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Life-cycle activity patterns of registered nurses in British Columbia : forecasting future supply and… Kazanjian, Arminée 1947-; Brothers, Kent; Wong, Gordon Mar 31, 1985

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LIFE-CYCLE ACTIVITY PATTERNS OF REGISTERED NURSES IN BRITISH COLUMBIA: FORECASTING FUTURE SUPPLY AND PROFESSIONAL LIFE EXPECTANCY Report S:l8 Prepared by: Division of Health Services Research & Development Office of the Coordinator The John F. McCreary Health Sciences Centre The University of British Columbia Vancouver, British Columbia V6T 1Z6 March, 1985 * ** *** LIFE-CYCLE ACTIVITY PATTERNS OF REGISTERED NURSES IN BRITISH COLUMBIA: FORECASTING FUTURE SUPPLY AND PROFESSIONAL LIFE EXPECTANCY Arminee Kazanjian, Dr.Soc.* Kent Brothers, Ph.D.** Gordon Wong, B.Sc.*** Research Associate, Division of Health Services Research and Development, The University of British Columbia Research Associate, Division of Health Systems, The University of British Columbia Progranmer/Analyst, Division of Health Services Research and Development, The University of British Columbia An earlier version of part of this work was presented at the Pacific Health Forum 83, Vancouver, B.C., September 23-24, 1983. March, 1985 This report is one of a series describing the distribution of health manpower and health resources in the Province of British Columbia. These reports, prepared for the Health Manpower Working Group of the Ministry of Health and for the Associations and Licensing bodies which provide the data, are working documents and comments or suggestions are welcome. HEAL TH MAJ'\PO\\'ER RESEARCH UNIT c o Ol'FICI:: or Tiil: C'OORDl!'\ATOR HL\L TH SCI I:: NCES C'l:NTRE PllO~E : 1604 l 228-4810 Mr. Chris Lovelace, Chai nnan, Health Manpower Working Group, Ministry of Health, 1515 Blanshard Street, Victoria, B. C., VBW 3C8 Dear Mr. Lovelace, 4th FLOOR 1.R.C. BUILDING THE UNIVERSITY or BRITISH COLUMBIA VANCOUVER. B.C' .. CAN ADA V6T l\\'5 January 30, 1985 It is with great pleasure and no lesser sense of gratification that I transmit to you and the members of the Health Manpower Working Group the completed report "Life-Cycle Activity Patterns of Registered Nurses in British Columbia: Forecasting Future Supply and Professional Life Expectancy". This report updates our earlier report on nurse supply and provides revised projections using an improved model. In addition, the report contains new data and analyses on the expected total professional lifespan and the average continuous professional lifespan of RNs based on the different life-cycle activity patterns of the eleven age-groups. We trust members of the Group and other planners will find useful applications of the projection model. Enc 1 . ; /slm. Sincerely your~ , l+-1<vi~/ 1 ~z Anninee Kazanjian, Dr.Soc., Research Associate, Division of Health Services Research and Development. A Research Unit fur the Health Manpower Working Group, Ministry of Health. British Columbia ACKNOWLEDGEMENTS The research on which this study is based is supported by a grant from the Ministry of Health, Government of British Columbia. The cooperation of the Registered Nurses' Association of British Columbia is gratefully acknowledged. - 1 -Table of Contents List of Tables.................................................. 11 Li st of Figures.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 I. INTRODUCTION.............................................. 1 I I • METHODS. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 3 III. BASIC PROJECTION MODEL STRUCTURE.......................... 7 IV. APPLICATION OF THE PROJECTION MODEL....................... 11 V. NEW REGISTRANT SUBMODEL. • . . . . • . • • • • • • • . • • • . • • . • . • . • • • • • . • • 12 VI. PROJECTIONS............................................... 16 Age Specificity........................................... 19 VII. PROFESSIONAL LIFE-EXPECTANCY.............................. 21 Computation of Professional Life Expectancies............. 23 VIII. CONCLUDING REMARKS AND PLANNING APPLICATIONS.............. 25 References Appendices A. Age-Specific Transition Probability Calculations B. RNABC 1975-80 New Registrant Proportionate Age Distribution C. Age-Specific Supply Projections for RNs, 1981-1985 D. Age-Specific Professional Life-Expectancy Projections for RNs E. Derivation of Computational Procedures to Obtain Professional Life Expectancies F. Age-Specific Supply Projections for RNs, 1985-1989 G. Age-Specific Supply Projections for RNs, 1981-1985 (modified) Table la,b 2 3 4 5 6 7 Figure 1 2 3 4 - 11 -List of Tables Page Illustrative Matrices of Frequency Counts (a) and Probabili-ties (b) for Membership State Transitions, Ages 30-34 ••••••• 1980 Membership State Vector for 30 Year Olds ••••••••••••••• An Example of the Basic Projection Model for 30 Year-01 d Nurses: Projection into 1981 from 1980 ••••••••••••••••• Infusion of New Registrants - An Example •••••••••••••••.••. Projected Membership Figures, 1981 - 1985 .•••••••••.••••••. Projected Increases in Nursing Stock Components, 1981 - 1985 ............................................... . Professional Life Expectancy for 30_Year-Old RNs ..•••.••... List of Figures Nurse Supply Projection Model •••••••••••.••••••••••.••...••• RNABC New Registrants 1918 - 1984 .•••••••••.•••••••••••••••• Trends in RN Stock - Projected vs. Actual Membership by Professional Membership Status •••••••••••••••••••••.•••.• RN Transition Probabilities by Age .•••••••••••••..•.• ••• . ••• 10 11 12 15 17 19 25 6 13 18 22 - 1 -I. INTROQUCTION Health manpower planning and in particular its quantitative research stage have not, until very recently, received much approbation as complex and necessary processes in the planning and operation of health care delivery systems. Recent efforts are mainly in the area of physician manpower. The first National Health Manpower Conference in Canada was held in October 19691 based on the belief that an attempt should be made to develop our human resources in the health field in some kind of rational manner. A rational planning approach is even more important for health care personnel than for those in primary markets, since microeconomic forces that equilibrate the latter do not apply as readily (if at all) to the health environment2• There is also some evidence that nurses' market work behaviour is appreciably different from that of other health occupations due mainly to the gender factor. Nursing is a female dominated profession and considerable variation in the amount of time spent in market work exists among individuals3• Thus, an in-depth study was undertaken to specifically quantify Registered Nurse (RN) supply/requirements in British Columbia and provide useful information to planners at various levels4. The conceptually simple quantitative stage in manpower planning is comprised of estimating current supply and requirements and forecasting future supply/requirements based on a set of reasonable underlying assumptions. The estimation of supply is the seemingly less complex of the two procedures and has traditionally enjoyed relatively more attention from researchers. The estimation of requirements has, - 2 -therefore, often remained unstudied. The paucity of efforts in this area has been especially characteristic of the health care industry because of its obvious and frequently cited perils of quantifying 'need' or 'demand' for services as precursors to developing estimates of personnel requirements. The misleadingly straightforward task of data collection can frequently generate apparently conflicting results. In-depth studies of nurse manpower supply or requirements for the specific purpose of long-term and province-wide nurse manpower planning have, so far, been lacking in Canada. Nationally, some data have been compiled recently in the form of working papers, conference proceedings, etc. 5 These often address specific, narrowly defined issues, useful for short-term planning purposes only. Frequently, anecdotal accounts are the only data presented as research evidence. Unfortunately, these sometimes unreliable findings are usually confusing and may even be misleading for planning and policy-making purposes. Although literature in this area is more readily available in the U.S. than in Canada, findings from these studies are generally not applicable to the Canadian situation. Most frequently, these studies focus only on economic 'demand' (i.e. willingness to pay), and its influence on the available numbers of practising RN stock at any given time. Yet a thorough understanding of the interaction dynamics of the macro- and micro-factors within a longitudinal framework is necessary for a comprehensive analysis of the situation. The larger study, on which this paper is based, was undertaken in order to attempt to diminish this research gap. Quantification and - 3 -analysis of supply data6 was the first step in the sequential progression of the research project. Projections of future supply and analyses of professional life expectancy reported here are an extension of that work, an improved version of the forecasting model first described in an earlier report. II. METHODS: The Registered Nurses' Association of B.C. (RNABC) provided the data in the form of a computerized file of their annual registration records with individual identifiers deleted. This database contained 52,312 records of which 24,658 were records of currently active, paid-up members at December 31st, 1980. Membership renewal forms are systematically completed by members on an annual basis at the same time dues are paid. The information contained within these forms, therefore, is primarily self-reported and subject to the usual shortcomings of such data. Certain items of information, however, are provided and/or verified for each member by RNABC which uses this information for other administrative and fiscal purposes. Throughout our study, we have been careful to note potential inconsistencies and provide qualifiers in the interpretation of self-reported data. Only simple descriptive statistics have been used where the data do not warrant more rigorous analysis. The latter type of analysis is carried out using data that are reliable and verifiable. In general, conceptual models depicting variables and processes that influence the number of 'trained' nurses available for employment - 4 -describe three points of entry to this active 'pool': production through the educational institutions, which generally are the primary source of supply (modified by registration requirements of professional organizations which define the proportion of graduate nurses qualified as RNs); ent~y to the active pool through migration (including immigration from other countries and interprovincial in-migration); and re-entry to the active pool (including those returning to nursing subsequent to an occupational shift, or time out of the labour force). The two exit points are described as pennanent (retirement, death), and temporary attrition (out-migration, emigration, occupational shift). Nurses in this latter category tan reverse the decision to stay out of the labour force and, as such, comprise a segment of the inactive 'pool' which includes non-practising members of the professional association as well as non-member stock in the province. The potential supply of nurses is, therefore, the combined 'pools' of those currently employed in nursing and those not employed (but with the required educa~ional attainment). Our preliminary analysis of membership data to ascertain what would constitute current practising stock proved enlightening. Several equally valid frameworks for counting supply were revealed from an analysis of membership data. The most comprehensive method for this province entailed using membership status (the specific categories will be discussed later), which provided us with the broadest definition of current supply. Membership status in conjunction with employment status was more specific than the fonner and provided a somewhat narrower definition of - 5 -current stock. A further refinement was classifying current stock by place of residence (in/out of province) as well as membership and employment status. The number of enumeration methods could increase by at least one more if one were to include the survey-approach, to reach a potentially wider population base (i.e. the non-registered but educationally qualified), who were trained outside B.C., and may be working in this province as "graduate" nurses in a variety of settings. However, in developing the projection model we chose, for various reasons, to use solely membership status rather than more specific employment data. The decisive factor was the generally greater reliability level of membership infonnation. Also, the RNABC data base did not contain easily retrievable historical information on employment but did have a five-year membership history record for all nurses (52,312) who had ever been RNABC members. We did, however, statistically test the validity of using membership status as a surrogate measure for employment status. Membership data for 1980 indicated a strong statistical relationship between membership status and employment status with approximately a four percent margin of error for all practising members (i.e. that a Practising member is employed in nursing is true 96 percent of the time). Differences in counting baseline figures have, of course, certain implications for the calculation of projected stock and this will be noted in the discussions. - 6 -Since the changes in membership status of individual nurses vary greatly, and are made based on individual decisions, some form of probabilistic model is required in order to make manpower projections. A simple, age-specific, projection model was, therefore, developed comprised of two submodels: a Markovian one to monitor yearly movements from one membership state to another and a linear submodel for the infusion of new stock (Figure 1). The advantage of using an age-specific model is that it does not require additional (and sometimes arbitrary) estimates of future incrementation and attrition rates based on a presumed overall age structure of future stock. The model is designed to apply the appropriate rates, given the demographic make-up of the stock for the year projected. In general, the model assumes that past trends in age-specific attrition rates, reactivations, and age structure of new registrants will not be appreciably different in the future. These assumptions, however, could be replaced by any other set of reasonable assumptions, to investigate the effect of various policy options. Figure 1 NURSE SUPPLY PROJECTION MODEL NEW STOCK :I CURRENT INACTIVE STOCK STOCK I ~ j - 7 -III. BASIC PRGJECTION MODEL STRUCTURE As a baseline model we have considered a discrete-time Markov model which involves the nurse's age and membership status at pre-detennined, equally-spaced points in time, in particular, December 31st, of each year. The model assumes that the likelihood of moving to any membership state depends only on the nurse's current age and membership state and not on the prior membership pattern for that individual. Although this is a statistically testable assumption, we have not investigated its validity, but rather have focused on the projections which result from this simple "first-order" model. For the purpose of this computation, the eight actual registration statuses then (1980) used by the RNABC were aggregated into three: 0 Non-members (who were once registered members); 1 Non-practising members; 2 Practising members The Markov model states that for a nurse aged x who is now in state i (i=O, l, or 2), there is a probability pij(x) that that nurse will be in state j one year later. For example, a Practising member (i•2) aged 30 may have a soi chance of remaining in that state (j=2), a Joi chance of dropping out (non-registered, j=O) and a 2oi chance of changing to non-practising (but registered, j=l). We would then have a probability vector, the elements of which sum to 1.0: - 8 -p 20 { 30 ) S • 30 I P21 C30) = .20 and p 22 ( 30 ) = • 50 All possible transition probabilities in this system are conveniently expressed in the form of a Mtransition matrix". for a given age x as follows: P(x) = p00Cx) p10Cx) P20Cx) Po1<x> Pu Cxl p21 Cx) Po2<x> P12Cx) p22 Cx) To obtain estimates of the probabilities. we used the membership histories of 52 1312 nurses (all records of members ever registered with RNABC). These five-year histories along with the current membership status became effectively a six-year history of an individual's level of nursing membership activity. An individual's history was. however, treated as 5 single transitions based on the assumption made by the "first order" model 1 and not as a string of transitions with two or more annual moves in a sequence. Although one could compute transition probabilities and hence forecasts for individual ages, the transition probability matrices here were derived for age groups. Single-age calculations whould have generally been considered ideal but in many cases the cell frequencies were too small to yield useful and reliable transition probabilities. As well, the lack of evidence that career orientations of 26 (or 31)-- 9 -year-old nurses are substantially different from those of 25 (or 30)-year-old ones provided yet another reason to group the data. Age categories were comprised of the usual five-year intervals, grouping those under 25 1 those 25-29 1 30-34, ••. 55-59; then 60-63 1 64-65 and those 66+. A number of factors were considered in selecting these categories; the clear identification of child-bearing age ranges, in order to delineate the influence of this factor was among the reasons for this grouping. The reason for the unusual groupings beyond 60 years of age was to more closely track the behaviour of a group approaching retirement age. We noted that many of those beyond retirement age continued to maintain practising membership; presumably some worked during those years. After close examination of the data for each age beyond 60, three age-groups were included comprising 60-63 year old, 64-65 year old and 66+ year old members respectively. The latter broad category was warranted by the small size of this sub-group. The calculation of the probability matrices is illustrated by the following example. Table l{a) shows the frequency counts of all transitions for nurses aged 30-34. The probabilities, shown in Table l(b), are obtained by dividing each frequency count by the corresponding sum. Thus, the probability of remaining active for this age group is .876 because out of the 15,580 cases in which nurses were practising on December 31 1 in 13,653 {or 87.6i) of those cases the nurse was also practising one year later. - 10 -Tables l(a) and (b): Illustrative Matrices of Freguenc~ Counts (a) and Probabilities (6) for Membe,rship tate Transitions, Ages 30-34 to: O from: (a) 1 2 Total 0 11843 110 609 12562 1 460 2610 680 3750 2 751 1176 13653.15580 to: from: 0 1 2 (b) 0 1 2 .943 .009 .048 .123 .696 .181 .048 .075 .876 In sunmary, the probability matrices were calculated with a computer program using age and six-year membership history data using the following steps: a) age-specific frequency distributions of transitions to/from one of 3 possible states were compiled from the six-year membership records of all nurses who had ever registered with the association. Each of 52,312 cases contributed up to five transitions to one of the 11 age-specific 3x3 matrices. Thus, a total of 232,843 individual membership transitions were tallied. b) Age-specific probability matrices were then calculated such that the rows of the matrices sunmed to 1.0. Usually, a single nurse contributed to two and sometimes three age-specific matrices. It should be noted that the larger baseline of 52,312 was used calculating the transition probabilities (instead of the currently registered membership of 24,658) in order to capture as broad a picture as possible by calculating all probabilities of reactivation regardless of how long ago the member's registration had expired. A detailed table of transition probabilities is included in Appendix A. - 11 -IV. APPLICATION OF THE PROJECTION MODEL We. took a stochastic view of the future behaviour of our population, given initial conditions. We could then project the state of our population one or more years into the future. The initial conditions were simple distributions of current membership status (an ordinal variable coded O through 2) by single ages, termed "membership state vectors". Membership state vectors for each age group were multiplied by the age-specific transition matrix to complete one iteration (one year) in the projections. It is important to note that the aging of the population was accounted for simply by shifting the age-reference at each iteration. Those aged n years at one iteration became n+l years old at the next iteration. As an example of this iterative scheme, note in Table 2 the December 1980 membership state vector for those 30 years of age. Table 2: 1980 Membership State Vector f~r 30 year Olds Past-Member Non-Practi sin~ Practisin~ (No Fee) (Partial Fee (Full Fee Total 0 1 2 318 160 754 1232 - 12 -The age-specific probability matrix used for 30-year-olds is that shown in Table l(b). Multiplication of the above vector (Table 2) and transition probability matrix (Table l(b)) yields the numbers projected for the next year (Table 3). In particular, the number of practising 31-year-old nurses is equal to the number of practising 30-year-old nurses who remain active (754 x .876) plus the number of non-practising 30-year-old members who become active (160 x .181) plus the number of past members 30 years of age who become active (318 x .048). The new numbers constitute the membership state vector for 31-year-old nurses for 1981. Table 3: An Example of the Basic Projection Model for 30 Year-Old Nurses: ProJection into 1981 from 1980 [318 160 75~ x "year n11 state - -. 943 • 009 • 048 .123 .696 .181 ~048 • 075 • 87§_ Matrix of Transi-tion Probabilities V. NEW REGISTRANT SUBMODEL = ~56 171 70~ "year n+l 11 state Tabl"e 3 does not take into account new registrants during the period. In order to quantify the infusion of new registrants into the projection, historical data were examined for possible trends or patterns. To gain more insight, these data were also analysed by place of graduation, but the increased complexity did not add to the accuracy of overall projections and was, therefore, not pursued further. Thus, only overall numbers of new registrants, regardless of place of - 13 -graduation, were used in the model. The charted data (Figure 2) indicated that a strong linear trend has dominated since the mid-1930s', wi~h upeaks" in new registrations occurring sporadically, and a line was therefore fitted to the data using least-squares. Thus, the number of new registrants (Y) was estimated in tenns of the year of registration (X), as Y =A+ B (X-1900) where A = -1233.6 and B = 39.32. For example, the projected number of new registrants in 1981 is y = -1233.6 + (39.32)(1981-1900) = 1951 A rough confidence belt could also be described here. At this time however, no error has been calculated for the model's output, since confidence limits for the Markov projections cannot be readily produced. We did, however, give serious consideration to using a weighted regression model for projecting the number of new registrants. Since there were numerous scenarios, all equally plausible, to justify the application of different weight factors to the years under consideration (1940-1980), we decided not to use a weighted model - at least not for the current version. In order to combine data from this new registrant submodel with that of the basic projection model, it was also necessary to derive the age distribution of new registrants. This distribution was obtained from the aggregate age distributions of five successive cohorts of inital registrants, spanning the same period as the membership data (1975-Figure 2 RNABC NEW REGISTRANTS 1918-1984 2600 • I R1ac111lon foe x11r1 1940-1980 I I fl) 2000 • .., c cu I I y - -1233.8 + 39.32(X - 1900J ~ .., fl) ( r1 - 0.94) ·-CJ G> 1600 •• 00 a: o excluded from regression • 0 ~ . .... G> ~ "°" .. z .._ •• 0 1000 • •• ... G> .. .c E :J z 6001 0 0 0 0 0 00 ~Cb° 0 0 cJJOO ) . 10 20 30 40 60 80 70 80 90 . Year (19--) - 15 -1980). The underlying assumption here is that, for the projection period 1980-1985, the age distribution of new registrants would remain the same. However, the model was designed to easily allow specification of the new registrant age distribution for each projection period. The estimation of the age of projected new registrants using the historical proportionate age distributions entailed the specification of how many new members would be, for example, 25 1 26, 27, etc. based on the historical information on age of new registrants. Table 4b, provides some sample age proportions for new registrants. A detailed table of new registrant age proportions is included in Appendix B. Table 4: Infuston of New Registrants - An Example a) ESTIMATION OF TOTAL NUMBER OF NEW REGISTRANTS IN 1981 USING THE LEAST SQUARES REGRESSION EQUATION (1940 - 1980) Y = A + B(X - 1900) Number of new registrants in 1981 = -1233.6 + (39.32 x 81) = 1951 b) CALCULATION OF 1981 NEW REGISTRANTS BY AGE Age Historical Proportion Total I I New (Appendix 8) x New Registrants = Registrants 30 0.0458 1951 89 31 0.0454 1951 89 32 0.0384 1951 75 33 0.0358 1951 70 ~ 0.0349 1951 68 - 16 -VI. PRnJECTIONS Three categories of membership activity are consistently used throughout. Members of the full-fee-paying Practising group (which includes Affiliates and Re-activations) are coded 2. ihe part-fee-paying Non-Practising group is coded 1. The non-renewals or past members are coded O. The latter two groups (0,1) comprise the inactive pool from which reactivations m~y take place. Also note that only the first two groups (1,2) are considered members of the RNABC, the payment of a fee qualifying them as members of the BC association. The straightforward procedural stages involved in forecasting future stock basically are those depicted in Figure 1. Starting from the 1980 actual membership distribution vectors (by single ages) and applying the age-specific transition probabilities to each vector, the Markov-based model produces age-specific projections, for the subsequent year, of numbers in each of the three membership states. The infusion of new (first-time member) stock by age into the uPractising" state (coded 2) based upon an average rate of growth of new members over the past 40-year period completes the projection procedure for one year. This then is one discrete iteration of the Markov model representing one transition period, or one year's membership increment. The results of one iteration provide a basis for the next iteration quite independently of any sequence of ·past iterations, a key assumption of the model we have developed and characteristic of the Markovian process we have discussed. Further work is being done to test that assumption by examining possible patterns in membership states. - 17 -The iteration process can be repeated as many times as annual projections are required. The error component however, is compounded with each repetition. Table 5 presents projected totals by membership status for each of the years, 1981 - 1985. A detailed age-specific projection table is presented in Appendix C. Table 5: Projected Membership Figures, 1981 - 1985 Year: 1980 Actual 1981 1982 1983 1984 1985 Membership Status Non- Total Practising Practising Members 1 3942 4233 4497 4738 4957 5165 2 20686 21557 22444 23341 24250 25164 1+2 24628 25790 26940 28079 29207 30329 Figure 3 graphs the projected trends for each of the paying membership states 1 and 2, separately and combined. Figure 3 and Tables 5 and 6 provide a sumnary of the projections computed from the model. Since the net change in the total count (including those in state O) is due to new registrant numbers less the number deleted from the system at age 75, increases in the number of new registrants, the larger of the two components, each year, produce an approximately linear increase in the total count. - 18 -The average annual growth rate is slightly higher for the part-fee-paying non-practising stock. However, the relative proportions of Figure 3 3!5 30 -.. ..,, c ID .. :» 0 • -"' IDli: 1!5 w CD ~ :::::> z 10 TRENDS IN RN STOCK Projected vs. Actual Membership by Professional Membership Status 5 o············ ·······c;················c;··············1t••·o·rrr•t•••••i9••••••••• 80 81 82 83 8~ 85 PROJECTION YEAR Legend o PROJECTED ·········· • ACTUAL - 19 -Table 6: Projected Increases in Nursing Stock Components, 1981-1985 Net Increase Annual Average Membership Status S Increase 1981 1982 1983 1984 1985 Practising (full-fee) 871 887 897 909 914 3.8 Non-Practising (part-fee) 291 264 241 219 208 5.2 practising and non-practising nurses have remained stable over the longer term. 7 Aie-Specificity It is instructive to study the probability matrices themselves (Appendix A) and note the age-specificity of the transition probabilities. The data show, for example, that among currently practising nurses 25-29 years of age, 86 percent will remain practising members next year while another 8 percent will become non-practising members; 6 percent will not renew their membership. In contrast, among currently practising nurses 45-59 years of age, 94 percent will renew their membership as practising members next year while 4 percent will renew as non-practising members and only 2 percent will drop their membership altogether. This same percentage distribution also applies to the 50-54 year-old group currently practising. Thus, the data clearly show that the attrition rate among practising nurses (the 2 to 0 transition probability) varies appreciably among the age-groups between a low of 2 percent (for those 45-54 years of age) and a high of 22 percent (for those 66 years of age and over). For - 20 -those approaching retirement age, the rate for the age-group 60-63 is already on the upswing and among the 64-65 year-old practising group, the data indicate 15 percent will let their membership expire in the following year. It is perhaps more instructive to note that among the fonner (1.e. 64-65 year-old currently pract1s1ng nurses), 74 percent will remain practising members the following year. Presumably, an appreciable proportion among this group will remain employed. Another interesting feature of the probability matrices pertains to the 0 to 2 transition statistic, indicating the likelihood of returning to a practising state once a member has dropped out. The data show that this is inversely proportional to age with, at best, 9 percent returning among those 18-24 years of age, 3 percent among those 35-39 years of age and expectedly, less than 0.2 percent returning at 64 and 65. The detailed transition probabilities for eleven age groups and for all ages -- as well as providing in-depth analyses of various types of attrition (for example, 2 to 1 vs. 2 to 0, or 2 to O vs. 1 to O) --provide extensive information on reactivation rates and patterns by age group. They indicate, for example, that at 30-34 years of age, a nurse whose membership is expired is five times more likely to return as a practising member (probability of 0.048, or almost 5i of the expired group will return as practising members) than as a non-practising member (probability of .009, or less than 1i will return as non-practising members). In comparison, a nurse 50-54 years of age is eight times more likely to return as a practising member (as opposed to non-practising). However, the size of this returning group (just under 2i) is much smaller than that of the 30-34 year-old group. The data also indicate - 21 -that staying power (2 to 2 transition) is greatest at 50-54 (.945), and, among the pre-retirement (under 60) age-groups, is lowest at 25-29 (.857). Expressed another way, while 95 percent of practising 50-54 year-old nurses will remain practising the following year, only 86 percent of their 25-29 year-old counterparts will do so. The details of the projections of stock over time show a particular age cohort's characteristic behaviour, and include the effect of aging and the influence of the child-bearing ages. This is best illustrated by Figure 4 which is based on the transition probabilities and provides, in epidemiological terminology, the survival curve of each membership status. VII. PROFESSIONAL LIFE-EXPECTANCY As well as projecting future stock, the age-specific transition matrices can be used to estimate professional life-expectancy of for Registered Nurses. For example, one may wish to know how many years a nurse who is presently aged 30 will practice, on average, before ceasing to practice. Alternately, noting that a nurse may cease to practice and then resume practising at a later date, one may wish to know how many years a 30-year-old nurse will practice, on average, before being deleted at age 75 . Answers to both of these questions are provided (indirectly) by the transition probability matrices. Detailed, age-specific, professional life expectancy projections are provided in Appendix D. Figure 4 w ~ ~ VJ w F :::J -m <( m 0 cc c... z 0 E VJ z <( ~ z cc - 22 -.--~~~~~~---..~~~~~~~-.-~~~....-0 : • CD . . ' . ' . . . . . . : I I I 0 .................................. . ........... ... .. ~ .................. : ................ (<J-" : : = /I . . . . . . . . . . . . . . . . : : : •<1 . l : : I I . : : : • <I  . . . . ' . . 0 ..... ~ ................. :··· ............... ~ .................. : ............ ,... C) I I I I . . . . • • • • • ~j i ·.~ ~i I I -;; "" . : . - : .... -: = = -;: • <I m -· ........ ~.c:.j ............... ... j .................. ~ ............ : .1 ...... f ........ , g ~ t I I - I -· . . .. . w u: : : u : • <I .t j i i .t i I ~ I ~ : : : 0 : I\ ! : : : .. : • g <I ' . • D. I ....... D.~ ............. .... ~ .................. j ............. 'C .• ; .• , ...... !!'.. . 0 C:· • • -· .:: • ! : : : .!! : .! .. : : : •:• •<l ~l l l !iJl!/ .t: : : A.: ~D.. : : : '= :e ti O<J ................ J .................. : .................. ~ ............. -1 .. 1: .... 'it.~,.... 0 I : I • I'> , ' • IC : ! ! • I <J : = = 1· oc I I I I I : : : : z . . . . . . . . . . . . : : : • : <l t--~~--1--~~--~~~-+~~~--~~~~o ~ - CD 0 c) All118\f80Hd NOlllSN\fHl - 23 -Computation of Professional Life Expectancies Lei e1j(x) denote the expected (average) number of years spent in membership state j from now untf 1 age 75 by a nurse who is presently aged x and who is in membership state f. (The age 75 fs selected because our data indicate many nurses remain fn practice beyond the nominal retirement of 65, but few beyond the age of 75.) In addition, let Ci(x) denote the expected number of years spent continuously fn membership state i from now until age 75 by a nurse who is presently aged x and who is in membership state i. Appendix E shows how the associated E(x) matrix and C(x) vector are derived mathematically from the P(x) matrices, and the basic reasoning is in the following paragraphs. A 30-year-old nurse who is currently practising has a probability of .876 of remaining in practice until the following year (from Table l(b)). Thus, ff we start with 1000 30-year-old practising nurses, the number will fall to 876 by the end of one year. The average number of nurses during the year is therefore about (1000 + 876)/2 = 938, so the average amount of time worked per nurse is (1.000 + .876)/2 = .938 years. Similarly, of these 1000 nurses, none are non-practising at the beginning of the year, but 75 will be by the end of the year, so that the average amount of time spent as a non-practising member is (O + .075)/2 = .038 years per nurse. Consider now the second year. The probability that the nurse will be active at the end of the second year, assuming that she is active at the end of the first year, is also .876, but since the probability of being active at the end of the first year is .876, the probability of - 24 -being active at the end of both years is (.876)2 = .767. During the second year we would therefore expect (.876 + .767)/2 = .822 years of work, so that over the two years we would expect .938 + .822 = 1.76 years of ncontinuous" work. A continuation of this reasoning over a 45-year period would yield the value of c2(30). However, to obtain the total probability that the nurse is practising at the end of two years we must also add the probability that she becomes non-practising at the end of the first year but resumes practising by the end of the second year (.075 x .181 = .014), and the probability that she becomes non-registered (i.~ •• drops out) by the end of the first year but re-registers by the end of the second year (.048 x .048 = .002). The overall probability that she will be practising at the end of the second year, given that she is practising at the outset, is therefore .767 + .014 + .002 = .784. The expected amount of time spent practising during the second year is therefore (.876 + .784)/2 = .830 years, and the total amount of time spent practising over the two years is .938 + .830 = 1.768 years. A continuation of this reasoning to age 75 leads to the value of professional life expectancy at age 30 (E22(30)). Fortunately, the mathematics given in Appendix E provides some shortcuts in performing these calculations, and the computer takes care of the rest. Table 7 shows E(30) and c2(30), indicating that a 30-year-old nurse who is currently practising will spend, on average, a total of 17.5 years as a practising member, 4.4 years as a non-practising member, and 23.1 years unregistered over the 45-year period up to age 75, and - 25 -will practice for an average of 10.0 years before leaving "practising" status for the first time. Table 7: Professional Life Expectancy for 30 Year-Old RNs Current Total Number of Years of Continuous Number of Status Membership in Years of Membership Status I 0 1 2 - - -0 33.6 2.6 8.9 1 25.5 6.2 13.3 2 23.1 4.4 17.5 10.0 VIII. CONCLUDING REMARKS AND PLANNING APPLICATIONS The purpose of the analysis presented in this report is twofold. The first, of course, is the interest in the results and the subject matter, nurse manpower. The second purpose of this report concerns its forecasting capacity and the statistical information provided by the analysis. The application of the Markov model to this setting provides a powerful tool to the decision-makers in this sector. Incorporation of the model into the planning process would provide further insight to both planners and researchers regarding the reliability of the forecasts and potential refinements of the model. Alternatively, the model is so designed as to provide easy conversion to a simulation model whereby the potential outcomes of various scenarios can be quantified providing the - 26 -planner with accurate information on several options from which to choose. The most obvious question, and one that fs currently being raised more frequently, fs regarding a generally aging population. What impact will this (general population) trend have on nurse manpower in particular? To illustrate, age-specific projections (Appendix C) indicate clearly a slight but steady aging of the membership over the short projected period. The 18-24 year-old practising group (state 2) is more than halved by 1982, mainly due to a rather conservative increase in new registrant numbers (for age-proportionate breakdown see Appendix B) combined with a substantial attrition rate (5.8S) for this age-group. However, this group appears to be holding its own by 1985 with approximately a 2 percent increase. Admittedly, in absolute numbers this category is proportionately small compared to others, however, it is the group with potentially the longest professional life expectancy. Our projections show the impact of some nurses in this group moving on to the next age category (25-29), thus contributing to the increase in these numbers for the next two years. However, the same (as in the youngest group) high attrition rate applied here results in a projected decline in numbers (by 3S) in 1983. Given this high attrition rate of the two youngest groups an overall aging of nurse manpower does not necessarily imply the certain depletion of stock. The projections (Appendix C) show that the older age-groups (30 and over) increase appreciably. As well, projections of - 27 -professional life expectancy delineate rather interesting life cycle activity patterns. Data in Appendix D indicate that, at 20 years of age, a currently practising member will spend an average of 20.4 years as a practising member, 5.0 years as a non-practising member, and 29.7 years unregistered over a period of 55 years until deletion from our counting system at age 75. However, a 30 year-old currently practising member is expected to spend an average of 17.5 years as a practising member and remain unregistered for 23.l years over a 45 year period until deletion. The ratio of years of practising membership to unregistered years is highest at 40 when, from a possible 35 year professional life expectancy period, an average of 15.4 years will be spent as a practising member and 16.1 years will be spent in the unregistered (state O) category. It is perhaps more important to examine the average number of continuous years of practising membership by age (Appendix D - last column), especially from the educator's point of view as well as from the employers' perspective who have invested various resources (for orientation or training of new recruits in the respective setting) which presumably may yield different rates of return. Not surprisingly, perhaps, the data show that the youngest nurses do not provide the highest continuous number of years of practising membership with the professional association (as a proxy measure for employment in the field). The lowest continuous years among the younger practising members is for 24 and 25 year-old nurses with an average of 8.1 years and equal to that of 53 year old nurses; the highest is for 40 - 28 -year old nurses with an average of 12.7 years. Continuous number of years of practising membership and total number of years of practising membership values converge at age 62 from which point on the two figures become almost identical. Appendix D also provides infonnation on those members currently non-practising (1) and unregistered (0). A twenty-year old non-practising member is expected to spend an average of 17 years of practising membership while her unregistered counterpart will spend 15 years in that category (practising). These compare favourably with their practising counterpart who, on the average, will spend 20.4 years in that category. In sharp contrast, at 30 years of age this margin of difference between practising/non-practising/unregistered categories is much wider and, unlike continuous years, this gap is inversely proportional to age, i.e. the younger a nurse returns to practising membership, the longer the total time she will spend in that category. This confirms and gives a time-defined value to the results produced by the age-specific transition probabilities (Appendix A). Therefore, life expectancy calculations of projected stock provide a solid base from which to start planning alternative courses of action. In sullll'lary, then, the forecasting capability developed in this report attempts to address two questions central to manpower planning. The first is how many nurses will there be in the province in the next five years, and the second, what is the time-frame involved in the nurses life-cycle activity patterns. - 29 -While professional membership status is used here only as a proxy measure, our analysis indicates this to be a valid and highly reliable measure. In 1980, · the baseline year from which projections were made, 96 percent of practising members were employed (or seeking employment) in nursing. In addition, another 28 percent of non-practising members were employed (or seeking employment) in the field. An appreciable number in this category are B.C. members who reside outside the province, while some are B.C. residents who may be working in some nursing capacity but not as RNs. Thus, future stock projections can be further refined by the application of the above fractions in order to obtain the number of nurses employed in the field for any given year. This further refinement of numbers, we have ascertained, is rather sensitive to economic conditions and opportunity structures. In 1984, the percentage employed (or seeking employment) in nursing among practising members was lower than in 1980 at 91 percent, however, the percentage employed (or seeking employment) in nursing among the non-practising members was higher at 36 percent. This information is readily available on an on-going basis8 and its application to the projections will provide a more narrowly defined estimate of future stock. One can be even more specific in projections of future stock by applying the most current figure on the percentage employed in a hospital setting, a community setting, etc. Finally, the value of a forecasting model lies, ultimately, in its predictive accuracy. In this regard our model ranks fairly high for short term projections. Although 1981 was a record year in that registration figures rose due to increased renewals and a relatively large number of new registrants, the total projected figures (25,790) - 30 -fell short (26,172 actual) by only 1.5 percent. In 1982, registration figures were more 11 normal 11 , 1.e. new registrant numbers were similar to the figure extrapolated from the 1940-1980 new registrant linear submodel and our projections for that year (26,940) surpassed the actual number (26,705) by less than one percent (0.9S). However, 1983 was a record low registration year when the practising membership figure in fact decreased by 0.65 percent (from 22,187 to 22,042). Our projections for total registrants (28,079) surpassed the actual number (26,744) by approximately 5 percent. This error, unfortunately, becomes compounded for further projections. For 1984, the difference between actual (27,265) and projected (29,208) is 7 percent, but we also noted that new registrant numbers appear to have stabilized at a level similar to those in the early seventies. Consequently, to take this type of evidence into consideration, we have included in Appendix F projections for the further period 1985-1989 using the 1984 currently registered stock as our database. The linear new registrant submodel has been replaced by the three-year (1982-1984) average number of new registrants, 1,410 (See Figure 2). Only time will tell, of course, whether in fact this oscillation in registration statistics have stablized and the hard-to-model period is well behind us. These years, as depicted in Figure 2, indicate that the historical trend is no longer valid and needs reconsideration - at least for the short tenn. The two different methods thus provide planners with alternative scenarios, the appropriateness of which will vary over time. New oscillatory experiences in registration notwithstanding, the margin of error for these 1985-1989 projections should not exceed a 1-2 percent margin. - 31 -Appendix G has been included to demonstrate the accuracy of the Markovian submodel, the larger of the two components of this forecasting capacity. In this third model, the new registrant submodel is comprised of actual new registration statistics for each year, 1981-1984, and the average for these years is used for the 1985 figure. The resulting projections for 1981-1985, using 1980 registration data as our baseline, provide us with an instance of perfect infonnation on new registrants and a test of the probabilistic submodel. These compare favourably with actual registration data for the four available years, the difference never exceeding one per cent. REFERENCES 1. Hacon, W.S. (1974), The Health Manpower Situation in Canada, Pan-American Conference on Health Manpower Planning, PAHO and WHO Scientific Publication No. 279: 28-34. 2. See, in particular, Evans, R.G. (1984), Strained Mercy: The Economics of Canadian Health Care, Toronto: Butterworths; among others, Ward, R.A. (1975), The Economics of Health Resources, Massachusets: Addison-Wesley Publ. Co.; Feldstein, P.J. (1979), Health Care Economics, New York: John Wiley & Sons, Inc. 3. See, for example, Benham, L. (1971), The Labour Market for Registered Nurses: A Three-Equation Model, The Review of Economics and Statistics 11(3): 246-252; Bognanno, M.F. (1970), An Economic Study of the Hours of Labour Offered by the Registered Nurse, Ph.D. thesis, University of Iowa, University Microfilms, Inc., Ann Arbor, Michigan. 4. Reports and papers from the larger study include: Kazanjian, A. and G.W. Wong (1982), Registered Nurses.!!!. British Columbia: A Report on the Supply Situation, Report S:ll, and Kazanjian, A. and S. Chan (1984), Nurse Requirements.!!!. British Columbia: An Analysis of the 1979-82 Trends, Report S:l6, Division of Health Services Research and Development, The University of British Columbia, Vancouver; and, Kazanjian, A. and A.J. Stark (1984), Registered Nurses in British Columbia: An Examination of the 1979-1983 Registration Statistics, Health Management Forum, forthcoming. 5. See, for example, Giovannetti, P., Primary Nursing - The Number One Solution. In Zilm, G., A. Heeton and M. Richmond (1982), Nursing Research: ~Base for Practice, Service and Education, Proceedings of National Nursing Research Conference, Vancouver, B.C., April 28-30: 16-27; Jenny, J.L. (1982), Issues Affecting Nurses' Hospital Employment of the 80's, Ottawa: Canadi~n Hospital Association; Lalonde, M. (1974), A New Perspective on the Health of Canadians: A Working Document by the Minister of National Health and Welfare, Ottawa: Infonnation Canada. 6. Kazanjian, A. and G. Wong (1982) Op.Cit. 7. See respective ROLLCALL reports for specific figures over time. 8. Ibid. APPENDICES APPENDIX A AGE-SPECIFIC TRANSITION PROBABILITY CALCULATIONS TRANSITIONS TRANSITION PROBABILITIES Status Status at End of Year Status at End ot Year at Start Age Range of Year 0 1 2 A11 0 1 2 0 383 7 39 429 0.893 0.016 0.091 ·18 - 24 1 57 148 63 268 0.213 0.552 0.235 2 445 407 6757 7609 0.058 0.053 0.888 0 4755 61 361 5177 0.918 0.012 0.070 25 - 29 1 403 1785 557 2745 0.147 0.650 0.203 2 1030 1497 15102 17629 0.058 0.085 0.857 0 11843 110 609 12562 0.943 0.009 0.048 30 - 34 1 460 2610 680 3750 0.123 0.696 0.181 2 751 1176 13653 15580 0.048 0.075 0.876 0 16853 107 589 17549 0.960 0.006 0.034 35 - 39 1 234 1915 446 2595 0.090 0.738 0.172 2 450 640 11701 12791 0.035 0.050 0.915 0 14773 107 430 15310 0.965 0.007 0.028 40 - 44 1 146 1211 221 1578 0.093 0.767 0.140 2 237 349 9256 9842 0.024 0.035 0.940 0 13452 64 309 13825 0.973 0.005 0.022 45 - 49 1 111 847 138 1096 0.101 0.773 0.126 2 177 298 7718 8193 0.022 0.036 0.942 0 11180 24 184 11388 0.982 0.002 0.016 50 - 54 1 115 626 101 842 0.137 0.743 0.120 2 126 221 5908 6255 0.020 0.035 0.945 0 9709 28 87 9824 0.988 0.003 0.009 55 - 59 1 109 767 54 930 0.117 0.825 0.058 2 129 241 4414 4784 0.027 0.050 0.923 0 7783 12 33 7828 0.994 0.002 0.004 60 - 63 l 124 573 36 733 0.169 0.782 0.049 2 166 208 1988 2362 0.070 0.088 0.842 0 3874 1 6 3881 0.998 0.000 0.002 64 - 65 1 54 233 9 296 0.182 0.787 0.030 2 101 74 509 684 0.148 0.108 0.744 0 16013 8 13 16034 0.999 0.000 0.001 66 & up 1 103 487 6 596 0.173 0.817 0.010 2 110 84 295 489 0.225 0.172 0.603 APPENDIX B RNABC 1975-1980 New Registrant Proportionate Ase Distribution Proportion or new t"eli9trants (Total W = 10,753) 0.0002 o.o 0.0001 0.0020 w 0.0160 0.0446 0.0658 0.0859 0.0928 0.0981 0.0865 0.0613 0.0458 0.0455 0.038~ 0.0358 :::::~::::z::::~::s::: s:::=====~=============s ======================== c::z:&:~~a::::::::::::: :::::::z::z::::~z::::z: =====~=========:::::::: ====~===~~~====~~s::::: ======================= ======================= =================== ========:========= o.oiso o.o 06 o.o 26 0.0206 0.0209 0.0155 0.0139 0.0137 0.0118 o.ool5 o.oo 1 o.oo 8 0.0082 0.0079 0.0073 0.0059 0.0048 0.0046 0.0038 O.OOIIZ 0.0039 0.0032 0.0020 0.0021 0.0031 0.0024 0.0018 0.0022 0.0010 0.0010 0.0010 0.0005 0.0005 0.0007 0.0002 o.o o.o 0.0001 o.o o.o o.o 0.0001 s:::::::::::::::: ------------------------------=========== :z:::::::: ========== s::::::: =------------======= ------------=----=---=---==== ==== s:: == == == == == = = s: = = = ======z=========== ===========~========= s:::::s:::~::::s::::::: =~~::a::::t:::::: ===== APPENDIX C A9e-Specific SUEElY Projections for RNs, 1981-1985 (Actual RNABC figures are shown in parentheses) Reg'd Non- Non- Reg'd Reg'd Reg'd Pract Pract Subtotal Age Group {O) (1) (2) (1 )+(2) 18-24: 56 51 1279 1330 25-29: 903 586 4073 4659 30-34: 2002 866 3729 4595 Year 1980 35-39: 3233 744 3458 4202 40-44: 3291 463 2592 3055 {Actual 45-49: 2861 329 2026 2355 data) 50-54: 2645 214 1606 1820 55-59: 2058 198 1068 1266 60-63: 1697 209 577 786 64-65: 844 93 150 243 66-75: 3875 189 128 317 Total: 23465 3942 20686 24628 (3955) (20720) (24675) 18-24: 53 42 833 875 25-29: 893 628 4288 4916 30-34: 1957 894 3952 4846 Projection 35-39: 3101 792 3725 4517 Year 1981 40-44: 3412 508 2892 3400 45-49: 2905 366 2169 2535 {1951 new 50-54: 2689 245 1696 1941 registrants) 55-59: 2221 214 1144 1358 60-63: 1757 223 582 805 64-65: 875 101 149 251 66-75: 4060 219 126 346 Total: 23923 4233 21557 25790 {4213) {21959) {26172) 18-24: 31 22 523 545 25-29: 887 661 4359 5020 30-34: 2019 945 4255 5199 Projection 35-39: 2898 800 3860 4661 Year 1982 40-44: 3531 584 3238 3822 45-49: 3001 388 2299 2687 {1991 new 50-54: 2749 270 1833 2104 registrants) 55-59: 2391 250 1217 1467 60-63: 1783 230 589 819 64-65: 888 100 148 248 66-75: 4212 247 123 370 Total: 24390 4497 22444 26940 (4518) (22187) (26705) Notes: - Pre-projection (1980) population has been adjusted to exclude cases with missing data on membership history or age. - Some totals may not add due to rounding. Appendix C (cont'd) Reg'd Non- Non- Reg'd Reg'd Reg'd Pract Pract Subtotal Age Grou2 (0) (1) (2) (1 )+(2) 18-24: 16 12 420 432 25-29: 876 649 4230 4879 30-34: 2063 1008 4540 5547 Projection 35-39: 2770 835 4045 4880 Year 1983 40-44: 3612 632 3506 4138 45-49: 3078 421 2511 2932 (2030 new 50-54: 2821 289 1924 2213 registrants) 55-59: 2514 278 1293 1572 60-63: 1789 233 581 815 64-65: 974 108 168 276 66-75: 4415 273 123 396 Total: 24927 4738 23341 28079 (4702) (22042) (26744) 18-24: 13 10 415 425 25-29: 826 608 3988 4596 30-34: 2107 1060 4790 5850 Projection 35-39: 2787 889 4316 5205 Year 1984 40-44: 3543 664 3716 4380 45-49: 3172 455 2664 3119 (2069 new 50-54: 2906 320 2088 2408 registrants) 55-59: 2665 305 1377 1682 60-63: 1819 235 595 830 64-65: 1070 122 180 302 66-75: 4600 289 122 411 Total: 25506 4957 24250 29207 (4374) (22891) (27265) 18-24: 13 10 422 433 25-29: 723 540 3717 4256 30-34: 2209 1137 5094 6230 Projection 35-39: 2748 906 4422 5328 Year 1985 40-44: 3482 719 3991 4710 45-49: 3335 502 2928 3431 (2109 new 50-54: 2971 337 2182 2519 registrants) 55-59: 2800 336 1489 1825 60-63: 1904 244 616 860 64-65: 1046 121 170 291 66-75: 4847 313 132 445 Total: 26078 5165 25164 30329 APPENDIX D AGE-SPECIFIC PROFESSIONAL LIFE EXPECTANCY PROJECTIONS FOR RNs Average Total Number of Years in Status Type: Continuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 36.5 4.4 16.1 18 1 32.7 6.3 18.0 2 30.7 5.0 21.3 8.3 0 36.2 4.3 15.6 19 1 32.3 6.2 17.5 2 30.2 5.0 20.8 8.3 0 35.8 4.1 15.0 20 1 31.9 6.2 17.0 2 29.7 5.0 20.4 8.2 0 35.5 4.0 14.4 21 1 31.4 6.1 16. 5 2 29.2 4.9 19.9 8.2 0 35.3 3.9 13.8 22 1 30.9 6.1 16.0 2 28.6 4.9 19.5 8.2 0 35.0 3.7 13.2 23 1 30.4 6.1 15.6 2 28.1 4.9 19.1 8.2 0 34.8 3.6 12.6 24 1 29.7 6.1 15.2 2 27.5 4.8 18.7 8.1 Status Coding: 0 = Non-Registered 1 = Non-Practising, Registered 2 • Practising, Registered Appendix D (cont'd) Average Total Number of Years in Status Type: Continuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 34.7 3.4 11.9 25 1 28.8 6.3 14.9 2 26.9 4.8 18.3 8.1 0 34.4 3.2 11.4 26 1 28.2 6.2 14.6 2 26.2 4.7 18.1 8.4 0 34.1 3.1 10.8 27 1 27.6 6.2 14.2 2 25.5 4.7 17.8 8.7 0 33.9 2.9 10.2 28 1 26.9 6.1 13.9 2 24.7 4.6 17. 7 9.0 0 33.7 2.8 9.6 29 1 26.2 6.1 13.6 2 24.0 4.5 17.5 9.5 0 33.5 2.6 8.9 30 1 25.5 6.2 13.3 2 23.1 4.4 17.5 10.0 0 33.2 2.5 8.4 31 1 24.8 6.2 13.0 2 22.4 4.3 17.3 10.3 0 32.8 2.3 7.9 32 1 24.1 6.1 12.7 2 21.6 4.2 17.1 10.8 0 32.5 2.2 7.3 33 1 23.4 6.1 12.5 2 20.9 4.1 17.0 11.1 0 32.2 2.1 6.8 34 1 22.6 6.2 12.2 2 20.1 4.0 16.9 11.6 Status Coding: O = Non-Registered 1 = Non-Practising, Registered 2 = Practising, Registered Appendix D (cont'd) Average Total Number of Years in Status Type: Continuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 31. 9 1.9 6.2 35 1 21.8 6.3 11.9 2 19.2 3.9 16.8 12.2 0 31.4 1.8 5.8 36 1 21.3 6.2 11.5 2 18.6 3.8 16.5 12.3 0 30.9 1. 7 5.3 37 1 20.8 6.2 11.0 2 18.0 3.8 16.2 12.4 0 30.5 1.6 4.9 38 1 20.4 6.2 10.5 2 17.4 3.7 15.9 12.5 0 30.0 1.5 4.5 39 1 20.0 6.1 9.9 2 16.8 3.6 15.6 12.6 0 29.5 1.4 4.1 40 1 19.7 6.1 9.2 2 16.1 3.5 15.4 12.7 0 29.0 1.3 3.7 41 1 19.3 6.1 8.7 2 15.6 3.5 14.9 12.5 0 28.4 1.2 3.4 42 1 18.8 6.0 8.2 2 15.2 3.4 14.4 12.2 0 27.9 1.1 3.0 43 1 18.4 5.9 7.7 2 14.7 3.4 13.9 12.0 0 27.3 1.0 2.6 44 1 18.1 5.8 7.1 2 14.2 3.3 13.5 11. 7 Status Cod;ng: 0 = Non-Registered 1 = Non-Practis;ng, Registered 2 = Pract;sing, Reg;stered Appendix D (cont'd) Average Total Number of Years f n Status Type: Continuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 26.8 0.9 2.3 45 1 17.7 5.7 6.5 2 13.8 3.3 13.0 11.4 0 26.1 0.8 2.0 46 1 17.3 5.6 6.1 2 13.3 3.2 12.5 11.1 0 25.5 0.8 1.8 47 1 16.9 5.5 5.6 2 12.9 3.1 11.9 10.7 0 24.8 0.7 1.5 48 1 16.5 5.4 5.1 2 12.5 3.1 11.4 10.4 0 24.1 0.6 1.3 49 1 16.1 5.3 4.6 2 12.1 3.0 10.9 10.0 0 23.4 0.5 1.1 50 1 15.9 5.1 4.1 2 11. 7 3.0 10.3 9.6 0 22.6 0.5 0.9 51 1 15.3 5.1 3.6 2 11.3 3.0 9.7 9.1 0 21.8 0.4 0.8 52 1 14.7 5.1 3.2 2 10.9 2.9 9.2 8.6 0 21.0 0.4 0.6 53 1 14.1 5.2 2.7 2 10.6 2.9 8.5 8.1 0 20.2 0.3 0.5 54 1 13.5 5.3 2.2 2 10.3 2.8 7.9 7. 5 Status Coding: 0 = Non-Registered 1 = Non-Practising, Registered 2 = Practising, Registered Appendix D (cont'd) Average Total Number of Years in Status Type: Cont;nuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 19.4 0.3 0.4 55 1 12.8 5.5 1.6 2 10.0 2.7 7.3 6.9 0 18.5 0.2 0.3 56 1 12.2 5.4 1.4 2 9.6 2.7 6.7 6.5 0 17.6 0.2 0.2 57 1 11.6 5.2 1.2 2 9.2 2.6 6.2 6.0 0 16.7 0.2 0.2 58 1 11.0 5.0 1.0 2 8.9 2.5 5.6 5.4 0 15.7 0.1 0.1 59 1 10.4 4.8 0.8 2 8.6 2.4 5.0 4.9 0 14.8 0.1 0.1 60 1 9.8 4.5 0.7 2 8.3 2.3 4.4 4.2 0 13.9 0.1 0.1 61 1 9.0 4.4 0.6 2 7.8 2.2 4.0 3.9 0 12.9 0.1 0.1 62 1 8.1 4.4 0.4 2 7.2 2.1 3.6 3.6 0 11.9 0.0 0.0 63 1 7.3 4.4 0.3 2 6.8 2.0 3.2 3.2 0 11.0 0.0 0.0 64 1 6.5 4.3 0.2 2 6.4 1.9 2.7 2.7 0 10.0 0.0 0.0 65 1 5.6 4.3 0.2 2 5.8 1.8 2.4 2.4 Status Cod;ng: 0 = Non-Registered 1 s Non-Practising, Registered 2 = Practising, Reg;stered Appendix D (cont'd) Average Total Number of Years in Status Type: Continuous Number of Current Years of Practising Age Status 0 1 2 Status (Type 2) 0 9.0 0.0 0.0 66 1 4.7 4.2 0.1 2 5.2 1.8 2.0 2.0 0 8.0 0.0 0.0 67 1 3.9 4.0 0.1 2 4.4 1.6 2.0 2.0 0 7.0 0.0 o.o 68 1 3.1 3.8 0.1 2 3.6 1.5 2.0 2.0 0 6.0 0.0 0.0 69 1 2.4 3.5 0.1 2 2.8 1.3 1.9 1.9 0 5.0 0.0 c.o 70 1 1.8 3.2 0.1 2 2.1 1.0 1.9 1. 9 0 4.0 0.0 o.o 71 1 1.2 2.8 o.o 2 1.4 0.8 1.8 1.8 0 3.0 0.0 0.0 72 1 0.7 2.3 0.0 2 0.9 0.5 1.6 1.6 0 2.0 0.0 o.o 73 1 0.3 1. 7 0.0 2 0.4 0.3 1.3 1.3 0 1.0 0.0 0.0 74 1 0.1 0.9 o.o 2 0.1 0.1 0.8 0.8 0 0.0 0.0 0.0 75 1 0.0 0.0 0.0 2 0.0 o.o o.o 0.0 Status Coding: 0 = Non-Registered 1 = Non-Practising, Registered 2 = Practising, Registered APPENDIX E Derivation of Computational Procedures to Obtain Professional Life Expectancies In order to calculate the expected time spent by a •1111ber in each of the 11e111bership states, let us first generalize P(x), the one-year transition aatrix at age x, to tl~1 ,x1 ), the transition .. trix from age x to age x. (i.e •• a period of x -x years)*. If we let p(x) denote the vector (of length 3) of 1 2 2 1 probabilities that an individual is 1n one of the three ,.._IM>ership states, then Then the expected time spent in each of the states, given an initial probability dfstribut1on of p(x0) at age x , is 0 75 where E(x) • Jx t(x,t)dt. A recursive approximation to E(x) may be obtained as follows: .x+l 7 s E(x) • / t(x.t)dt +I t(x,t)dt x · x+1 • /x+l t(x, t)dt + t(x,x+l} I 75 t (x+l, t)dt X Xfl • 1X+l t(x,t)dt + P(x)E(x+l) II( • ~[•(x,x} + t(x,x+1)] + P(x)E(x+1) ~~[I + P(x)] + P(x)E{x+l) •~I + P(x)[~I+E(x+1)] ,5 Since E(7S) • J t(1s,t)dt • 0, we may readily compute the E matrices from the P matrices by working from 75 E(?s} backwards. The following approximation to Ci(x). the expected amount of time spent continuously in state i for a member already fn state i. is obtained similarly: • An i11111ed1ate consequence of this definition is that t(x ,x ) • t(x ,x )t(x ,x }. Note also that P(x) • l 3 1 2 2 3 t(x.x+1), and that t(x,x)•I, the identity .. trix. APPENDIX F Age-S~ecific Su~~ll Projections for RNs 1. 1985-1989 (Assumed number of new registrants each year would be average of new registrants during 1982-1984 period) Reg'd Non- Non- Reg'd Reg'd Reg'd Pract Pract Subtotal Age Groue (0) (1) (2) (1)+(2) 18-24: 96 14 708 722 25-29: 1090 361 3420 3781 30-34: 2166 858 4298 5156 Year 1984 35-39: 2912 921 4037 4958 40-44: 3638 643 3584 4227 (Actual 45-49: 3266 415 2600 3015 data) 50-54: 2952 358 1955 2313 55-59: 2726 270 1374 1644 60-63: 1827 199 606 805 64-65: . 1139 103 183 286 66-75: 4766 212 117 329 Total: 26578 4354 22882 27236 18-24: 45 19 476 495 25-29: 997 424 3215 3639 30-34: 2128 913 4340 5253 Projection 35-39: 2910 874 4094 4968 Year 1985 40-44: 3546 728 3780 4508 45-49: 3441 452 2862 3313 (1410 new 50-54: 3007 343 2069 2412 registrants) 55-59: 2872 330 1437 1767 60-63: 1916 211 621 832 64-65: 1064 114 164 278 66-75: 4979 245 129 375 Total: 26905 4652 23188 27840 18-24: 32 12 330 342 25-29: 866 434 3033 3467 30-34: 2124 924 4290 5214 Projection 35-39: 2860 902 4188 5091 Year 1986 40-44: 3481 754 3946 4700 45-49: 3612 510 3093 3603 (1410 new 50-54: 3078 352 2188 2540 registrants) 55-59: 2937 363 1494 1857 60-63: 2135 246 677 924 64-65: 985 108 154 262 66-75: 5238 273 133 407 Total: 27348 4878 23527 28405 Note: - Some totals may not add due to rounding. Appendix F (cont'd) Reg'd Reg'd Non- Non- Reg'd Reg'd Pract Pract Subtotal Ase Group (0) (1) (2) (1)+(2) 18-24: 23 8 294 303 25-29: 760 416 2822 3237 30-34: 2056 923 4176 5099 Projection 35-39: 2963 927 4354 5281 Year 1987 40-44: 3303 761 3991 4752 45-49: 3771 582 3363 3945 (1410 new 50-54: 3197 366 2297 2663 registrants) 55-59: 3027 387 1573 1960 60-63: 2245 281 716 997 64-65: 1018 99 165 264 66-75: 5419 298 130 428 Total: 27783 5048 23881 28929 18-24: 20 8 289 297 25-29: 698 397 2676 3073 30-34: 1954 902 4023 4926 Projection 35-39: 3022 946 4461 5407 Year 1988 40-44: 3201 779 4068 4847 45-49: 3878 624 3562 4186 (1410 new 50-54: 3294 398 2487 2885 registrants) 55-59: 3118 401 1616 2017 60-63: 2402 303 745 1047 64-65: 1101 117 184 301 66-75: 5534 308 127 435 Total: 28222 5183 24239 29423 18-24: 18 8 290 297 25-29: 481 347 2456 2803 30-34: 2001 901 3980 4881 Projection 35-39: 2952 950 4452 5403 Year 1989 40-44: 3331 809 4259 5068 45-49: 3812 657 3689 4346 (1410 new 50-54: 3435 417 2620 3037 registrants) 55-59: 3194 432 1751 2183 60-63: 2570 326 776 1102 64-65: 1169 129 185 314 66-75: 5687 324 132 455 Total: 28648 5301 24590 29891 APPENDIX G Aae-SEecific SuEEll Projections for RNs, 1981-1985 (Used actual number of new registrants 1980-1984, and the average for these years for 1985. Actual RNABC figures are shown in parentheses) Non- Non- Reg'd Reg'd Reg'd Pract Pract Subtotal Age Group {O) Cl) - <il (1 )+(2) 18-24: 56 51 1279 1330 25-29: 903 586 4073 4659 30-34: 2002 866 3729 4595 Year 1980 35-39: 3233 744 3458 4202 40-44: 3291 463 2592 3055 (Actual 45-49: 2861 329 2026 2355 data) 50-54: 2645 214 1606 1820 55-59: 2058 198 1068 1266 60-63: 1697 209 577 786 64-65: 844 93 150 243 66-75: 3875 189 128 317 Total: 23465 3942 20686 24628 (3955) (20720) (24675) 18-24: 53 42 850 892 25-29: 893 628 4344 4973 30-34: 1957 894 3979 4873 Projection 35-39: 3101 792 3740 4532 Year 1981 40-44: 3412 508 2900 3407 45-49: 2905 366 2174 2540 (2084 new 50-54: 2689 245 1699 1943 registrants) 55-59: 2221 214 1145 1359 60-63: 1757 223 583 806 64-65: 875 101 150 251 66-75: 4060 219 126 346 Total: 23923 4233 21689 25922 (4213) (21959) (26172) 18-24: 32 22 456 478 25-29: 890 666 4163 4829 30-34: 2021 947 4166 5112 Projection 35-39: 2898 801 3813 4614 Year 1982 40-44: 3531 585 3213 3798 45-49: 3001 388 2283 2671 (1415 new 50-54: 2749 271 1824 2095 registrants) 55-59: 2391 250 1211 1461 60-63: 1783 230 586 816 64-65: 888 100 147 247 66-75: 4213 247 122 369 Total: 24396 4506 21985" 26491 (4518) (22187) (26705) Rotes: - Pre-projection (1980) population has been adjusted to exclude cases with missing data on membership history or age. - Some totals may not add due to rounding. Appendix G (cont 1 d) Non- Non- Reg 1 d Reg'd Reg'd Pract Pract Subtotal Age Group (0) ( 1) (2) (1)+(2) 18-24: 14 10 306 315 25-29: 868 635 3778 4413 30-34: 2060 1002 4322 5325 Projection 35-39: 2769 833 3920 4753 Year 1983 40-44: 3612 632 3443 4074 45-49: 3078 420 2472 2892 (1374 new 50-54: 2821 289 1900 2189 registrants) 55-59: 2514 278 1279 1557 60-63: 1789 233 575 808 64-65: 974 108 166 274 66-75: 4414 273 122 395 Total: 24912 4712 22283 26995 (4702) (22042) (26744) 18-24: 9 7 289 296 25-29: 790 562 3339 3901 30-34: 2091 1036 4440 5476 Projection 35-39: 2780 880 4116 4996 Year 1984 40-44: 3541 661 3611 4272 45-49: 3171 453 2602 3056 (1441 new 50-54: 2905 318 2050 2368 registrants) 55-59: 2665 304 1355 1659 60-63: 1818 234 584 818 64-65: 1069 121 178 299 66-75: 4599 288 119 408 Total: 25437 4866 22683 27549 (4374) (22891) (27265) 18-24: 9 7 308 315 25-29: 654 463 2966 3429 30-34: 2164 1084 4617 5701 Projection 35-39: 2731 886 4155 5041 Year 1985 40-44: 3476 712 3848 4560 45-49: 3333 498 2847 3346 (1579 new 50-54: 2969 334 2130 2464 registrants) 55-59: 2799 334 1460 1793 60-63: 1902 242 602 844 64-65: 1045 120 167 287 66-75: 4845 312 129 441 Total: 25928 4993 23229 28222 

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