h e o r e t i c a l s p e c i f i c a t i o n of the behavioural h o s p i t a l equation the next step i s to test the r e l a t i o n s h i p of the independent variables (x^, x^, x^ . . . .x^) to the dependent variables (CASEX and DAYEX), that i s , to examine the extent to which these inde-pendent variables explain the dependent v a r i a b l e s . This i s done using regression analysis. More s p e c i f i c a l l y , we wish: (i) to quantify the r e l a t i o n s h i p between the s i z e variables 2 B 2 ( — , — , — and — ), case variables (case mix complexity, s p e c i a l i z a t i o n , \J L» U U age and sex, average length of stay), education expense v a r i a b l e , out-patient expense v a r i a b l e and wage l e v e l v a r i a b l e s , to the two dependent var i a b l e s , average cost per case (CASEX) and average inpatient expense per day (DAYEX). 95 ( i i ) to determine which of the several independent variables are important, e s p e c i a l l y the case complexity variables (CMPXC1, RNI), f o r describing or p r e d i c t i n g the dependent v a r i a b l e s (CASEX and DAYEX). In ordinary l e a s t squares regression a n a l y s i s , values of the dependent variables are predicted from a l i n e a r function of the form: .1 Y = A + B,X, + B„X„ + + B where Y"*" represents the estimated value for Y, A i s the Y intercept, and the are regression c o e f f i c i e n t s . The A and c o e f f i c i e n t s are 1 2 selected i n such a way that the sum of squared residuals (Y - Y ) i s minimized. The smaller the deviations of the observed values from t h i s l i n e (and consequently the smaller the sum of squares of these devia-' 14 t i o n s ) , the closer the best f i t t i n g l i n e w i l l be to the data. In the next chapter, the regression models w i l l be tested, and r e s u l t s provided, from which conclusions can be drawn about the most appropriate case complexity variables to be used i n the p r e d i c t i o n of h o s p i t a l costs. 96 Reference Notes, Chapter 3 1. The d e s c r i p t i o n of the h o s p i t a l cost equation and the variables used here are borrowed d i r e c t l y from the previous work of these authors. S i m i l a r l y the computer programs needed to derive these equations were also borrowed from t h i s same source. I am greatly indebted to both Robert Evans and Morris Barer for providing t h i s t e c h n i c a l assistance and eliminating what would have otherwise been a very time consuming task. 2. These depreciation costs were excluded from the analysis because the data base which records t h i s expenditure does not report actual depreciation costs, but rather financing costs. The r e l a t i o n s h i p between these two costs i s uncertain, so the decision was made to exclude them. 3. The l a t t e r two v a r i a b l e s described here were developed by Barer (1977) and were not included i n the Evans and Walker (1972) model. 4. Both Evans and Walker (1972) and Barer (1977) included a t h i r d variable—namely depreciation expenses. However, the suspect nature of the data a v a i l a b l e to develop t h i s v a r i a b l e , and i t s r e l a t i v e l y i n s i g n i f i c a n t p r e d i c t i v e power, lead to i t s exclusion from the Alberta model. 5. The data were unavailable because these seven h o s p i t a l s are Federal h o s p i t a l s and expenditure and f a c i l i t i e s data were not r e a d i l y a v a i l a b l e at the p r o v i n c i a l l e v e l . 6. These h o s p i t a l s were a t y p i c a l because, i n four cases, they had unusually long lengths of stay. In the f i f t h case, the h o s p i t a l was a s p e c i a l i z e d children's h o s p i t a l . In the f i r s t s e r i e s of regression equations, these h o s p i t a l s were included but they u n f a i r l y biased the r e s u l t s against the RNI, causing i t to have an i n s i g n i f i -cant regression c o e f f i c i e n t i n some equations. 7. See HS-1, p. 13. 8. See HS-2, p. 52. 9. The HS-1 and HS-2 forms do not provide a breakdown of the inpatient and outpatient shares of radiology and laboratory department expenses, emergency services, etc. This was estimated on the basis of the r e l a t i v e proportion of inpatient and outpatient a c t i v i t y . The method of a l l o c a t i o n was the same as that used by Barer (1977). For d e t a i l s , the interested reader should contact the author. 97 10. It i s not p r e c i s e l y true that DAYEX i s GASEX divided by ALS, since t o t a l cases r e f e r s to separations within the s p e c i f i e d time period ( i . e . the year) while t o t a l patient days includes a l l patient days i n the year period. I f a patient i s admitted before the end of the year and separated i n the new year, the patient days w i l l be d i s t r i b u t e d between the two ^.calendar years for the purpose of c a l c u l a t i n g t o t a l patient days. e.g. i f patient A arr i v e d December 20 1981 and leaves January 20 1982, she counts as one case and 20 days i n 1982 and 11 days and no case i n 1981. S i m i l a r l y , someone who stayed throughout a f u l l year would generate 365 (or 366)days i n that year, but no separations. 11. In Chapter 2, footnote 19, two other s p e c i a l i z a t i o n variables were described. As they are a l t e r n a t i v e measures, only one measure, SPCLC1, was chosen for i n c l u s i o n i n the a n a l y s i s . 12. Di r e c t quotation i s interrupted here because the order of the columns i s d i f f e r e n t . 13. In Barer's a n a l y s i s , s i x f a c t o r s , not nine, accounted for 80 percent of the t o t a l variance. 14. For a much more de t a i l e d exposition of regression analysis see Draper and Smith (1966), Neter and Wasserman (1974), Kleinbaum and Kupper (1978). APPENDIX 3.1 Table 3.3. Values for Most of the Independent Variables and the Two Dependent Variables (CASEX and DAYEX) Used i n the Regression Analysis HOSPITAL NO. BEDS ALS OCC CASEX . DAYEX CMPXC1 SPCLC1 RNI 1 45 5.8 .606 534.14 91.48 0.81 1.41 0.78 2 46 5.7 .448 888.33 161.75 0.86 1.28 0.85 3 80 8.3 .821 745.09 79.70 • ' 0.89 0.56 0.84 4 30 8.1 .605 875.22 106.08 0.83 1.56 0.85 5 30 6.7 .492 637.35 111.25 0.83 1.29 0.72 6 30 6.0 .573 742.23 124.51 0.81 1.86 0.72 7 16 8.2 .661 773.84 77.61 0.71 2.90 0.79 8 21 6.9 .712 586.34 88.05 0.74 2.45 0.78 9 60 10.2 .672 1010.39 102.73 0.86 0.91 0.86 10 52 6.2 .739 530.17 84.57 0.75 1.80 0.77 11 39 17'. 7 .798 956.87 61.92 0.83 1.45 0.85 12 30 9.9 .488 969.10 99.78 0.65 4.48 0.80 13 30 9.6 .282 1757.10 160.77 0.72 3.76 0.93 14 65 6.4 .606 768.52 116.26 0.91 0.67 0.79 15 784 9.3 .795 1383.79 147.25 1.13 0.55 1.07 16 928 9.4 .747 1306.55 139.62 1.10 0.36 0.97 17 726 7.1 .801 1030.70 142.90 1.07 0,;30 0.98 18 117 6.8 .663 631.58 89.56 0,92 0.53 0.89 19 20 5.4 .615 543.96 101.18 0.78 1.80 0.82 20 61 7.1 .802 641.06 79.14 0.92 0.68 0.75 HOSPITAL NO. BEDS ALS OCC 21 30 6.5 .549 22 47 6.9 .515 23 25 4.9 .430 24 27 4.4 .781 25 22 5.3 .333 26 25 5.8 .524 27 30 6.5 .823 28 34 5.6 .716 29 47 6.8 .820 30 70 7.1 .657 31 26 8.0 .585 32 76 8.8 .797 33 559 8.7 .841 34 555 8.2 .839 35 977 7.5 .901 36 1236 11.4 .749 37 50 6.4 .563 38 42 7.5 .676 39 50 4.9 .622 40 32 5.7 .693 41 73 4.6 .985 42 42 6.8 .700 43 36 5.1 .551 44 40 9.7 .491 CASEX DAYEX CMPXC1 SPCLC1 RNI 693.97 106.36 0.76 2.20 0.85 687.28 105.09 0.86 1.05 0.89 495.78 101.89 0.90 1.77 0.83 399.17 91.94 0.78 1.93 0.72 697.83 128.07 0.73. 2.61 0.89 778.24 124.23 0.77 2.10 0.77 484.60 77.10 0.86 1.17 0.78 524.10 91.39 0.82 1.03 0.87 465.02 70.38 0.86 0.93 0.70 845.07 121.76 0.92 0.53 0.85 723.34 108.37 0.83 1.70 0.90 2970.52 338.59 1.75 14.53 1.38 1050.64 120.03 1.05 0.34 1.02 989.46 120.11 1.02 0.22 0.89 967.29 127.74 1.12 0.40 0.89 1769.82 158.26 1.17 0.68 1.16 502.16 77.96 0.81 1.38 0.74 771.04 107.15 0.76 1.59 0.70 593.89 120.20 0.84 0.80 0.82 575.79 103.40 0.83 1.01 0.82 572.01 125.55 0.88 0.94 0.64 575.49 103.88 0.87 0.93 0.72 584.22 113.97 0.76 2.04 0.66 985.49 90.38 0.69 3.56 0.82 HOSPITAL NO. BEDS ALS OCC 45 8 10.4 .835 46 34 4.8 .505 47 130 6.0 .859 48 50 8.5 .579 49 20 8.9 .627 50 25 4.4 .674 51 72 6.5 .722 52 64 6.3 .726 53 27 4.9 .645 54 10 9.3 .685 55 55 4.6 .677 56 28 13.6 .723 57 33 4.5 .447 58 30 7.9 .733 59 68 6.3 .668 60 50 7.7 .649 61 72 14.2 .580 62 35 5.0 .728 63 206 7.5 .913 64 207 7.4 .792 65 26 7.2 .671 66 34 9.8 .470 67 30 13.8 .557 68 22 5.9 .454 CASEX DAYEX CMPXC1 SPCLC1 RNI 1472.68 92.42 0.72 4.80 0.94 476.16 98.00 0.84 1.19 0.65 734.53 122.67 0.93 0.45 0.80 895.44 95.94 0.91 1.02 0.85 693.61 86.85 0.72 3.15 0.83 551.15 121.36 0.82 1.80 0.65 764.78 116.25 0.81 1.33 0.77 663.37 106.76 0.82 0.94 0.80 745.08 151.76 0.99 1.07 0.67 1214.81 129.74 0.72 3.57 0.83 414.26 90.78 0.87 0.89 0.76 1159.08 79.69 0.84 2.16 0.96 807.86 175.46 0.85 1.37 0.85 852.34 110.50 0.70 2.54 0.83 573.61 88.40 0.71 2.06 0.72 563.53 74.07 0.86 0.93 0.82 1730.43 91.43 0.89 1.46 0.99 505.09 101.18 0.86 0.81 0.76 708.49 95.43 1.06 0.57 0.87 773.92 105.21 1.03 0.66 0.94 453.44 65.32 0.87 1.45 0.74 1119.94 114.88 0.79 2.13 0.85 1660.17 129.23 0.80 2.34 0.84 728.35 127.56 0.73 2.77 0.93 HOSPITAL NO. BEDS ALS OCC 69 61 8.6 .680 70 237 6.2 .803 71 30 4.7 .183 72 18 8.8 .661 73 20 12.8 .767 74 43 5.7 .705 75 31 10.6 .743 76 71 5.2 .620 77 25 5.7 .595 78 56 6.8 .557 79 50 5.3 .759 80 31 6.2 .642 81 25 6.5 .720 82 223 7.2 .890 83 32 6.7 .789 84 31 7.7 .669 85 47 5.4 .703 86 34 4.2 .793 87 25 7.1 .559 88 47 6.4 .518 89 100 6.0 .751 90 75 6.6 .699 91 50 6.4 .732 92 30 6.5 .434 CASEX DAYEX CMPXC1 SPCLC1 RNI 782.06 93.21 0.75 1.80 0.77 648.88 103.82 1.00 0.30 0.85 975.34 215.50 0.78 2.54 0.97 927.37 80.99 0.79 4.68 1.06 964.38 74.74 0.74 3.17 0.97 475.89 82.98 0.87 1.01 0.83 827.80 67.52 0.77 1.77 0.73 802.29 154.17 0.93 0.58 0.73 451.30 76.20 0.83 1.62 0.81 770.95 103.82 0.84 0.94 0.78 405.59 73.59 0.87 1.30 0.83 724.43 115.17 0.86 0.95 0.83 530.81 78.85 0.86 1.36 0.79 993.74 137.78 1.02 0.89 0.88 503.43 76.02 0.71 1.12 0.91 624.25 86.81 0.84 1.06 0.87 520.09 87.25 0.82 0.86 0.72 346.93 84.34 0.80 1.00 0.67 850.73 118.70 0.81 3.39 0.92 792.36 108.40 0.88 1.15 0.90 650.11 109.91 0.94 0.57 0.82 646.54 90.34 0.81 1.09 0.74 572.69 96.69 0.88 0.70 0.84 708.91 118.25 0.87 1.73 0.70 HOSPITAL NO. BEDS ALS OCC 93 34 5.9 .524 94 66 8.1 .705 95 21 9.4 .547 96 31 6.6 .713 97 30 8.7 .756 98 24 6.1 .529 99 37 7.9 .693 100 35 4.5 .824 101 70 7.4 .635 102 52 11.7 .599 103 35 7.1 .642 104 14 10.7 .705 105 37 6.9 .580 106 48 8.7 .706 107 80 6.1 .591 108 135 8.4 .907 109 34 4.9 .715 110 25 7.1 .518 111 29 7.0 .478 112 365 10.6 .603 CASEX DAYEX CMPXC1 SPCLC1 RNI 525.35 826.19 774.29 545.52 1465.13 668.07 547.79 487.41 700.14 999.69 695.01 930.82 516.46 844.13 600.68 754.94 562.31 569.21 859.92 1110.60 92.49 0.80 101.32 0.88 111.56 0.77 82.59 0.78 67.24 0.69 105.62 0.74 73.09 0.75 81.14 0.73 95.11 0.81 90.97 0.89 99.93 0.81 96.31 0.71 79.05 0.75 101.16 0.87 99.70 0.84 92.16 0.84 114.44 0.87 79.53 0.72 119.08 0.69 123.93 1.07 1.59 0.84 0.75 0.80 2.35 0.77 1.54 0.86 3.54 1.01 2.34 0.90 2.46 0.85 2.40 0.69 1.08 0.90 0.93 0.87 1.40 0.87 4.79 0.80 2.74 0.85 0.81 0.83 0.83 0.88 0.82 0.78 1.01 0.65 1.11 0.98 4.68 0.79 0.62 0.85 103 Chapter 4. Empirical Results The purpose of t h i s chapter i s to examine the r e s u l t s of the regression analysis and assess the explanatory power of the behavioural cost equation developed i n Chapter 3. To r e i t e r a t e b r i e f l y , t h i s behavioural cost equation consists of two components—a f i x e d (per bed) and a va r i a b l e (per case) component. Thus, t o t a l h o s p i t a l costs and average h o s p i t a l costs are a function of s i z e of the h o s p i t a l (number of beds) and number and type of patients (cases). To account for v a r i a t i o n across hospi t a l s i n terms of d i f f e r e n t type of patients, cost per case i s standardized to include inpatient costs only. Outpatient, emergency, teaching, research and non-departmental expenses have been r e -moved to reach a measure of "pure" inpatient costs. I t i s also standard-ized i n terms of case mix by the RNI or the case complexity v a r i a b l e , CMPXC1, and s p e c i a l i z a t i o n v a r i a b l e , SPCLC1, derived from information theory. Twelve a d d i t i o n a l variables are included to adjust f o r the influence o f — (i) age-sex, to F g ( i i ) average length of stay, ALS ( i i i ) wage l e v e l s within a h o s p i t a l , WAGE1 (iv) s k i l l mix of non-medical s t a f f personnel, WAGE2 Two other v a r i a b l e s , which are not included i n inpatient costs, but which may have an e f f e c t on inpatient a c t i v i t y , are included. These are an education expense v a r i a b l e , EDRAT and an outpatient expense v a r i a b l e , OUTXPD. 104 This behavioural cost equation i s borrowed from the work of Evans and Walker (1972) and Barer (1977) so j u s t i f i c a t i o n f o r the nature of the model i s not provided here. The purpose of t h i s study i s to assess the r e l a t i v e merits of the two measures of case mix (RNI and complexity measures, CMPXC1 and SPCLC1, derived from information theory) and to develop an appropriate model for h o s p i t a l budgeting purposes i n Alberta. Analysis of the r e s u l t s w i l l be i n three parts: ( i ) an evaluation of the RNI compared with information theory measures of case mix. ( i i ) a discussion of the s i g n i f i c a n c e of the regression c o e f f i c i e n t s and the extent to which they meet a p r i o r i expectations. ( i i i ) s e l e c t i o n of the "best" equation and i t s a p p l i c a t i o n to the budgetary process. Each part w i l l be considered i n terms of cost per day (DAYEX) and cost per case (CASEX). 4.1. An Evaluation of the RNI Compared to Information Theory  Measures of Case Mix The most d i r e c t means of assessing the power of the case mix measures i n explaining the dependent v a r i a b l e s , DAYEX and CASEX, i s to look at a simple regression equation which contains only one independent v a r i a b l e . Table 4.1 shows the r e s u l t s of t h i s simple regression analysis. In equation I, CMPXC1 i s the independent v a r i a b l e with DAYEX as the 2 dependent v a r i a b l e . The adjusted R r e s u l t i s 0.369 which means that case complexity, measured i n t h i s way, explains approximately 37 percent of the variance i n h o s p i t a l costs per day. When SPCLC1 (the h o s p i t a l s p e c i a l i z a t i o n v a r i a b l e derived from information theory) i s added i n equation I I , an a d d i t i o n a l 14 percent of variance i s explained, r a i s i n g Table 4.1. DAYEX Equations with A l t e r n a t i v e Case Complexity Variables I II III IV 2 Adjusted R 0.369 0.513 0.609 0.182 F 66.03 59.36 16.75 25.70 MSE 708.80 547.92 439.03 919.50 CMPXC1 t 152.34 8.13* 143.68 8.68* 123.45 3.73* SPCLC1 t 7.93 5.77* 9.3.9 4.27* F F 3 are s i g . RNI t 134.30 5.07* Constant t -23.08 -1.43 -29.52 -2.08* -16.25 -0.62 -5.71 -0.26 Indicates s i g n i f i c a n c e at 0.05 l e v e l . 106 the adjusted R value to 0.513. In equation I I I , the age-sex variables are included to add another 10 percent explanatory power and to increase 2 the adjusted R to 0.609. This compares with equation IV which has DAYEX as the dependent v a r i a b l e and the RNI as the independent v a r i a b l e . 2 The adjusted R value of t h i s equation i s 0 . 1 8 2 — s i g n i f i c a n t l y lower than the equation with CMPXC1. Another set of equations i s provided i n Table 4.2. The set con-tains the same independent variables as Table 4.1 but the dependent v a r i a b l e here i s CASEX instead of DAYEX. The explanatory power of the independent variables i s not as strong as those i n the DAYEX equation. 2 The adjusted R value for the f i r s t equation with CMPXC1 i s only 0.238. It increases to 0.492 when SPCLC1 i s added, and to 0.631 with the age-2 sex factor scores. Equation IV, with the RNI, gives an adjusted R of 0.497, a s i g n i f i c a n t increase over the explanatory power of the same va r i a b l e i n the DAYEX equation. To assess whether the complexity variables (CMPXC1 or RNI) are picking up e f f e c t s of factors other than case mix, such as s i z e of the h o s p i t a l or average length of stay, we need to examine t h e i r explanatory power when they are included with other variables measuring these factors d i r e c t l y . For t h i s purpose, as we described i n Chapter 3, we adopted the model developed by Evans and Walker (1972 and Barer (1977) which includes variables for s i z e , capacity, wage l e v e l s , education and out-patient expenses as well as case complexity. Table 4.3 and Table 4.4 show the regression c o e f f i c i e n t s for d i f f e r e n t combinations of these v a r i a b l e s with DAYEX and CASEX as the respective dependent v a r i a b l e s . The tables are structured to show the explanatory power of the basic model and to hi g h l i g h t the ad d i t i o n a l explanatory power 107 Table 4.2. CASEX Equations with A l t e r n a t i v e Case Complexity Variables I II III IV 2 Adjusted R 0.238 0.492 0.631 0.497 F 35.73 54.73 18.28 110.78 MSE 97218.48 64851.81 ' 47052.64 • 64171.14 CMPXC1 t 1312.41 5.98* 1190.27 6.61* 1610.66 4.71* SPCLC1 t 111.79 7.48* 38.13 1.68 F F V 9 3 are s i g . RNI t 2329.54 10.53* Constant t -322.35 -1.71 -413.16 -2.67* -625.84 -2.29* -1151.20 -6.18* Indicates s i g n i f i c a n c e at 0.05 l e v e l . 108 that occurs with the successive i n c l u s i o n of the ease mix complexity variables.; Equation I i n Table 4.3 shows the explanatory power of the basic 2 model without the case complexity measure. The adjusted R value i s 0.408. The main v a r i a b l e d r i v i n g t h i s s i g n i f i c a n t r e s u l t i s INVDFR, the si z e v a r i a b l e which has a large p o s i t i v e c o e f f i c i e n t . BDDFR, the other s i z e v a r i a b l e , i s also p o s i t i v e and s i g n i f i c a n t . The only other 1 s i g n i f i c a n t v a r i a b l e i s OUTXPD suggesting that outpatient a c t i v i t y influences inpatient costs. Close examination of the c o r r e l a t i o n c o e f f i c i e n t s between the independent variables reveals a high p o s i t i v e c o r r e l a t i o n (0.83) between EDRAT and BDDFR. This m u l t i c o l l i n e a r i t y of the independent variables may account for the unexpected negative r e s u l t of EDRAT.^ One of these variables must be eliminated from the regression equation i f r e l i a b i l i t y of regression c o e f f i c i e n t s i s to be ensured. Subsequent equations exclude EDRAT and r e t a i n BDDFR. The independent s i g n i f i c a n c e of EDRAT without BDDFR was tested i n equations VIII and IX. In both of these equations, EDRAT changed i t s sign from negative to p o s i t i v e , although i t s t - s t a t i s t i c was s t i l l not s i g n i f i c a n t . We turn again to the main point of t h i s s e c t i o n — t o evaluate the r e l a t i v e explanatory power of the case complexity v a r i a b l e s . Equation III i n Table 4.3 contains s i x of the seven o r i g i n a l v a r i a b l e s i n the basic model (EDRAT i s excluded) and introduces CMPXC1, one of the 2 information theory measures of case mix. The o v e r a l l adjusted R value improves from 0.414 to 0.651 with the addition of t h i s v a r i a b l e — a n increase i n explained variance of nearly 24 percent. When SPCLC1 i s 2 added, i n Equation IV, the adjusted R increases by another 10 percent, to 0.759. The introduction of the age-sex factor scores i n equation V 2 increases the R value to 0.798. Equation VI contains CMPXC1 and the Table 4.3. DAYEX Equations with Size, U t i l i z a t i o n , Wage, Indirect Expense, Case Complexity and S p e c i a l i z a t i o n Variables I II III IV V VI VII VIII IX 2 Adjusted R F MSE 0.408 11.95 665.03 0.414 14.05 659.20 0.651 30.63 391.85 0.759 44.71 270.86 0.798 26.75 227.40 0.755 22.36 275.63 0.488 16.11 575.52 0.793 25.99 232.86 0.751 42.92 279.53 INVDFR t 10681.60 6.02* 10699.07 6.06* 12502.24 9.08* 10010.49 8.34* 9742.43 7.65* 11016.08 8.05* 8659.48 5.02* 10088.98 7.96* 10290.40 8.50* BDDFR t 14.26 2.33* 12.90 3.44* -1.63 0.49 7.61 2.46* 6.06 1.84 -2.49 -0.83 7.29 1.94 ALS t -0.24 • -0.21 -0.26 -0.23 -0.47 -0.54 -1.98 -2.59* -1.73 -2.17* -1.69 . -1.93 -2.23 -1.91 -1.59 -1.99* -1.75 -2.29* WAGE1 t 33.01 1.37 32.43 1.36 34.27 1.86 12.94 0.83 6.91 0.43 20.19 1.17 35.18 1.58 6.01 0.37 11.50 0.72 WAGE2 t 75.86 1.28 76.88 1.31 25.90 0.57 111.94 2.80* 82.00 2.12* 60.18 1.42 125.60 2.23* 76.59 1.96* 106.92 2.64* OUTXPD t 445.99 5.29* 443.13 5.31* 146.91 2.01* 38.14 0.61 -9.69 -0.15 3.22 0.45 325.52 3.91* -19.97 -0.31 30.50 0.48 EDRAT t -82.24 -0.28 132.89 1.04 214.82 1.63 CMPXC1 t 174.16 8.52* 137.24 7.70* 129.77 3.95* 221.75 7.72* 152.05 5.12* 151.16 9.25* SPCLC1 t 8.35 6.89* 9.18 4.60* 7.81 4.35* 7.64 6.55* 3 are s i g . 3 are s i g . 3 are s i g . RNI t 111.03 4.03* Constant t * -90.19 -1.40 -90.06 -1.40 -166.26 -3.30* -184.65 -4.40* -140.46 -3.02* -198.30 -4.02* -198.51 -3.01* -150.41 -3.23* -188.89 -4.43* Indicates significance at 0.05 l e v e l . age-sex factor scores and excludes SPCLC1. The adjusted R i s 0.755. These equations should be compared with equation I I I , the a l t e r n a t i v e 2 equation using the RNI as a measure of case mix. The adjusted R i s 2 0.488, which i s only 0.07 greater than the adjusted R for the basic equation (equation I I ) . The RNI adds much less to the explanatory power 2 of the basic equation than CMPXC1 (R increased by 0.24) CMPXC1 plus 2 2 age-sex factor scores (R increased by 0.34) or CMPXC1, SPCLC1 and 2 age-sex fa c t o r scores (R increased by 0.38). Table 4.4 contains the same set of regression equations as Table 4.3 but the dependent v a r i a b l e here i s cost per case, CASEX. It should be noted that the CASEX equation, as s p e c i f i e d i n Chapter 3, contained average length of stay (ALS) as an independent v a r i a b l e . Preliminary t e s t i n g of t h i s equation revealed a strong c o r r e l a t i o n between INVCFR and ALS (.64) i n d i c a t i n g m u l t i c o l l i n e a r i t y between the independent v a r i a b l e s . It i s not immediately apparent, a p r i o r i , why the two variables should be correlated. As an a l t e r n a t i v e , OCC was substituted for ALS i n the CASEX equation to provide an independent measure of u t i l i z a t i o n . Equation I represents the basic model without any case complexity 2 v a r i a b l e s . The adjusted R i s 0.630—63 percent of variance i n cost per case among ho s p i t a l s i s explained by these seven v a r i a b l e s . In equation II with CMPXC1 added, an a d d i t i o n a l 16 percent of v a r i a t i o n i s 2 2 explained (adjusted R i s 0.790). The adjusted R i s further increased to 0.885 when SPCLC1 i s added (equation I I I ) , and to 0.897 with the age-sex factor scores (equation IV). By comparison 71 percent (adjusted 2 R = 0.710) of t o t a l variance i s explained when the RNI i s used as the case mix v a r i a b l e (equation V I ) — a n increase i n explanatory power of Table 4.4. CASEX Equations with Size, U t i l i z a t i o n , Wage, Indirect Expense, Case Complexity and S p e c i a l i z a t i o n Variables I II I l l IV V VI VII VIII 2 Adjusted R F MSE 0.630 28.01 47211.55 0.790 53.21 26797.84 0.885 96.18 14642.26 0.897 54.83 13119.36 0.875 46.51 16013.34 0.710 35.00 36989.67 0.894 55.85 13578.63 0.878 101.03 15548.07 INVCFR t 19741.91 11.22* 20276.86 15.28* 16416.77 15.42* 16312.68 13.77* 17084.41 13.18* 15477.88 8.88* 16858.31 14.34* 17237.34 16.38* BDCFR t 13.42 2.33* 0.49 0.11 9.55 2.72* 7.59 2.07* -0.57 -0.16 8.06 1.55 OCC t 628.58 3.35* 415.52 2.90* 463.46 4.37* 460.01 4.16* 414.88 3.41* 576.50 3.47* 466.33 4.15* 482.44 4.43* WAGE1 t 390.93 1.91 401.14 2.61* 142.10 1.21 156.27 1.27 256.93 1.92 379.89 2.10* 147.65 1.18 134.94 1.12 WAGE2 t 177.15 0.35 -247.68 -0.65 550.71 1.87 463.57 1.58 341.81 1.06 653.28 1.44 445.58 1.49 533.91 1.76 OUTXPD t 3692.08 5.13* 1200.20 1.97* -29.60 -0.63 -285.43 -0.57 -173.08 -0.31 2309.09 3.37* -413.52 - 0.82 -101.80 -0.21 EDRAT t 165.80 0.63 731.76 0.37 474.78 0.32 461.34 0.33 1110.29 0.72 -785.91 -0.34 2577.58 2.66* 3494.35 3.57* CMPXC1 t 1498.21 8.96* 1136.68 8.77* 1252.43 C 5.04* 1951.28 8.92* 1481.26 6.55* 1267.80 10.23* SPCLCl t 84.18 9.30* 69.94 4.66* 56.03 4.11* 77.38 8.63* F l F 9 1 i s s i g . 2 are s i g . 1 i s s i g . RNI t 1235.34 5.45* Constant t * Indicates -1201.01 -2.00* significance a -1699.97 -3.73* t 0.05 l e v e l . -1888.35 -5.60* -1860.02 -4.95* -2298.54 -5.72* -2384.05 -4.15* -1997.69 -5.31* -1977.82 -5.72* 112 8 percent over the basic model (equation I) but only equivalent to h a l f the amount added by CMPXC1 to the same basic equation. As i n the DAYEX equation, m u l t i c o l l i n e a r i t y e x i s t s between EDRAT and INVCFR i n the CASEX equation. In equations VII and VIII, BDDFR i s excluded, r e s u l t i n g on t h i s occasion i n a p o s i t i v e and s i g n i f i c a n t EDRAT v a r i a b l e . In Table 4.6, however, EDRAT i s excluded from the CASEX equations I I , I I I , IV, V, VI, VII. In these s i x equations BDCFR i s p o s i t i v e and s i g n i f i c a n t . The general conclusion from Tables 4.3 and 4.4 i s that the RNI does not explain as much of the i n t e r - h o s p i t a l cost v a r i a t i o n s as CMPXC1 (the information theory case complexity measure). When SPCLC1 and the age-sex factor scores are added the explanatory power of the information theory approach i s further enhanced. I t would seem that our a p r i o r i reservations, discussed i n Chapter 2, about the RNI and i t s use of charges as a proxy f o r costs, are j u s t i f i e d . Cross su b s i d i z a t i o n among various departments and d i f f e r e n t categories of patients, i s common pra c t i c e i n American h o s p i t a l s . This d i s t o r t s the charge structure so that charges for a p a r t i c u l a r case may not r e f l e c t the actual cost of tre a t i n g that case. 4.2. Significance of the Regression C o e f f i c i e n t s In t h i s section our attention i s focused on the regression c o e f f i c i e n t s reported i n Tables 4.3 and 4.4. The v a r i a b l e s , i n both the DAYEX and CASEX equations, with the greatest magnitude and degree of s i g n i f i c a n c e are INVDFR i n DAYEX and INVCFR i n CASEX. These va r i a b l e s , together with BDDFR and BDCFR,. m e e t a p r i o r i e x p e c t a t i o n s — t h a t as h o s p i t a l s i z e increases, average cost 113 per day and per case increases. The OCC va r i a b l e i n the CASEX equations has a strong p o s i t i v e c o e f f i c i e n t i n a l l equations. A r i s e i n OCC r e s u l t s from an increase i n either admiss^ ions or i n length of stay. I f the r i s e i n OCC i s due to the l a t t e r , the OCC c o e f f i c i e n t shows the p o s i t i v e influence of length of stay on cost per case, as the e f f e c t of length of stay i s not represented i n other independent v a r i a b l e s . If the r i s e i n OCC i s due to an increase i n admiss-ions, the net impact of t h i s v a r i a b l e on cost per case i s more complex, as other independent variables (INVCFR, BDCFR) are also functions of the .- e l e v e l of admissions. As an example of the net impact of admissions on cost per case, consider a 'representative' h o s p i t a l with 400 beds and 12,000 admissions. Assume an increase i n admissions of 5 percent (12,600) which would r e s u l t i n an approximate increase i n the occupancy rate of nearly 4 percent, holding length of stay constant. According to equation I I I , Table 4.4, the net impact on cost per case i s (-0.002) x 16416.77 + (-.64) x 9.55 + (0.04) x 463.46 = -$20.40. An increase of admissions by 5 percent, other things equal, reduced the representative h o s p i t a l s cost per case by approximately $20. By contrast, assume an increase of average length of stay by 5 percent (or about h a l f a day), holding admissions constant. The net impact on cost per case i s (.05) x 463.46 = $23.17, an increase of approximately $23. The wage va r i a b l e s , WAGE1 and WAGE2, are p o s i t i v e , but i n most equations not s i g n i f i c a n t . In the DAYEX equations (Table 4.3), WAGE1 i s never s i g n i f -icant and WAGE2 i s s i g n i f i c a n t i n f i v e out of the nine equations. There i s no obvious explanation for t h i s . However, Barer's (1977) WAGE1 and WAGE2 c o e f f i c i e n t s were not always s i g n i f i c a n t . In the CASEX equations (Table 4.4), two of the WAGE1 c o e f f i c i e n t s are s i g n i f i c a n t , while none of the 114 WAGE2 c o e f f i c i e n t s are s i g n i f i c a n t . Again there i s no obvious explanation f o r t h i s i n s u b s t a n t i a l and e r r a t i c performance. The next two variables are outpatient expense, OUTXPD, and education expense, EDRAT. They were included i n Evans' and Walker's (1972) and Barer's (1977) models to determine the influence of these a c t i v i t i e s on inpatient care and to tes t the success of i s o l a t i n g non-direct inpatient expenditure from t o t a l h o s p i t a l expenditure. OUTXPD i s p o s i t i v e and s i g n i f i c a n t i n four of the nine DAYEX equations (Table 4.3) and p o s i t i v e and s i g n i f i c a n t i n three of the eight CASEX equations (Table 4.4). P o s i t i v e and s i g n i f i c a n t c o e f f i c -ients suggest that outpatient a c t i v i t y does a f f e c t inpatient costs. Thus the cost of outpatient a c t i v i t y goes beyond the accounting items i d e n t i f i e d and eliminated from inpatient expenditure. In t h i s sense, i t imposes an i n d i r e c t cost on inpatient a c t i v i t y . Evans and Walker (1972) detected a p o s i t i v e and s i g n i f i c a n t c o e f f i c i e n t for t h e i r outpatient v a r i a b l e i n a l l t h e i r CASEX equations. Hence t h e i r claim that "an outpatient f a c i l i t y c l e a r l y imposes i n d i r e c t costs on the rest of the h o s p i t a l operation" (Evans and Walker, 1972, 408). The e r r a t i c performance of OUTXPD here makes i t d i f f i c u l t to make any f i r m statement on the e f f e c t of outpatient a c t i v i t y on inpatient costs i n the Alberta s e t t i n g . EDRAT, on the other hand, was found to co r r e l a t e highly with another independent v a r i a b l e i n both the DAYEX and CASEX equations. In each case i t was the va r i a b l e serving the same function: BDDFR and BDCFR resp e c t i v e l y . EDRAT was excluded from the DAYEX equations i n Table 4.3 and when i t was i n -cluded i n the CASEX equations i n Table 4.4, i t was not s i g n i f i c a n t except i n equations VII and VIII when BDCFR was excluded. In these two equations i t was both p o s i t i v e and s i g n i f i c a n t suggesting education a c t i v i t y has an i n d i r -ect cost e f f e c t on inpatient care. 115 The case mix complexity v a r i a b l e , GMPXC1, derived from information theory i s s i g n i f i c a n t and p o s i t i v e i n both DAYEX and CASEX equations. The range for h o s p i t a l complexity measures i s 0.65 to 1.75, showing a substantial degree of v a r i a t i o n i n case mix. This case mix v a r i a t i o n r e s u l t s i n quite dramatic differences i n average per day and per case costs. For instance (using the estimates f o r CMPXC1 i n equation IV, Table 4.3 and equation I I I , Table 4.4)' a h o s p i t a l with a case complexity value of 1.0 w i l l expect to have patient day costs and case costs $27.45 and $227.34 higher, respectively, than another h o s p i t a l which, c e t e r i s paribus, has a case complexity value of 0.80. This substantial difference i n costs has important p o l i c y implications for the reimbursement of h o s p i t a l s , i l l u s t r a t i n g quite c l e a r l y that a f l a t rate per patient day or per case i s inadequate to take account of case mix v a r i a t i o n . The RNI i s p o s i t i v e and s i g n i f i c a n t i n both the DAYEX and CASEX equat-2 ions. However, i t s contribution to the adjusted R of the equation i s not the same as i s that of CMPXC1. This can be seen by comparing DAYEX equations I I , I I I , VI and VII i n Table 4.3. Equation II i s the basic model (without 2 EDRAT) with no case mix complexity v a r i a b l e s . The adjusted R for t h i s equat-ion i s 0.414. Equation III i s the basic model plus the CMPXC1 va r i a b l e arid 2 i t s adjusted R i s 0.651. Adding the age-sex factor scores i n equation VI, 2 2 the adjusted R increases to 0.755 . Equation VII i s the basic model i n c l u d -ing the RNI. The addition of the RNI only improves the explanatory power of the equation by 7 p e r c e n t — t h i s i s s i g n i f i c a n t l y l e s s than the 24 percent added by CMPXC1 or the 34 percent added by CMPXC1 and the age-sex factor scores. In the CASEX equations (Table 4.4) the RNI performs better r e l a t i v e to CMPXC1 than i t s r e l a t i v e performance i n the DAYEX equations. The RNI i n 116 equation VI adds 8 percent to the adjusted R of the basic model; CMPXC1 i n equation II adds 16 percent and 24 percent when the age-sex factor scores are included (equation V). These comparisons: indicate that the information theory measure again contributed more to the understanding of i n t e r - h o s p i t a l cost v a r i a t i o n than the RNI. The SPCLCl v a r i a b l e i s s i g n i f i c a n t but p o s i t i v e i n the DAYEX and CASEX equations. This r e s u l t i s s u r p r i s i n g — t h e a p r i o r i b e l i e f was that av,more sp e c i a l i z e d h o s p i t a l ( i . e . a h o s p i t a l with a r e l a t i v e l y smaller range of case types) would be r e l a t i v e l y l e s s c o s t l y than a les s s p e c i a l i z e d h o s p i t a l . Hence the a p r i o r i expected sign i s negative. This anomalous p o s i t i v e and s i g n i f i c a n t c o e f f i c i e n t was also obtained by Evans and Walker (1972). Further examination of th i s unexpected r e s u l t was not possible due to time constraints but a tentative explanation i s posited here. Close inspect-ion of the raw data (Appendix 3.2) reveals a few hospita l s which have an a t y p i c a l combination of CMPXC1 and SPCLCl values. For instance, h o s p i t a l 32 has a CMPXC1 of 1.75 (the highest f o r a l l Alberta hospitals) and a SPCLCl value of 14.53 (the highest among a l l Alberta h o s p i t a l s ) . This means that the ho s p i t a l has a very complex caseload but i t i s also highly s p e c i a l i z e d , i . e . i t has a r e l a t i v e l y l i m i t e d range of diagnoses. Conversely, there are some hos p i t a l s where the reverse s i t u a t i o n e x i s t s . For instance h o s p i t a l 47 has a CMPXC1 value of 0.93, i n d i c a t i n g that i t i s s l i g h t l y below "average" i n terms of i t s ".case complexity. Its SPCLCl value, however, i s very low (0.45) sugg-esting that i t i s a very generalized h o s p i t a l t r e a t i n g a range of diagnoses. Hospital 76 i s s i m i l a r i n th i s respect having a CMPXC1 value of 0.93 and a SPCLCl value of 0.58. These h o s p i t a l s have one major factor i n common-—their r e l a t i v e i s o l a t i o n . This explains t h e i r generalized case-load as they are 117 regional centres drawing from wide, diverse catchment areas. It would be an i n t e r e s t i n g exercise to exclude these hospi t a l s from the data set and see what e f f e c t t h i s has on the sign of the parameter estimate. However, t h i s r e f i n e -ment i s beyond the scope of the present study. F i n a l l y , the remaining v a r i a b l e s are the age-sex fa c t o r scores. Their c o e f f i c i e n t s must be l e f t l a r g e l y unexplained as there i s no obvious i n t e r p r e t -ations of these scores. Three out of nine scores are s i g n i f i c a n t i n the DAYEX equations but only one out of nine i n the CASEX equations. They increase the explanatory power of the basic equation with CMPXC1 by 10 percent (compare equations I I I and VI, Table 4.3). However, i f they are added to the basic equation which includes SPCLC1 as well as CMPXC1, they only explain ah addit-i o n a l 4 percent of t o t a l variance (see equations IV and V, Table 4.3). The combined e f f e c t of these factor scores on the CASEX equations i s even les s obvious. When added to the basic equation including CMPXC1, they add 8 per-cent to explained variance (compare II and V, Table 4.4). However, when SPCLC1 i s included, they add only 1 percent to explained variance (compare equations I I I and IV, Table 4.4). 4.3 Selection of the "Best" Equation In the f i r s t section of t h i s chapter we examined the r e l a t i v e merits of the information theory measures of case mix complexity and the Resource Need Index. In the second section the regression c o e f f i c i e n t s f o r the independent variables were examined i n d i v i d u a l l y . In t h i s section we t r y to i d e n t i f y the equation of "best f i t " . C r i t e r i a f o r assessing a "best f i t " equation are both s t a t i s t i c a l and p r a c t i c a l i n nature. The s t a t i s t i c a l c r i t e r i a include: 2 2 (i ) a maximum R value. The higher the R , the greater the amount of variance explained by the independent v a r i a b l e s . 118 ( i i ) an o v e r a l l s i g n i f i c a n t F value. This test i s used to determine whether a l l the independent variables taken together s i g n i f i c a n t l y contribute to the pre d i c t i o n of the dependent v a r i a b l e . ( i i i ) a s i g n i f i c a n t t - s t a t i s t i c f o r each of the regression c o e f f i c i e n t s . This test determines whether i n d i v i d u a l independent variables s i g n i f i c a n t l y contribute to the p r e d i c t i o n of the dependent v a r i a b l e . The p r a c t i c a l c r i t e r i a are: (i ) ease of data c o l l e c t i o n . I t i s important that data be r e a d i l y a v a i l a b l e so that analysis can occur on a regular basis with minimal time and e f f o r t expended. ( i i ) low cost. Both the data and resources required f o r the analysis should be inexpensive. ( i i i ) a l i m i t e d number of v a r i a b l e s . This w i l l make i n t e r p r e t a t i o n s t r a i g h t -forward. Tables 4.5 and 4.6 have been compiled so that the i d e n t i f i c a t i o n of the "best" equations can be made by systematically applying the above set of c r i t e r i a . 4.3.1. DAYEX or CASEX? The choice between funding h o s p i t a l s on a cost per day (DAYEX) or a cost per case (CASEX) basis i s a dec i s i o n to be made by the reimbursing agency. Cost per day reimbursement could encourage longer lengths of stay and an i n -crease i n the number of admissions. Most provinces i n Canada have t o t a l bud-get reimbursement, where the t o t a l budget i s determined prospectively on the basis of t o t a l patient days. In t h i s sense i t i s s i m i l a r to cost per day reimbursement predicted prospectively for a year. The tendency of cost per day reimbursement to encourage longer lengths of stay has resulted i n a s h i f t towards prospective cost per case reimburse-ment by a number of reimbursing agencies i n the United States. The anticipated disadvantages of t h i s approach are: (i) i t may encourage an increased number 119 of admissions, ( i i ) i t may lead h o s p i t a l administrators to code patients into " l u c r a t i v e " disease categories, ( i i i ) i t may a f f e c t q u a l i t y of c a r e — the i n -stitutionrmay "use fewer resources to produce each admission,.regardless of case type" ( K l a s t o r i n , Watts, T r i v e d i , 1978, 22). However, these l a t t e r two disadvantages, i n t h i s context, are u n l i k e l y to be r e a l problems. For one, the methodology of both the information theory measure of case mix complexity and the RNI does not encourage inappropriate coding. In the case of informat-ion theory, the r e l a t i v e concentration of a diagnosis determines i t s weight: inappropriate coding by a number of h o s p i t a l s would d i l u t e i t s concentration and reduce i t s value. In the case of the RNI, the matrix of charges from which the RNI i s calculated, i s c o n f i d e n t i a l information, retained by CPHA. Second, the suggestion of reduced q u a l i t y of care i s u n l i k e l y to be a serious problem because the physicians, who determine the nature of care, are biased towards higher rather than lower resource use because i n most cases patients are covered by insurance; and because the costs associated with running the h o s p i t a l are not t h e i r r e s p o n s i b i l i t y . Furthermore there are q u a l i t y controls imposed on the system i n the form of peer review and u t i l i z a t i o n review. The following discussion treats the DAYEX and CASEX equations independently. 4.3.2. The equation of "best f i t " Tables 4.5 and 4.6 contain what the author considers to be the potent-i a l l y most useful equations for use i n the budgeting process. The RNI i s not included i n any of these equations because the f i r s t two sections of t h i s chapter showed that the RNI was not as powerful a predictor of h o s p i t a l costs, as the information theory measures of case mix complexity and s p e c i a l i z a t i o n . 2 These two measures were responsible f o r a much larger adjusted R value than the RNI i n both DAYEX and CASEX equations. In terms of the p r a c t i c a l c r i t - r . : e r i a , both CMPXC1 and SPCLCl are r e a d i l y computed through the current morbid:1'.' i t y system at l i t t l e cost. RNI reports for a l l Alberta h o s p i t a l s f or one Table 4 .5. DAYEX Equations with Information Theory Case Complexity and S p e c i a l i z a t i o n Variables 0.796 25.01 229.68 9724.08 7.58* 6.84 1.52 -1.72 -2.15* 7.19 0.45 81.61 2.09* -7.86 -0.12 -44.26 -0.26 129.15 3.90* 9.22 4.58* 3 are s i g -140.18 -2.99* 10088.98 7.96* -1.59 -1.99* 6.01 0.37 76.59 1.96* 19.97 -0.31 132.89 1.04 152.05 5.12* 7.81 4.35* 3 are s i g . -150.41 -3.23* 9742.43 7.65* 6.06 1.84 -1.73 -2.17* 6.91-0.43 82.00 2.12* -9.70 -0.15 129.77 3.95* 9.18 4.60* 3 are sig, -140.46 -3.02* 9783.73 7.91* 6.09 1.86 -1.71 -2.19* 7.51 0.49 80.98 2.13* 127.73 4.29* 9.17 4.62* 3 are si g . -139.46 -3.04* 7.63 2.47* -2.05 -2.73* 10.93 0.72 118.25 3.07* 141.17 8.53* 8.54 7.30* -188.27 -4.54* 4.95 1.51 -1.79 -2.26* 136.68 4.59* 8.82 4.49* 3 are s i g -58.91 -2.35* VII 10401.10 8.59* i n d i c a t e s significance at 0.05 l e v e l . 121 year would cost $20,000. Equation 1 i n Table 4.5 includes a l l the independent v a r i a b l e s . It sat-2 i s f i e s 2 out of the 3 s t a t i s t i c a l c r i t e r i a — h i g h adjusted R (0.796), and s i g n i f i c a n t o v e r a l l F. However, not a l l the i n d i v i d u a l c o e f f i c i e n t s are significant—BDDFR, WAGE1, OUTXPD, EDRAT and 6 of the 9 age-sex factor scores are i n s i g n i f i c a n t at the 5 percent l e v e l . In terms of p r a c t i c a l c r i t e r i a a l l v a r i a b l e s are e a s i l y obtainable at low cost. The number of variables i n t h i s equation i s not reduced to a minimum, as evidenced by the number of i n s i g n i f -icant v a r i a b l e s . This makes i n t e r p r e t a t i o n s l i g h t l y more complicated and un-wieldy than i f only s i g n i f i c a n t v a r i a b l e s were included. Equation I I i n Table 4.5 i s the same as equation I with no BDDFR v a r i a b l e . This was dropped because of the high c o r r e l a t i o n between the two independent v a r i a b l e s , BDDFR and EDRAT. The e f f e c t of dropping BDDFR i s minimal—a s l i g h t -2 l y smaller adjusted R and the EDRAT c o e f f i c i e n t i s now p o s i t i v e but s t i l l remains i n s i g n i f i c a n t . 2 In equation I I I , EDRAT was removed and BDDFR included. The R value i s now s l i g h t l y higher than equations I and I I . In subsequent equations, BDDFR i s retained and EDRAT excluded to reduce e f f e c t s of m u l t i c o l l i n e a r i t y . Equation IV, Table 4.5 excludes both EDRAT and OUTXPD. I t was decided that i f EDRAT was to be removed, on other grounds, i t was l o g i c a l to exclude OUTXPD, both because i t has an i n s i g n i f i c a n t regression c o e f f i c i e n t and the purpose and construction of the v a r i a b l e was the same as for EDRAT. The r e s u l t i s a "better" equation i n terms of the s p e c i f i e d c r i t e r i a . The adjust-2 ed R i s minimally higher than f o r equations I to I I I . The o v e r a l l F value i s more s i g n i f i c a n t and 8 out of the 16 regression c o e f f i c i e n t s are s i g n i f i c a n t . In terms of the p r a c t i c a l c r i t e r i a i t i s not very d i f f e r e n t from the other three equations, except that i n t e r p r e t a t i o n i s more straightforward, as a re s -u l t of the reduced number of v a r i a b l e s . 122 As the age-sex factor scores account for the highest proportion of i n s i g n i f i c a n t c o e f f i c i e n t s , and because t h e i r i n d i v i d u a l meaning i s not c l e a r , they were excluded from equation V. The r e s u l t i s a 4 percent 2 decrease i n explained variance (R = 0.761) but t h i s i s small considering that nine variables were dropped from the equation. Six out of the seven remaining regression c o e f f i c i e n t s are s i g n i f i c a n t , and removal of the age-sex factor scores makes computing of the variables l e s s complex. Equation VII i s the same as equation V without the WAGE va r i a b l e s . This elimination produces an equation with s i g n i f i c a n t regression c o e f f i c i e n t s f o r a l l f i v e v a r i a b l e s . The small number of variables minimizes the amount of data c o l l e c t i o n and computing required. However, there i s a drop i n the o v e r a l l explanatory power of the equation (adjusted R 2 = 0.742). Equation VI i s a compromise between equations V and VII. The WAGE var i a b l e s are excluded but the age-sex factor scores are included. 2 The adjusted R value i s improved by only 3 percent and s t i l l only 3 of the 9 age-sex factor scores are s i g n i f i c a n t . Thus the s e l e c t i o n of the "best" equation i s a trade-off both i n 2 s t a t i s t i c a l and p r a c t i c a l terms. Equation IV has the highest adjusted R (0.800) and sixteen explanatory variables (including the 9 age-sex factor scores). However, eight of these v a r i a b l e s are not s i g n i f i c a n t . Equation VII, on the other hand, has only f i v e explanatory variables 2 which are a l l s i g n i f i c a n t . This i s o f f s e t by a reduced R (0.742). Table 4.6 gives a s i m i l a r range of equations as Table 4.5 with 2 CASEX as the dependent v a r i a b l e . Equation I has a high adjusted R value of 0.897 but only s i x of the eighteen regression c o e f f i c i e n t s are s i g n i f i c a n t . In equation I I , EDRAT was dropped because of i t s high 2 c o r r e l a t i o n with BDCFR. The r e s u l t was a s i m i l a r adjusted R (0.898) Table 4.6. CASEX Equations with Information Theory Case Complexity and S p e c i a l i z a t i o n Variable I II III IV V VI 2 Adjusted R 0.897 0.898 0.899 0.887 0.897 0.884 F 54.83 58.60 62.71 125.93 69.76 169.87 MSE 13119.36 12995.04 12898.32 14375.63 13195.25 14829.80 INVCFR t 16312.68 13.77* 16282.39 13.85* 16421.80 14.37* 16396.71 15.94* 16111.57 14.09* 15909.57 15.57* BDCFR t 7.59 2.07* 8.47 3.41* 8.56 3.47* 10.41 4.60* 8.27 3.34* 10.08 4.42* OCC t 460.01 4.16* 460.51 4.19* 455.31 4.17* 464.07 4.42* 416.78 3.84* 401.58 3.90* WAGE1 t 156.27 1.27 158.94 1.30 176.42 1.51 145.62 1.29 WAGE2 t 463.57 1.58 457.48 1.57 429.01 1.50 542.19 1.93 OUTXPD t -285.43 -0.57 -267.49 -0.54 EDRAT t 461.34 0.33 CMPXC1 t 1252.43 5.04* 1244.31 5.06* 1191.95 5.29* 1133.88 9.37* 1217.67 5.40* 1181.32 10.31* SPCLCl t 69.93 4.66* 70.43 4.74* 69.95 4.73* 84.16 9.79* 71.79 4.90* 82.29 9.89* F F 1 9 1 i s s i g . 1 i s s i g . 1 i s s i g . 2 are s i g . Constant t * -1860.02 -4.95* -1852.76 -4.97* -1821.11 -4.96* -1884.45 -5.69* -1199.47 -6.32* -1173.57 -9.61* Indicates significance at 0.05 l e v e l . 124 but no change i n the number of s i g n i f i c a n t c o e f f i c i e n t s . In equation 2 I I I , both EDRAT and OUTXPD were excluded—adjusted R ..remained unchanged at 0.899; s i x of the f i f t e e n regression c o e f f i c i e n t s were s i g n i f i c a n t . In equation IV, the age-sex fa c t o r scores were removed together with EDRAT and OUTXPD. The r e s u l t was a s l i g h t drop (1 percent) i n the 2 adjusted R to 0.887, with f i v e of the seven c o e f f i c i e n t s p o s i t i v e . Equation VI was the same as equation IV except the two i n s i g n i f i c a n t 2 v a r i a b l e s , WAGE1 and WAGE2, were excluded. The adjusted R remained almost the same (0.884) and a l l f i v e c o e f f i c i e n t s were s i g n i f i c a n t . The age-sex factor scores were returned i n equation V with no s i g n i f i -cant increase i n explanatory power (0.897) but an increase i n the number of i n s i g n i f i c a n t c o e f f i c i e n t s from zero to seven. Once again the s e l e c t i o n of the "best" equation i s a trade-off among competing, or non-independent, c r i t e r i a . Equation III has the 2 highest adjusted R but both the WAGE variables are i n s i g n i f i c a n t and eight of the nine age-sex factor scores are i n s i g n i f i c a n t . Equation VI 2 has a s l i g h t l y .lower R value but a l l f i v e independent variables are s i g n i f i c a n t and le s s e f f o r t i s required for data c o l l e c t i o n and computing. 4.3.3. Ap p l i c a t i o n of the estimated cost equation to the  budgeting process The l a s t section presented a number of a l t e r n a t i v e equa-tions which could be used i n the budget se t t i n g process. I t was proposed that e i t h e r equation IV or VII i n Table 4.5 be used i f h o s p i t a l s are to be reimbursed on a cost per day basis or equations I I I or VI, Table 4.6 be used i f h o s p i t a l s are to be reimbursed on a cost per case basis. 125. For purposes of i l l u s t r a t i o n here, we look at how a cost per case equat-ion (equation I I I , Table 4.6) could be incorporated into the budget s e t t i n g process. This equation i s : CASEX = -1821.11 + 16421.80 INVCFR +8.56 BDCFR (-4.96) (14.37) (3.47) + 1191.95 CMPXC1 + 69.95 SPCLC1 + age-sex factor scores (5.29) (4.73) (1 i s s i g n i f i c a n t ) + 176.42 WAGE1 + 429.01 WAGE2 + 455.31 OCC (1.51) (1.50) (4.17) R 2 = 0.899 MSE = 12898.3 From t h i s equation i t i s possible to compare the actual cost of a hospit-a l with i t s predicted cost. (Predicted cost here means the average cost per case that i s predicted i f the h o s p i t a l i s operating as an "average" Alberta h o s p i t a l having taken account of differences i n s i z e , u t i l i z a t i o n , case mix, age of patients, wages.) Table 4.7 shows how t h i s comparison can be made. For a p a r t i c u l a r hos-p i t a l , the actual cost per case Y i s compared with the predicted cost per case Y. The differe n c e between the actual and predicted cost A= Y - Y, and the r e l a t i v e d i f f e r e n c e A/Y can also be seen. From t h i s one can i d e n t i f y the hosp i t a l s which are r e l a t i v e l y more expensive or r e l a t i v e l y l e s s expensive. (The percentages i n column 5, Table 4.7, with, a negative sign i n d i c a t e that the h o s p i t a l exceeded i t s predicted costs).. Some of these hospit a l s are oper-ating at a l e v e l which i s 20 percent above t h e i r predicted average cost per case. S i m i l a r l y there are a number of hospital s which are operating below t h e i r predicted costs, as indicated by the p o s i t i v e sign. T h i r t y hospitals are operating at a l e v e l which i s 10 percent or more below predicted costs. 126 Table 4.7. Actual and Predicted Cost per Case i n 112 Alberta Hospitals Actual and Predicted Cost per Case i t a l No. Actual Cost Y Predicted Cost Y Difference Y - Y Y - Y pel Y 1 534 584 +50 +9.4 2 888 748 -140 -15.8 3 745 810 +65 +8.7 4 875 791 -84 -9.6 5 637 663 +26 +4.1 6 742 705 -37 -5.0 7 774 821 +47 +6.1 8 586 620 +34 +5.8 9 1010 890 -120 -11.9 10 530 605 +75 +14.1 11 957 1084 +127 +13.3 12 969 1056 +87 +9.0 13 1757 1907 +150 +8.5 14 768 733 -35 -4.7 15 1384 1317 -67 -4.8 16 1307 1327 +20 +1.5 17 1030 986 -44 -4.4 18 632 703 +71 +11.2 19 544 575 +31 +5.7 20 641 693 +52 +8.1 21 694 520 -174 -25.1 22 687 690 +3 +0.4 23 496 637 +141- +28.4 24 399 465 +66 +16.8 25 698 739 +41 +5.9 26 778 610 -168 -21.6 27 485 594 +109 +22.5 28 524 483 -41 -7.8 Actual and Predicted Cost per Case Hospital No. Actual Cost Y 29 465 30 845 31 723 32 2971 33 1051 34 989 35 967 36 1770 37 502 38 771 39 594 40 576 41 572 42 575 43 584 44 985 45 1473 46 476 47 735 48 895 49 694 50 551 51 765 52 663 53 745 54 1215 55 414 56 1159 57 808 58 852 59 574 60 564 61 1730 Predicted Cost Difference Y - Y percent Y Y - Y Y 612 +147 +31.6 729 -116 -13.7 651 -72 -10.0 2944 -27 -0.9 1057 +6 +0.6 982 -7 -0.7 1121 +154 +15.9 1711 -59 -3.3 636 +134 +26,7 630 -141 -18.3 524 -70 -11.8 528 -48 -8.3 567 -5 -0.9 478 -97 -16.9 545 -39 -6.7 1076 +91 +9.2 1220 -253 -17.2 431 -45 -9.5 664 -71 -9.7 951 +56 +6.3 744 +50 +7.2 617 +66 +12.0 662 -103 -13.5 519 -144 -21.7 674 -71 -9.5 956 -259 -21.3 448 +34 +8.2 1220 +61 +5.3 608 -200 -24.8 568 -284 -33.3 617 +43 +7.5 727 +163 +28.9 1726 -4 -0.2 128 Actual and Predicted Cost per Case Hospital No. Actual Cost Predicted Cost Difference Y - Y percent Y Y Y - Y Y 62 505 484 -21 -4.2 63 708 897 +189 +26.7 64 774 889 +115 +14.9 65 453 562 +109 +24.1 66 1120 1102 -18 -1.6 67 1660 1275 -385 -23.2 68 728 686 -42 -5.8 69 782 757 -25 -3.2 70 649 751 +102 +15.7 71 975 1146 +171 +17.5 72 927 898 -29 -3.1 73 964 911 -53 -5.5 74 476 536 +60 +12.6 75 828 917 +89 +10.7 76 802 627 -175 -21.8 77 451 512 +61 +13.5 78 771 806 +35 +4.5 79 406 569 +163 +40.1 80 724 644 -80 -11.0 81 531 584 +53 +10.0 82 994 866 -128 -12.9 83 503 572 +69 +13.7 84 624 622 -2 -0.3 85 520 577 +57 +11.0 86 347 491 ; +144 +41.5 87 851 810 -41 -4.8 88 792 738 -54 -6.8 89 650 594 -56 -8.6 90 647 633 -14 -2.2 91 573 566 -7 -1.2 92 709 769 +60 +8.5 93 525 605 +80 +15.2 94 826 723 -103 -12.5 Actual and Predicted Cost per Case Hospital No. Actual Cost Predicted Cost Difference Y — Y percent Y Y Y - Y Y 95 774 696 -78 -10.1 96 546 537 -9 -1.6 97 1465 1445 -20 -1.4 98 668 652 -16 -2.4 99 574 730 +155 +27.0 100 487 607 +120 +24.6 101 700 651 -49 -7.0 102 1000 998 -2 -0.2 103 695 740 +45 +6.5 104 931 1026 +95 +10.2 105 516 656 +140 +27.1 106 844 805 -39 -4.6 107 601 555 -46 -7.7 108 755 667 -88 -11.7 109 562 588 +26 +4.6 110 569 724 +155 +27.2 111 860 943 +83 +9.7 112 1111 1143 +32 +2.9 130 Closer examination of the ho s p i t a l s operating at a l e v e l which i s at l e a s t 10 percent greater than t h e i r predicted average cost per case revealed that these were mostly small h o s p i t a l s . As a consequence, .the i n d i v i d u a l costs involved i n maintaining those hospit a l s at t h e i r higher than expected cost per case rate i s r e l a t i v e l y small. The more i n t e r e s t i n g cases of costs and savings occur i n the large h o s p i t a l s , as they are the most expensive to run. We examined t h e i r actual and predicted costs and calculated the costs or savings as a r e s u l t of t h e i r operation. Of the seven hospit a l s i n the over 300 bed category, three of them were operating at a l e v e l i n excess of t h e i r predicted costs. Their combined over-spending was costing an extra $3.5 m i l l i o n . The four remaining hospita l s i n t h i s bed s i z e category were operating below t h e i r predicted cost and a c t u a l l y saving $8 m i l l i o n . One very large h o s p i t a l , operating at 15.9 percent under i t s predicted cost, was under-spending by $6.5 m i l l i o n . We then looked at another eight h o s p i t a l s i n the 100-299 bed category. A s i m i l a r pattern emergedv-four h o s p i t a l s were operating i n excess of t h e i r predicted costs and four were operating below t h e i r predicted costs. Those hospital s which were over-spending did so by a combined amount of $2.5 m i l l i o n . Those hospita l s which were under-spending were saving $4 m i l l i o n i n t o t a l . When we look at the f i f t e e n l a r g e s t h o s p i t a l s together, about one-half of the ho s p i t a l s are operating at a l e v e l which i s higher than predicted a f t e r standardization f o r difference i n s i z e , case mix etc. The t o t a l cost of t h i s over-spending i s about $6 m i l l i o n . Of the eight h o s p i t a l s who are operating at a l e v e l below t h e i r predicted costs, they are saving approx-imately $12 m i l l i o n . The general p o l i c y implications of t h i s analysis are that resources 131 from hospit a l s operating i n excess should be r e d i s t r i b u t e d to h o s p i t a l s which are operating below costs. The f i n a l method of determining t h i s r e d i s t r i b u t -ion depends upon the p r o v i n c i a l governmenti However, i t i s not proposed that budget requirements should be determined s o l e l y on the basis of the expected costs, as predicted by the regression a n a l y s i s . It should be done i n conjunction with other budget review processes including the p r o v i n c i a l government's knowledge of the i n d i v i d u a l h o s p i t a l s . For instance, small r u r a l h o s p i t a l s may f u l f i l a broader s o c i a l r o l e than s i m i l a r sized urban h o s p i t a l s . This may be manifest i n higher average lengths of stay, thus reducing hardship and inconvenience to patients l i v i n g i n outlying areas. Higher average length of stay usually r e s u l t s i n higher o v e r a l l costs, so these h o s p i t a l s may spend more than t h e i r urban equivalents. Factors l i k e t h i s should be taken into consideration i n the f i n a l a l l o c a t i o n of resources. At the same time, however, i t should be remembered that the most important factors a f f e c t i n g cost differences have been included i n the regression analysis, so adjustments of t h i s nature should only be minor. Some comments are desirable on the absolute amounts of expenditure involved. At f i r s t s i ght, i t appears that the amounts are small by which hospital s are over- or under-spending. The t o t a l budget for the operation of a l l Alberta public hospitals was, for 1978-79, i n the order of $530 m i l l i o n . I n i t i a l l y , the amounts of money involved i n any r e d i s t r i b u t i o n of resources of the order of $20 m i l l i o n i s r e l a t i v e l y small i n r e l a t i o n to t h i s t o t a l budget. Nevertheless, one should not draw the conclusion too h a s t i l y that present financing arrangements are generally adequate. The above analysis i s structured to deal with r e l a t i v e v a r i a t i o n i n cost a t t r i b u t a b l e to v a r i a t i o n i n case mix etc. By v i r t u e of the character of regression analysis, 132 i n essence the estimation of a ' l i n e of.best f i t ' , elements of the cost structure remain unexplained-—not merely the unexplained cost v a r i a t i o n contained i n the r e s i d u a l , but also the e x i s t i n g absolute l e v e l s of h o s p i t a l costs. I t must be stressed that cost predictions based on case mix v a r i a t i o n s cannot account f or i n e f f i c i e n c i e s due to administrative structures or varying medical p r a c t i c e patterns that may be widespread i n the h o s p i t a l system. Other means must be devised to tackle i n e f f i c i e n c i e s from such sources. Possible methods were l i s t e d i n Chapter 1. Nevertheless, a l l o c a t i o n formulae based on case mix v a r i a t i o n are Innately capable of pr e d i c t i n g expected changes i n h o s p i t a l costs, and thus provide a means to constrain p o t e n t i a l e s c a l a t i o n i n costs due to unnecessarily c o s t l y developments i n the adminis-t r a t i v e structure or medical p r a c t i c e . Moreover, the consistent a p p l i c a t i o n of t h i s a l l o c a t i o n formula, such that the budgets of r e l a t i v e 'overspenders' are reduced (and i n a manner than i s seen to be j u s t ) , ought to reduce the incentive of h o s p i t a l s , e s p e c i a l l y major h o s p i t a l s , to demand s u b s t a n t i a l l y greater funds. This would i n turn contribute to a l l e v i a t i n g the escalation of t o t a l expenditure by reducing the 'leap frog' element i n budget requests. 133 Reference Notes, Chapter 4 This negative, i n s i g n i f i c a n t EDRAT c o e f f i c i e n t was unexpected because Evans and Walker (1972) and Barer (1977) found EDRAT to be po s i t i v e and s i g n i f i c a n t , i n d i c a t i n g that education has an i n d i r e c t cost e f f e c t on inpatient costs. 2. The RNI i s compared to CMPXC1 with the age-sex factor scores because age i s adjusted for i n the construction of the RNI. 134 Chapter 5. Summary and Conclusion This chapter, though somewhat r e p e t i t i o u s , i s a s e l f contained summary of the preceding broader study. A concise statement about the purpose, method, r e s u l t s and implications of the study permits easy perusal by p o l i c y makers and government o f f i c i a l s , who may not be able to read the work i n i t s e n t i r e t y . Hospital cost containment has become a p r i o r i t y f o r p r o v i n c i a l govern-ments i n Canada and reimbursing agencies i n the United S t a t e s — a consequence of the dramatic r i s e i n the rate of h o s p i t a l cost increases over the l a s t f i f t e e n years. This increase (discussed i n Chapter 1) i s the r e s u l t of a combination of fa c t o r s , predominant of which i s the increase i n resource use per patient day. This means a more intensive use of manpower, medical tech-nology, laboratory t e s t s , drugs, etc. Obviously the l e v e l of resource use var i e s f o r d i f f e r e n t cases, depending upon the nature of the i l l n e s s and i t s s e v e r i t y . Thus the problem f o r the p r o v i n c i a l government i s not only a reduction i n the rate of increase of h o s p i t a l costs, but also an equitable a l l o c a t i o n of the a v a i l a b l e resources to the h o s p i t a l s , having taken adequate account of t h e i r diverse case mix. Approaches to the reduction of the rate of increase of costs can be undertaken at a h o s p i t a l , regional and p r o v i n c i a l l e v e l . At the h o s p i t a l and regional l e v e l , cost containment can be attempted through global budgeting, u t i l i z a t i o n review, peer review, i n d u s t r i a l engin-eering, r e g i o n a l i s a t i o n of services and/or regional planning and management of services. Examples of ways of reducing costs at a p r o v i n c i a l l e v e l include a reduction i n the number of beds; s u b s t i t u t i o n of some forms of h o s p i t a l care f o r cheaper a l t e r n a t i v e s ; a change i n the method of payment to physicians (from f e e - f o r - s e r v i c e to s a l a r i e d or sessional payment). This thesis has 135 examined s p e c i f i c a l l y the issue of an equitable d i s t r i b u t i o n of a v a i l a b l e resources to the competing h o s p i t a l s , a problem at the p r o v i n c i a l l e v e l . In p a r t i c u l a r , i t has examined the problem of standardizing f o r the heterogen-eous nature of the h o s p i t a l product, suggesting a method of reimbursement that i s not based on a f l a t rate per case or per day f o r a l l h o s p i t a l s , but that takes case mix v a r i a t i o n across h o s p i t a l s into consideration. This approach has cost saving implications because i t means that the reimbursement process no longer needs to be ad hoc and incremental. Rather i t allows fo r informed decisions to be made on the appropriate l e v e l and d i s t r i b u t i o n of resources. Chapter 2 reviews methods of measuring output i n hospitalncost studies. In e a r l i e r studies, standardization for v a r i a t i o n i n h o s p i t a l output occurred by grouping h o s p i t a l s according to the number of services or f a c i l i t -ies a v a i l a b l e at the h o s p i t a l . I t was assumed that h o s p i t a l output was r e l -ated to the range of f a c i l i t i e s a v a i l a b l e so that h o s p i t a l s i n each group had an homogeneous output. A s l i g h t v a r i a t i o n of t h i s method was to group hospit-als according to the numbers of s p e c i f i c services or procedures actually, per-formed. This approach to standardization was an attempt to compare hospita l s on the basis of u t i l i z a t i o n of s p e c i f i c services rather than on the basis of the a v a i l a b l e stock of f a c i l i t i e s or services. The basic assumption here was that each h o s p i t a l ' s output was r e l a t e d to the quantity of services performed. These two basic assumptions oversimplify the way ho s p i t a l s operate. One cannot assume that the u t i l i z a t i o n of a service or f a c i l i t y w i l l be the same for a l l h o s p i t a l s merely because the service or f a c i l i t y e x i s t s i n the h o s p i t a l . Nor can one assume that the presence of c e r t a i n f a c i l i t i e s or a c e r t a i n number of s p e c i f i c services or procedures performed w i l l r e s u l t i n a s i m i l a r case mix at each h o s p i t a l . Standardization of output i n terms of case mix per se seemed a better 136 approach than r e l y i n g on proxies such as the presence or absence of f a c i l i t -ies and services. The development 1of the International C l a s s i f i c a t i o n of Diseases Adapted allowed t h i s to occur i n a systematic manner. A number of techniques have been used to standardize for case mix v a r i a t i o n including (i) f a c t o r proportions of diagnosis or s p e c i a l t y groupings; ( i i ) information theory which ranks hospi t a l s according to the complexity of cases based upon the assumption that the more concentrated cases are more complex; ( i i i ) the Resource Need Index which ranks h o s p i t a l s according to case mix complexity measured i n terms of average charge data. The International C l a s s i f i c a t i o n of Diseases Adapted (ICDA) has been used as the basis for obtaining the diag-n o s t i c groupings for each of these approaches to case mix standardization. More recently, an a l t e r n a t i v e c l a s s i f i c a t i o n scheme has been developed, which attempts to group diagnoses according to resource u t i l i z a t i o n . These groups are c a l l e d Diagnosis Related Groups (DRGs) and the proxy f o r resource.'.utiliz-ation i s average length of stay. Thus diagnoses within a Major Diagnostic Category are d i f f e r e n t i a t e d on the basis of t h e i r length of stay. These DRGs can be used i n conjunction with cost information or information theory to rank h o s p i t a l s according to t h e i r case mix complexity. The advantages and disadvantages of each of these approaches to case mix standardization are discussed i n Chapter 2. In i t s e f f o r t s to contain h o s p i t a l costs,- the government of Alberta r e -sorted to the reduction of h o s p i t a l budgets i n r e a l terms. As a consequence, the government was faced with more ho s p i t a l s appealing t h e i r budget a l l o c a t -ions, claiming they could not operate within the set l i m i t s . Their argument was familiar—"We should receive a larger budget than h o s p i t a l X because we have a much more complex caseload". The government had l i t t l e defence for i t s method of resource a l l o c a t i o n , which was p r i m a r i l y based on l a s t year's costs with a f a c t o r added for 137 i n f l a t i o n . It could not accurately compare h o s p i t a l performance and costs because i t had no systematic way of standardizing for differences i n case mix across h o s p i t a l s . The budget analysts saw the Resource Need Index (RNI), developed by CPHA, as a p o t e n t i a l t o o l to a s s i s t them i n t h i s process. The Resource Need Index i s described i n d e t a i l i n Chapter 2. B a s i c a l l y i t i s an index (to two decimal places) that i s used to rank hospit a l s accord-ing to t h e i r case mix complexity. A l l cases are a l l o c a t e d to one of 3490 morbidity categories defined i n terms of 349 d i f f e r e n t diagnoses, 5 age groups and whether or not surgery was performed. Each morbidity category i s assigned a weight derived from average charge data. The r e l a t i o n s h i p between the aver-age charge for a l l patients and the c e l l average gives the r e l a t i v e value for that c e l l . The Resource Need Index f o r a h o s p i t a l i s determined by m u l t i p l y -ing the number of patients i n any one c e l l by the value for that c e l l ( c a l l e d the Resource Need Units f or that c e l l ) then summing across a l l c e l l s and d i v -i d i n g by the t o t a l number of patients. Thus h o s p i t a l A which has an RNI of 2.00 uses on average twice as many resources per case as h o s p i t a l B which has an RNI of 1.00 The main c r i t i c i s m of the RNI approach to case mix standardization i s i t s basic assumption that average h o s p i t a l charges are a proxy for average h o s p i t a l costs. Charges do not ne c e s s a r i l y r e f l e c t actual costs because i n most American hospit a l s there i s a c e r t a i n amount of cross su b s i d i z a t i o n of costs between various departments. There i s also cross su b s i d i z a t i o n of pat-ients with Blue Cross payers subsidizing Medicare or Medicaid patients. Fur-thermore, the RNI has never been used i n the Canadian s e t t i n g , so the assump-t i o n that American charge data was. a good proxy for Canadian h o s p i t a l costs had not been tested. The government of Alberta requested an evaluation of the Resource Need Index. This was the i n i t i a l request that prompted t h i s study. As a means to 138 t h i s evaluation, i t was decided to.compare the RNI and another measure of case mix complexity i n t h e i r a b i l i t y to standardize h o s p i t a l output accurate-l y f o r case mix v a r i a t i o n . The information theory approach developed by Evans and Walker (1972) was chosen as the standard f o r comparison because of i t s consistent, good performance i n accounting for case mix differences elsewhere i n Canada and the U.S. The information theory approach to case mix standardization i s also de-scribed i n d e t a i l i n Chapter 2. B r i e f l y , information ".theory can be used to accord a value to a h o s p i t a l which r e f l e c t s the case mix complexity of the h o s p i t a l . Relative weights for 188 diagnostic categories (Canadian Morbidity L i s t ) were predetermined on the basis of the assumption that the r e l a t i v e concentration of a diagnostic category i s a measure of i t s r e l a t i v e complexity. An index f o r each h o s p i t a l i s derived by multiplying the number of patients i n a h o s p i t a l i n each diagnostic category by the r e l a t i v e weight of that diagnos-t i c category, summing across a l l categories and d i v i d i n g by the t o t a l number of patients for the h o s p i t a l . Hospitals can then be ranked according to t h i s index of case mix complexity. An average h o s p i t a l has a value of 1.00. The methodology used to compare these measures of case mix complexity i s described i n Chapter 3. To summarize: the information theory measure of case mix complexity or the Resource Need Index was included i n a regression equation along with a number of other independent variables (measures of hos-p i t a l s i z e , capacity, wage l e v e l s , s k i l l mix of non-medical s t a f f attending patients, outpatient a c t i v i t y , teaching a c t i v i t y ) to assess the extent to which i t could explain the dependent variables-—average inpatient cost per case or per day. The r e s u l t s i n Chapter 4 show that the RNI i s not as good a predictor of h o s p i t a l costs as the information theory measure. When the RNI v a r i a b l e i s included i n the regression equation, together with the other i n -dependent v a r i a b l e s , i t adds only 7 percent to the explanatory power of the 139 equation explaining v a r i a t i o n s i n average cost per day, and 8 percent to the explanatory power of the equation explaining v a r i a t i o n s i n average cost per case. On the other hand, when the information theory measure of case mix complexity i s added to the equation (replacing the RNI), the explanatory power of the equation for v a r i a t i o n s i n average cost per day, i s increased by 23 percent, and that for v a r i a t i o n s i n average cost per case, by 16 percent. When the age-sex f a c t o r scores are added,* a further 11 percent of v a r i a t i o n i n average cost per day i s explained, and a further 8 percent of v a r i a t i o n i n average cost per case. This i s f a i r l y conclusive evidence that the informat-ion theory approach to case mix standardization i s superior to the Resource Need Index. Having established the r e l a t i v e s u p e r i o r i t y of the information theory measure of case mix complexity, we can suggest how information theory can be used to improve the h o s p i t a l budget s e t t i n g process i n Alberta. E s s e n t i a l l y i t can be used to evaluate the r e l a t i v e costs of hospitals a f t e r standardization f o r differences i n s i z e , case mix and a number of other f a c t o r s . This can be done using regression analysis i n the same way as i t has been done i n t h i s study. The dependent v a r i a b l e s , average inpatient cost per day and per case can be obtained for a l l h o s p i t a l s from the h o s p i t a l annual return (HS-1 and HS-2). The independent variables (described i n Chapter 3) can be obtained from t h i s source, or, i n the case of the information theory case mix complexity and s p e c i a l i z a t i o n v a r i a b l e s , from the PAS abstract. This record of patient information codes diagnosis according to the International C l a s s i f i c a t i o n of Diseases Adapted (ICDA) and groups t h i s information into 188 broad diagnostic categories (Canadian Morbidity L i s t ) . Barer (1977) showed that the information theory case mix complexity weights were very stable over time i n d i c a t i n g that a h o s p i t a l ' s case 140 mix does not change s i g n i f i c a n t l y from one year to the next. Therefore the case mix weights developed here do not need to be computed each year and can be used i n subsequent years with revised cost estimates. Regression analysis allows the budget analysts to determine the extent to which the independent v a r i a b l e s explain average cost per case or per day. I t also enables them to i d e n t i f y h o s p i t a l s which are r e l a t i v e l y more expensive or r e l a t i v e l y l e s s expensive than would be expected given t h e i r c h a r a c t e r i s t i c s of s i z e , u t i l i z a t i o n , case mix. Table 4.7 shows how t h i s comparison and i d e n t i f i c a t i o n of high and low cost hospi t a l s can be made. Thus corresponding adjustments can be made: to i n d i v i d u a l h o s p i t a l budgets so as ultimately to achieve a more equit-able d i s t r i b u t i o n , o f resources o v e r a l l . This study and i t s findings has a number of important p o l i c y implications: ( i ) The a p p l i c a t i o n of s t a t i s t i c a l techniques used here has been shown to make an important contribution to the budget s e t t i n g process; such techniques can thus make a desirable input • into the policymaking process. ( i i ) Information theory can be used to develop case complexity v a r i a b l e s which r e a l i s t i c a l l y represent case mix v a r i a t i o n i n h o s p i t a l s . These va r i a b l e s allow budget analysts and p o l i t i c i a n s to address the key issue of standardizing h o s p i t a l output to take account of case mix d i f f e r e n c e s — a fundamental step towards developing a system of resource a l l o c a t i o n s to ho s p i t a l s that i s both e f f e c t i v e and equitable. ( i i i ) There are only a l i m i t e d number of h o s p i t a l parameters whose measurement i s necessary for the e f f e c t i v e incorporation of t h i s approach into the budget s e t t i n g process. Therefore i t can be achieved at minimum cost and i s a p o l i t i c a l l y v i a b l e s o l u t i o n to a complex and 141 d i f f i c u l t problem. (iv) P o l i c y makers may continue to neglect t h i s process at t h e i r own p e r i l . 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