Aust. N.Z. J. Med. (1975), 5, pp 401-407

A Forecast of Requirements for the Treatment of Chronic Renal Failure in Victoria A. J. McBride" From the Hospitals Computer Services, Victoria

Summary: A forecast of requirements for the treatment of chronic renal failure in Victoria. A. J. McBride, Aust. N.Z.J. Med., 1975, 5, pp. 401-407. Using a Markov chain mathematical model, dialysis and transplantation requirements for Victoria in the next five to ten years have been predicted. The numerical constants in the model are based on data from past Australian experience. Predictions showed a steady rise in numbers requiring dialysis and transplantation. Home dialysis numbers will probably double within five years but hospital dialysis numbers will only increase by 50% in the same period. If as many patients as possible were trained for home dialysis on entering the treatment programme, home dialysis numbers could triple in five years, but hospital dialysis numbers would be correspondingly reduced. It is hoped that this model will enable planning authorities to allocate, resources for renal failure treatment in a more rational manner.

Forecasts of dialysis and renal transplantation requirements have been made by Farrow et al." and Kerf' for England and Europe respectively. Their work pointed towards very large increases in home dialysis requirements. However, these forecasts are not directly applicable to Australia where there has been more emphasis on transplantation. It has also been noted by Mathed that transplantation survival is much higher in Australia than elsewhere. This study was undertaken to forecast future requirements for renal failure treatment in Victoria. All the data used in this analysis has

'

Research Assistant. McBride, Hospitals Computer Services, North Science Block, Monash University, Clayton, Victoria 31 68 Accepted for publication: 19 March, 1975

Correspondence: A. J.

come from Australian patients and was mostly extracted from the reports of the Australian Kidney Foundation Maintenance Dialysis Suivey' and the National Transplant Survey.6

Method f

The method used was basically that of Farrow et al.' They constructed a mathematical model which simulated the movements of patients through the various stages of chronic renal failure treatment. Their model was based on a flow chart of 26 states. This has been amended to 23 states to suit Australian conditions. Each state represents a certain stage of treatment undergone for one month, e.g. a month on dialysis. There is a progression of patients from state to state corresponding to patients undergoing transplants, rejecting their grafts, returning to dialysis and so on. Farrow er al.' analysed this movement using the Markov Chain principle. This utilises the probabilities of a patient moving from one state to another in any one month, and hence the expected movements of patients based on these probabilities. The probabilities were estimated using Australian data covering total Australian experience where possible. Some probabilities however were impossible to calculate empirically. A sample of Victorian renal physicians were asked to give estimates of these values, and averages over the sample were used in the model. The method and the probabilities used are given in more detail in the appendix. Starting with the situation as at the end of October, 1973, the model was then used to forecast for a ten year period.

Assumptions The model was based on several assumptions: 1. A patient can only make one move in any one month. Although in reality a patient could pass through several states in a single month, this is unusual. Any error introduced by this will be negligible. 2. Probabilities remain constant with time. 3. Probabilities are independent of previous progress through the various states. This has been found to be valid overseas.' However, it has not been possible to test this on Australian data. 4. Survival rates from home and hospital, dialysis are assumed equal. Although not strictly true, this makes little difference to the results. 5. Patient and graft survival for second transplants are assumed to be the same as for first transplants. 6. Patients are only considered for two transplants. After two failed transplants, all patients are established on permanent dialysis.

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Results

In the following text, and in the discussion, all figures relating to input rates of new patients into the programme imply an annual rate, i.e. 80 indicates 80 per year. In 1973 the number of new patients entering the programme in Victoria was 78. This input rate has been increasing by about 8% and therefore is likely to range between 84 and 120 patients in the next five years. Table 1 shows forecasts for input rates of 84 new patients, 120 new patients and for an input rate increasing exponentially from 84 to 120 over five years.

m

c,

E

Q)

*m c,

2 200

84

loo

'

TABLE 1 Forecasted transplant and dialysis situations at the end of two and five year periods, as from October 1973, assuming an average waiting for a first transplant of seven months.

84 exponentially increasing to 120

New Patients per year

78'

Forecast year

0

2

5

2

5

2

5

59

64

73

70

95

86

100

39

55

67

57

79

65

87

98

119

140

127

174

151

I87

74 33

80 41

81 51

86 42

110

59

109 49

116 66

23

24

26

25

34

31

36

11

12

I2

16

15

17

26

28

30

38

37

38

Hospital dialysis patients Home dialysis patients Total dialysis patients Annual transplant rate Annualdeath rate Annual rejection rate(exc1. deaths) Monthly transplant beds Annual patients starting home dialysis training

84

120

* Initial situation as at October 1973, with an input rate of 78 being

120 84-120

2

5

FIGURE 1 . The forecasted numbers on dialysis (on the ordinate) for various annual input rates of new patients, assuming an average transplant waiting time of seven months.

dialysing only a small proportion of those waiting for a first transplant, and a large proportion of those whose grafts reject. The second policy was one of home dialysing as many patients as possible as soon as they enter the programme. As would be expected, under this latter policy, home dialysis numbers increased substantially at the expense of hospital dialysis numbers. The differences in home and hospital dialysis numbers under the two policies are shown in Figure 2.

equivalent to 22 per million population.

The forecasted dialysis numbers for these different input rates is shown more explicitly in Figure 1. This also shows the extent to which facilities will have to be expanded to cater for an input rate of 180 new patients which corresponds to 50 patients per million population in Victoria. Increases in the average waiting time for a first transplant had little effect on transplantation rates, death rates and rejection rates, but increased the numbers on dialysis (Table 2). Two different home dialysis policies were studied. The first was the current policy of home

TABLE 2 Forecasted dialysis situations for different average transplant waiting times. The input rate is assumed to rise exponentially from 84 to 120 per year. Average transplant Waiting times Forecast year Hospital dialysis patients Home dialysis patients Total

7 months

12 months

2

5

2

5

70 57

95 79

89

58

122 81

127

174

147

203

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--- home dialysis hospital dialysis

loo initial

90 established

Home dialysis figureshave been obtained from the Austin Hospital renal unit. Average costs over all their patients have been used and this reflects their patients/machine mix, which has been assumed to be typical. The estimated costs are shown in Table 3. The purchase price of home dialysis machines has been corrected to allow for the use of each machine by several patients during its lifetime. Total dialysis costs, based on the cost estimates and the forecasted numbers on dialysis for an increasing input rate are shown in Figure 3. Actual figures for the October 1973-April 1974 period have now become available and these are compared with previous periods and the forecasted figures in Table 4. TABLE 3 Estimated dialysis costs in dollars per patient as at October 1973

12 (months) waiting time FIGURE 2. The forecasted numbers on dialysis for various transplant waiting times and for two home dialysis policies; the current policy of home dialysis for those patients being established on a relatively long term basis on dialysis (ESTABLISHED), and the policy of home dialysing all suitable patients entering the programme (INITIAL). An exponentially increasing input of 84-120 patients per year over five years has been assumed.

Costs for dialysis facilities have been estimated and applied to these figures. The estimates of Stewart et al.' for 1972 have been used as a basis. They divided dialysis treatment costs into initial establishmentcosts (machine purchase, training) and annual continuing costs (staff, supplies machine maintenance and outpatient attendances). Hospital staff costs in Victoria have risen by an average of 16% per year in the past two years.' As staff costs represent at least 75% of total hospital costs, all the hospital dialysis figures of Stewart et al. have been inflated by 16% to bring costs to an October 1973 level.

Establishment Costs Hospital dialysis Home dialysis-machine purchase* Kiil dialyser boards' Training

100 1800 500

2700 5000

Continuing Costs (per annum) Hospital dialysis Home dialysis

8600

3900

* Corrected for average use. Discussion

Dialysis The input rate of new patients into the renal failure treatment programme is likely to range between 84 and 120patients in the next five years if present trends continue. With this kind of steady increase, dialysis numbers increase by about 15 per year. For constant input rates of 84 and 120 patients, the corresponding increases are 8 and 18 per year respectively (Table 1). Hospital dialysis figures increase by about 7 per year (3-8) and home dialysis by 7 per year (6-10). The percentage of dialysis patients undergoing treatment at home increases slightly from 40% to about 45%. The rise in home dialysis numbers is steady but not dramatic and is only slightly

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--- initial policy estab. policy

1.4

-

-

1.0-

5

Increasing the input rate by 43% to 120 produces an increase of 18 dialysis patients per year. For full treatment of renal failure in the community, overseas studies have suggested that the annual intake of new patients should be A figure of between 33 and 80 per 52 million has been suggested for Scotland for patients up to 65 years old.I2 Fifty per million in Victoria, corresponds to 180 patients. With this annual input rate, at least 260 patients would be undergoing dialysis in five years time-an increase of 41% on those forecasted for an increasing input of 84 to 120 and an increase of 170% on present numbers. '3

-

1.2-

NO.

a.w. = 12 a.w. = 7

-

0.8I

I

2

5

years FIGURE 3. The forecasted dialysis costs for the two home dialysis policies (see Fig. 2) and two average transplant waiting time in months (a.w.). An input rate of 84-120 patients per year has been assumed.

greater than the increase in hospital dialysis numbers. The home dialysis training rate increases correspondingly to between 26 and 38 per year, the latter being more likely. The continuing increase in hospital dialysis numbers is a disturbing trend at a time of rapidly increasing hospital costs. Alternative forms of treatment for these patients should therefore be investigated, e.g. dialysis centres, to alleviate the increasing pressure on costly hospital facilities. A solution such as this could substantially increase the home dialysis training rate. Input Rates Higher input rates of new patients have the effect of increasing both the numbers of transplants and the numbers on dialysis. The increase in dialysis numbers in the first five years is eight patients per year when the input rate is a constant 84.

Transplants Under the assumptions of the model, the transplant rate is directly proportional to the input rate. Therefore, it remains fairly stable for a constant input rate. The transplant rate will therefore probably range between 80 and 116 in five years time. The monthly number of transplant beds required will.range correspondingly from 12 to 17. Transplant Waiting Times Increases in the average waiting time for a first transplant have little effect on transplantation, death rates and home dialysis numbers (Table 2).

TABLE 4 Comparison of previous experience, the forecasts for first six months and actual outcome at end of April, 1974 Six month period ending

Data New patients Hospital dialysis patients Home dialysis patients Transplants Deaths Rejections (excluding deaths) Patients with functioninggrafts Total in programme

April October April April 1973 1973 1974 1974 Actual Actual Actual Forecast 33

48

36

38

60

60

60

55

24 33 10

38 41

12

44 38 12

46 37 17

13

15

5

11

142

160

185

178

226

258

289

279

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However, for an increasing input rate of 84 to 120 over five years, there is an increase in the average waiting time from seven to twelve months producing a corresponding increase of around 30% in hospital dialysis numbers. Home Dialysis Policy As waiting times for transplants increase, hospital dialysis facilities will bear the brunt of the demand (Table 2). With no other alternatives available, there comes a time when it becomes more desirable, for patients and hospitals, to train an increasing number of patients for home dialysis on entering the programme. This steadily increases home dialysis numbers and home dialysis becomes the major means of dialysis (Figure 2). The maximum number of patients suitable for home dialysis has been estimated at 70% (assumption 8). With this policy, home dialysis numbers are about 45% higher than the forecasts for the current policy (Figure 2). Hospital dialysis numbers show a relative decrease. Home training rates increase at a corresponding rate to the home dialysis numbers. Although establishment costs for home dialysis are $5,00O/patient against $100/patient for hospital dialysis, annual continuing costs are under one half ($3,900 against $8,600) (Table 3). Therefore the increase in home dialysis numbers under the alternative policy gradually narrows the gap in costs between the two policies (Figure 3). However, the current policy remains less expensive for at least five years, unless the average transplant waiting time increases to twelve months. Under this condition, and with an exponentiaIly increasing input rate of 84-120, the costs become equal at five years, the annual cost being $1,530,000 (October 1973 dollars). Equilibrium As the total of patients being treated increases, so do the numbers of patients dying. However, no forecasts show the death rate reaching the input rate. An equilibrium state is therefore an unlikely occurrence. The demands for dialysis facilities will steadily increase, even though the transplant rate may not. This is in contrast to forecasts made in England and Europe’’ 2 . where an equilibrium state was forecasted after 13-15

405

years. This difference can probably be explained by the higher survival rates for Australian transplant patients (53% against 44% at two years). Limitations The above results have been based on Australian data. Most of the survival rates have been calculated from data covering the whole of Australian experience. However, these survival rates tend to change as technology, experience and selection criteria change. The latter will undoubtedly influence future results, and these changes have not been allowed for in the forecasts presented. Clearly, therefore, the model has to be validated periodically. Only six months’ figures are available at the moment, and these show differences from previous figures (Table 4). Reasonable validation will be possible when the October 1974 figures become available early in 1975. However, because of certain of the assumptions made, these figures are intended to show the direction of future changes, and not to provide exact estimates. Analysis of Data Analysis of the data to obtain the probabilities provided two points of interest. Firstly, graft survival for transplant patients after the first three months was equal to patient survival for home dialysis patients (92% per year), and better than hospital dialysis survival (86%). This compares favourably with overseas experience which shows lower graft survivaL2* These results do, however, reflect the different types of patients in each group. Secondly, of those patients rejecting their grafts after the initial three months, only onefifth of them survived to return to dialysis. A similar finding was reported in E ~ r o p e . ~ Conclusions

These forecasts indicate that dialysis and transplant numbers are likely to increase steadily but not dramatically in the next few years. Home dialysis numbers will probably double within five years but hospital dialysis numbers only appear likely to increase by about 50% in the same period. If as many patients as is possible were trained for home dialysis on entering the treat-

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ment programme, home dialysis numbers could triple in five years, but hospital dialysis numbers would be correspondingly reduced. The high success rate of Australian transplant operations seems likely to shield this country from the large expansions forecast overseas. Acknowledgements

This study was commissioned by the Renal Failure SubCommittee of the Hospitals and Charities Commission of Victoria. Victorian renal physicians have supplied data fiom their own units and have provided invaluable advice. Dr. J. Leigh of Hospitals Computer Services-Victoria has also provided helpful advice and criticism throughout the study. I would like to thank them all for their help and encouragement.

2 N D TRANSPLANTATION

Appendix

The model was based on two mathematical concepts. The first is that of expected outcome. If the probability of an event is P, then the expected number of occurrences of the event after n trials is equal to nP. For example, if 10 patients are waiting for a transplant, and the probability of a patient receiving one in any one month is 0.2, then we expect that (10 x 0.2) = 2 patients will receive a transplant. The second concept is the Markov Chain principle. This states that the situation of a system at any point in time is dependent only on its immediately preceding state. So if Si is a vector denoting the number of patients in the various states at time i, and T is a matrix of transition probabilities (i.e. tij is the probability of moving from state i to state j in any one month) then the situation at month ( i + l ) is = TS,. The model used allows for two different home dialysis policies to be considered. Currently, most patients have home dialysis only if they are unsuitable for transplantation, or if waiting for a second transplant. Under this policy, states 2 and 3 are rarely entered, and most patients are trained in states 18 and 19. However, as the average waiting time for a transplant increases, home dialysing all suitable patients waiting for a first transplant may become more attractive to doctors and patients alike. Most training is then done in states 2 and 3. The twenty-three different states, and the possible' movements between the states are shown in the flowchart in Figure 4. The most important stages of renal treatment are all included

PATIENTS CAN D I E I N ANY OhE OF THE STATES

FIGURE 4. Flowchart of the renal treatment model Square boxes represent single monthly states and circular boxes represent recurring monthly states.

and each state represents a stage of treatment with distinct transition probabilities (i.e. distinct survival chances, distinct transplant chances and so on). For example the first three months of both transplantation and rejection are chosen as states because they are recognised as periods of high risk-after this all succeeding months have very similar risks and can be considered together in a single recurring state. The matrix of transition probabilities is shown in Table 5. References 1. FARROW, S. C., FISHER,D J. H. and JOHNSON, D. B. (1971): Statistical approach to planning an integrated Haemodialysis/Transplantationprogramme, Brir. med. f. 2, 671. 2. FARROW,S. C., el al. (1972): Dialysis and transplantation: The national picture over the next five years, Brir med. J. 2, 686. 3. KERR,D. N. S.(1973): Provision of services to patients with chronic uremia, Kidney Inrernarional3, 197. 4. MATHEW, T. H. (1974): Treatment of endstage renal failure by integrated dialysis and transplantation, Med. J. Ausr. 2, 492. 5. Australian Kidney Foundation Maintenance Haemodialysis Survey -six monthly reports (1971-1974). 6. National Transplant Survey-six monthly reports (1971-1974). 7. STEWART, J. H., TOP,N. D., MARTIN, S . , SCHAWROWAS, E.,FLAWY..SHIEL. A. G. R. and MAHONY, J. F. (1973): The costs of domiciliary maintenance haemodialysis, Med. J. Ausr. 1, 156. 8. Hospitals and Charities Commission of Victoria -Annual Reports (1971-1973). 9. MCGEOWN,M. G. (1972): Chronic renal failure in Northern Ireland 1968-1970, Lancei. 1, 307. 10. MODAN, B., BOTT-KANNER, G., BARNOACH, N., LESLAU, V and ELIAHOU. H. E. (1971): Chronic renal disease in Israel. Validity of death certificates, Isrod J. med. Sci. 12, 1550. I!. STEVENS L. E. REEWTSMA K. LATIMER R. G. MAXWELL J. G. WEAVER. D. H. and'W&, J. S. (1470s A regional iroject in daemddialysis and transplantation, Arch. Surg. 100, 506. A. C., 12. PENDREIGH, D. M., HEASMANM. A,, H o w i n L. F. KENNEDY MACDOUGALL, A. I., MACLEOD,M., ROBSON, j . s. anh STEWAR;,w. K. (1972): Survey of chronic renal failure in Scotland, Lancer. 1, 304. 13. Royal College of Physicians (1972): Report of Joint Committee on Maintenance Dialysis and Transplantation in the Treatment of Chronic Renal Failure, Royal College of Physicians, London.

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A forcast of requirements for the treatment of chronic renal failure in Victoria.

Using a Markov chain mathematical model, dialysis and transplantation requirements for Victoria in the next five to ten years have been predicted. The...
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