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Does prevention save costs?
Journal of Health Economics 24 (2005) 715–724
Does prevention save costs? Considering deferral of the expensive last year of life Afschin Gandjour ∗ , Karl Wilhelm Lauterbach Institute of Health Economics and Clinical Epidemiology, University of Cologne, Cologne, Germany Received 11 June 2004; received in revised form 22 August 2004; accepted 22 November 2004 Available online 20 March 2005
Abstract Published cost-effectiveness analyses may overstate the cost-effectiveness ratio of preventive care if they do not explicitly model the costs of the last year of life, which is postponed by prevention. To determine the degree of overestimation, the authors built a statistical model using Medicare expenditure data on survivors and decedents. The model shows that the cost-effectiveness ratio of prevention may decrease by up to US$ 11,000 per quality-adjusted life year saved when expenditure data on the last year life are used. The model is able to explain more than half of the median cost increase of published cost-effectiveness analyses on clinical preventive services. © 2005 Elsevier B.V. All rights reserved. JEL classification: I120 Keywords: Cost-effectiveness; Model; Statistical; Prevention
Prevention prevents rising health care dollars is the view held by many clinicians, health care decision makers, and journalists. Empirical evidence, however, suggests that most clinical preventive services increase societal costs (Stone et al., 2000; Coffield et al., 2001). A systematic review of primary and secondary clinical preventive services shows that an additional life year in full health (quality-adjusted life year; QALY) comes at a median price ∗ Corresponding author. Present address: Institut f¨ ur Gesundheits¨okonomie und Klinische Epidemiologie, Universit¨at zu K¨oln, Gleueler Straße 176-178, 50935 K¨oln, Germany. Tel.: +49 221 4679112; fax: +49 221 4302304. E-mail address: [email protected] (A. Gandjour).
0167-6296/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jhealeco.2004.11.009
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A. Gandjour, K.W. Lauterbach / Journal of Health Economics 24 (2005) 715–724
of US$ 14,000 (Stone et al., 2000). From the perspective of a third party payer prevention may be more cost-effective, particularly if co-payments for preventive services exist. On the other hand, many experts in the field believe that increasing life expectancy, be it through prevention or treatment, does not significantly alter health care costs from a societal perspective once the costs of the last year of life are considered. Indeed, the costs of the last year of life make up a large fraction of lifetime medical expenditures (Hogan et al., 2001; Stooker et al., 2001; Brockmann, 2002; Hoover et al., 2002). Increasing life expectancy, the reasoning goes, simply postpones the expensive last year of life adding little to lifetime costs. This assumption is in line with the “compression-of-morbidity” hypothesis, which states that changes in life style will compress the period of senescence near the end of life (Fries, 1980). Prevention might actually decrease lifetime costs if we considered the fact that the costs of the last year of life decrease with age (Levinsky et al., 2001; Yang et al., 2003). The main reason is less aggressive care at higher age resulting in a decrease in expenditures for hospital care (Levinsky et al., 2001). Lifetime costs would decrease even further if future health care costs and the expensive last year of life were discounted to present value. The farther the costs ahead in the future, the smaller their present value. The rationale behind discounting is that we prefer a dollar today to a dollar tomorrow because it allows to increase our consumption of goods (Lipscomb et al., 1996). Most studies analyzing the impact of aging on health care costs have used average expenditure data, which do not separate between the costs of survivors and decedents. Only a few studies on the effect of population aging on national health care expenditures have analyzed the impact of using separate expenditure data as opposed to average expenditure data (Roos et al., 1987; Madsen et al., 2002). Little is known, however, how using expenditure data on the last year of life affects societal costs when we consider treatment of an individual. Therefore, the goal of our study was to analyze how the cost-effectiveness ratio of preventive care would change if expenditures for the last year of life were explicitly considered. To this end, we analyzed clinical preventive measures in the general population. Our study differs from the ones by Roos et al. (1987) as well as Madsen et al. (2002) in focusing on individual aging as opposed to population aging. Population aging is not only the result of an increase in life expectancy (i.e., individual aging), but also of a decrease in the fertility rate.
1. Methods 1.1. Data We obtained U.S. expenditure data on survivors and decedents at each age between the ages 65 and 100 years from Yang et al. (2003) who had analyzed the Medicare current beneficiary survey (MCBS) Cost and Use files for the years 1992–1998 (Fig. 1). The MCBS files carry data from a representative sample of more than 10,000 Medicare beneficiaries per year (Adler, 1994). The Cost and Use files include all health care services whether covered by Medicare or not. The two most prominent health care services not covered by Medicare, prescription drugs and long-term facility care, are thus included. Expenditures are in 1998 dollars. In addition, we used a U.S. life table (Social Security Online, 1999).
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Fig. 1. Medicare expenditures by age and time to death (Yang et al., 2003, Copyright ©. The Gerontological Society of America. Reproduced by permission of the publisher).
1.2. Model We built a deterministic model with a societal perspective. The target population consisted of 65-year-old males and females with an average risk of death. We calculated how the cost-effectiveness ratio of prevention would change if we used separate expenditure data for survivors and decedents, i.e., last year of life data. The comparator was an average-cost analysis using average-cost data of survivors and decedents. Assuming that previous costeffectiveness analyses on prevention have all used the average-cost method, the comparator had a median cost-effectiveness ratio of US$ 14,000 per QALY in 1998 dollars (Stone et al., 2000). In order to isolate the impact of using separate expenditure data for survivors and decedents, we kept all other cost and benefit components typically considered in a cost-effectiveness analysis constant. Therefore, our primary calculation did not directly use the median cost-effectiveness ratio as an input factor, but determined only its change when using last year of life data. It was not until the last step of the analysis that we explicitly used the median cost-effectiveness ratio in order to subtract the savings by using last year of life data, thus estimating the median cost-effectiveness ratio based on last year of life data. The impact of using last year of life data was measured in terms of costs per life year gained. In detail, we took the following steps: (1) From the life table we took probabilities of death at each age and transformed them into probabilities of death under preventive care. (2) For each cost-analysis method we determined lifetime costs and life expectancy of preventive care compared to no preventive care. Thus, we performed a marginal analysis for each method. (3) We determined the incremental cost-effectiveness ratio of using one cost-analysis method compared to the other.
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(4) We subtracted the incremental savings by using last year of life data from the median cost-effectiveness ratio of preventive care (US$ 14,000 per QALY). 1.2.1. Determining mortality rates under prevention As a measure of the effectiveness of prevention, we took the hazard ratio of prevention as compared to no prevention. The hazard ratio is the ratio of the hazard rates of prevention and no prevention and approximates the relative risk of death. Assuming a constant hazard rate h over lifetime, the probability that an event occurs during the following year is expressed by an exponential function (Kuntz and Weinstein, 2002): p(d) = 1 − exp(−h)
(1)
where p(d) is the probability of death. If we know p(d) , we are able to calculate the hazard rate h by rearranging equation (1) (Kuntz and Weinstein, 2002): h = − ln(1 − p(d) )
(2)
Therefore, if we take the probabilities of death at each age from the life table, we are able to calculate the average hazard rate of the general population at each age. The hazard rate of prevention hP can be calculated by multiplying the population’s average hazard rate by the hazard ratio of prevention HRP : hP = − ln(1 − p(d) ) × HRP
(3)
If we want to calculate the probability of death under prevention (p(d)P ), we need to transform back the hazard rate of prevention (hP ) by using equation (1): p(d)P,i = 1 − exp(ln(1 − p(d)P,i ) × HRP )
(4)
where i is an index for age. The probability of survival under prevention p(s)P is then calculated as follows: p(s)P,i = 1 − p(d)P,i = exp(ln(1 − p(d)P,i ) × HRP )
(5)
1.2.2. Determining marginal costs and life years gained Multiplying the probabilities of survival as calculated from equation (5) yields the cumulative survival probability at each age. If we then multiply cumulative survival probabilities with the probability of survival and the expenditures for survivors at each age, repeat the calculation with the probability of death and the expenditures for decedents, add up costs for all ages, then we get lifetime costs of 65-year-old (target population): k 100 100 C = Ck = p(s)P,65 × C(s)65 + p(d)P,65 × C(d)65 + p(s)P,i−1 k=65
k=66
i=66
× [p(s)P,i × C(s)i + p(d)P,i × C(d)i ] where C is the cost; i, k the age; C(s) the cost of survivors; C(d) the cost of decedents.
(6)
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The discounted expected value of lifetime costs (EV) is calculated as follows: EV = p(s)P,65 × C(s)65 + p(d)P,65 × C(d)65
k p(s)P,i−1 × [p(s)P,i × C(s)i + p(d)P,i × C(d)i ] 100 i=66 + k−65 (1 + r) k=66
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(7)
where r is the annual discount rate. If we want to determine how a given hazard ratio affects the expected value, we need to insert the right side of equations (4) and (5) into equation (7): EV = exp(ln(1 − p(d)P,65 ) × HRP ) × C(s)65 + (1 − exp(ln(1 − p(d)P,65 ) × HRP ))
100 exp(ln(1 − p(d)P,i−1 ) × HRP ) i=66 × [exp(ln(1 − p(d)P,i ) × HRP ) × C(s)i 100 + (1 − exp(ln(1 − p(d)P,i ) × HRP )) × C(d)i ] (8) × C(d)65 + k−65 (1 + r) k=66 If we want to compare prevention with no prevention, we first need to calculate the expected value of lifetime costs based on the hazard ratio of interest (absence of prevention has a hazard ratio of 1.0) and then determine the difference:
EVP = EVP − EVP¯
(9)
where EVP is the expected value of prevention, EVP¯ is the expected value of no prevention, and EVP is the change in the expected value or the marginal discounted lifetime cost of prevention. In order to calculate the number of discounted life years (LYs) with and without prevention, we need to determine the cumulative survival probabilities at each age, discount them, and add them up: k p (s)P,i 100 i=65 (10) LYs = k−65 (1 + r) k=65
If we want to determine how a particular hazard ratio affects the number of discounted life years, we need to insert the right side of equation (5) into equation (10): k exp(ln(1 − p ) × HR ) P (d)P,i 100 i=65 (11) LYs = (1 + r)k−65 k=65
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1.2.3. Determining the incremental cost-effectiveness of using last year of life data We determined marginal lifetime costs (Eq. (9)) both for the last year of life and the average-cost method. In order to assess the magnitude of the cost difference between both methods, we divided it by the number of life years gained through prevention ( LYs) (Eq. (11)):
EVP(LYOL-AC)
EVP − EVP(AC) =
LYs LYs(P) − LYs(P) ¯
(12)
where EVP(LYOL) is the marginal lifetime cost of prevention using last year of life data,
EVP(AC) is the marginal lifetime cost of prevention using average-cost data, LYs(P) are the life years with prevention, and LYs(P) ¯ are the life years without prevention. Usually, cost savings are not divided by an effectiveness gain because a negative cost-effectiveness ratio may not be interpreted properly given that it may result from cost savings or lower effectiveness. Yet we performed the division because in our analysis the negative sign was clearly attributable to cost savings. In the base case analysis we discounted costs and life years at an annual rate of 3% (Lipscomb et al., 1996). 1.3. Ancillary analyses In a two-way analysis we examined how changing the discount rate and the hazard ratio affected the cost difference between both approaches divided by the number of life years gained. In another two-way analysis, we assessed the impact of the hazard ratio together with an extension of the model up to the age of 119. Due to the lack of expenditure data beyond the age 100, we varied the change of age-related expenditures for decedents and survivors compared to the previous age.
2. Results Fig. 2 shows the relationship between the hazard ratio and marginal lifetime costs of prevention compared to no prevention. Marginal lifetime costs were calculated by the last year of life and average-cost method, respectively. Lowering the hazard ratio increases lifetime costs based on both methods, but less so for the last year of life method: the last year of life method accounts for the fact that the high costs of those who die dominate age-specific costs. Hence, when the last year of life is postponed, average age-specific costs fall. In contrast, the average-cost method, which does not distinguish between survivors and decedents, overestimates average age-specific costs by not accounting for a decrease in the proportion of decedents. In order to assess the magnitude of cost savings from using the last year of life method (as shown as the difference between the two graphs in Fig. 2), we divided cost savings by the number of life years gained. Fig. 3 shows that the ratio of lifetime savings to life years gained is in the range of US$ 4900–6600 per life year gained and increases slightly with a decreasing hazard ratio of prevention. The reason for the fairly constant ratio is that a decrease in the hazard ratio increases life expectancy almost proportionally to savings.
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Fig. 2. Relationship between the hazard ratio of prevention and marginal lifetime costs of prevention compared to no prevention (=hazard ratio of 1.0). Lifetime costs were calculated by considering expenditures for survivors and decedents (last year of life analysis) or average expenditures (average-cost analysis).
Fig. 3. Relationship between the hazard ratio of prevention and the reduction in the cost-effectiveness ratio of prevention by using last year of life data as opposed to average-cost data.
2.1. Ancillary analyses A two-way analysis simultaneously varying the discount rate (0–10%) and the hazard ratio (0.01–0.99) showed that even the most extreme case yielded a cost per life year gained ratio above US$ 4800. Another two-way analysis varying the rate of change of age-related expenditures for decedents and survivors between the ages of 101 and 119 together with the hazard ratio had little impact on the results: a change in age-related expenditures for decedents (survivors) from −10% to +10% yielded a cost difference per life year gained between US$ 5000 and US$ 13,700 (US$ 5000 and US$ 9300).
3. Discussion The model shows that the cost-effectiveness ratio of prevention improves by US$ 4900–6600 per life year saved once we use expenditure data on the last year life as op-
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posed to average-cost data. The result was very robust to changes in the discount rate and hazard ratio as well as extrapolation of age-related expenditures beyond the age of 100. As an example of the impact of using last year of life expenditure data, consider vigorous exercise in males at average risk, which reduces the hazard rate by 10% thus leading to a hazard ratio of 0.9 (Lee et al., 1995). In this example, use of last year of life expenditure data decreases the cost per life year gained ratio by US$ 5033. In other words, using average-cost data overestimates the cost-effectiveness ratio of vigorous exercise by US$ 5033 per life year gained. The reduction in the cost-effectiveness ratio of prevention would be even larger if we calculated the cost per QALY ratio. Taking into consideration that elderly people have on average a 30% reduction in health-related quality of life (Johannesson et al., 1997; Sisk et al., 1997), the overestimation in terms of costs per additional QALY is between US$ 7000 and US$ 9500. Hence, the model is able to explain more than half of the median cost increase of published cost-effectiveness analyses on clinical preventive services, which show that an additional QALY comes at a median price of US$ 14,000 (Stone et al., 2000). Converting results in 2004 dollars by the Consumer Price Index increases the degree of overestimation even further, to between US$ 8200 and US$ 11,000 per additional QALY. The model is not without limitations yet. An important limitation is its generalizability to preventive services for target groups other than the general population (which, of course, also contains sick individuals). The absolute cost difference between survivors and deceased as well as between deceased of different ages is probably disease-dependent. In our analysis we considered the average expenditure pattern across all diseases. Thus, our results hold for the average disease pattern, but might not apply to each disease. As a further limitation, one may question transferability of our results to preventive services starting before the age of 65. Due the lack of cost data on survivors and decedents before the age of 65, our model was confined to prevention starting at age 65. Given our finding, however, that the marginal cost-effectiveness ratio was stable independent from the gain in life expectancy it seems unlikely that a further delay of death (which is the result of earlier prevention) changes the marginal cost-effectiveness ratio considerably. Relatively minor limitations concern the assumptions of our model. While our exponential distribution of survival data is probably the most frequently used distribution, there are alternatives such as the Weibull or the Gamma distribution. Further, we used a multiplicative model, which assumes that prevention decreases the baseline hazard rate by a fixed relative rate. In contrast, an additive model presumes that prevention reduces the baseline hazard rate by a fixed absolute rate (Kuntz and Weinstein, 2002). The appropriateness of a model depends on the disease. Finally, one may argue that in line with the “compression-of-morbidity” hypothesis (Fries, 1980) we not only need to consider the preventive effect on postponing death, but also on reducing morbidity. The argument goes that leaving out a morbidity reduction underestimates the cost-saving potential of prevention. However, our analysis built on previous ones in that we kept all other cost and benefit components typically considered in a costeffectiveness analysis constant (which, of course, includes the avoidance of disease due to prevention) and only analyzed how the cost-effectiveness ratio changed when considering the expenditures of the last year of life.
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For future research, we recommend to collect data on the costs of survivors and deceased for different target groups and ages before 65. These data would help to analyze whether or not our results can be transferred to specific groups and earlier prevention.
Acknowledgements The authors would like to thank for Zhou Yang, Edward Norton, and Sally Stearns for providing Medicare expenditure data and two anonymous reviewers for helpful comments.
References Adler, G.S., 1994. A profile of the medicare current beneficiary survey. Health Care Financing Review 15 (4), 153–163. Brockmann, H., 2002. Why is less money spent on health care for the elderly than for the rest of the population? Health care rationing in German hospitals. Social Science and Medicine 55 (4), 593– 608. Coffield, A.B., Maciosek, M.V., McGinnis, J.M., Harris, J.R., Caldwell, M.B., Teutsch, S.M., Atkins, D., Richland, J.H., Haddix, A., 2001. Priorities among recommended clinical preventive services. American Journal of Preventive Medicine 21 (1), 1–9. Fries, J.F., 1980. Aging, natural death, and the compression of morbidity. The New England Journal of Medicine 303 (3), 130–135. Hogan, C., Lunney, J., Gabel, J., Lynn, J., 2001. Medicare beneficiaries’ costs of care in the last year of life. Health Affairs 20 (4), 188–195 (Millwood). Hoover, D.R., Crystal, S., Kumar, R., Sambamoorthi, U., Cantor, J.C., 2002. Medical expenditures during the last year of life: findings from the 1992–1996 Medicare current beneficiary survey. Health Services Research 37 (6), 1625–1642. Johannesson, M., Meltzer, D., O’Conor, R.M., 1997. Incorporating future costs in medical cost-effectiveness analysis: implications for the cost-effectiveness of hypertension. Medical Decision Making 17 (4), 382– 389. Kuntz, K., Weinstein, M., 2002. Modelling in economic evaluation. In: Drummond, M., McGuire, A. (Eds.), Economic Evaluation in Health Care. Oxford University Press, Oxford, pp. 141–171. Lee, I.M., Hsieh, C.C., Paffenbarger Jr., R.S., 1995. Exercise intensity and longevity in men. The Harvard Alumni Health Study. The Journal of the American Medical Association 273 (15), 1179–1184. Levinsky, N.G., Yu, W., Ash, A., Moskowitz, M., Gazelle, G., Saynina, O., Emanuel, E.J., 2001. Influence of age on Medicare expenditures and medical care in the last year of life. The Journal of the American Medical Association 286 (11), 1349–1355. Lipscomb, J., Weinstein, M.C., Torrance, G.W., 1996. Time preference. In: Gold, M.R., Siegel, J.E., Russell, L.B., Weinstein, M.C. (Eds.), Cost-Effectiveness in Health and Medicine. Oxford University Press, New York, Oxford, pp. 214–235. Madsen, J., Serup-Hansen, N., Kristiansen, I.S., 2002. Future health care costs—do health care costs during the last year of life matter? Health Policy 62 (2), 161–172. Roos, N.P., Montgomery, P., Roos, L.L., 1987. Health care utilization in the years prior to death. The Milbank Quarterly 65 (2), 231–254. Sisk, J.E., Moskowitz, A.J., Whang, W., 1997. Cost-effectiveness of vaccination against pneumococcal bacteremia among elderly people. The Journal of the American Medical Association 278 (16), 1333– 1339. Social Security Online, 1999. Period life table, http://www.ssa.gov/ (accessed April 26, 2003).
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Stone, P.W., Teutsch, S., Chapman, R.H., Bell, C., Goldie, S.J., Neumann, P.J., 2000. Cost-utility analyses of clinical preventive services: published ratios, 1976–1997. American Journal of Preventive Medicine 19 (1), 15–23. Stooker, T., van Acht, J.W., van Barneveld, E.M., van Vliet, R.C., van Hout, B.A., Hessing, D.J., Busschbach, J.J., 2001. Costs in the last year of life in The Netherlands. Inquiry 38 (1), 73–80. Yang, Z., Norton, E.C., Stearns, S.C., 2003. Longevity and health care expenditures: the real reasons older people spend more. The Journals of Gerontology. Series B, Psychological Sciences and Social Sciences 58 (1), S2–S10.
Does prevention save costs? Considering deferral of the expensive last year of life Afschin Gandjour ∗ , Karl Wilhelm Lauterbach Institute of Health Economics and Clinical Epidemiology, University of Cologne, Cologne, Germany Received 11 June 2004; received in revised form 22 August 2004; accepted 22 November 2004 Available online 20 March 2005
Abstract Published cost-effectiveness analyses may overstate the cost-effectiveness ratio of preventive care if they do not explicitly model the costs of the last year of life, which is postponed by prevention. To determine the degree of overestimation, the authors built a statistical model using Medicare expenditure data on survivors and decedents. The model shows that the cost-effectiveness ratio of prevention may decrease by up to US$ 11,000 per quality-adjusted life year saved when expenditure data on the last year life are used. The model is able to explain more than half of the median cost increase of published cost-effectiveness analyses on clinical preventive services. © 2005 Elsevier B.V. All rights reserved. JEL classification: I120 Keywords: Cost-effectiveness; Model; Statistical; Prevention
Prevention prevents rising health care dollars is the view held by many clinicians, health care decision makers, and journalists. Empirical evidence, however, suggests that most clinical preventive services increase societal costs (Stone et al., 2000; Coffield et al., 2001). A systematic review of primary and secondary clinical preventive services shows that an additional life year in full health (quality-adjusted life year; QALY) comes at a median price ∗ Corresponding author. Present address: Institut f¨ ur Gesundheits¨okonomie und Klinische Epidemiologie, Universit¨at zu K¨oln, Gleueler Straße 176-178, 50935 K¨oln, Germany. Tel.: +49 221 4679112; fax: +49 221 4302304. E-mail address: [email protected] (A. Gandjour).
0167-6296/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jhealeco.2004.11.009
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A. Gandjour, K.W. Lauterbach / Journal of Health Economics 24 (2005) 715–724
of US$ 14,000 (Stone et al., 2000). From the perspective of a third party payer prevention may be more cost-effective, particularly if co-payments for preventive services exist. On the other hand, many experts in the field believe that increasing life expectancy, be it through prevention or treatment, does not significantly alter health care costs from a societal perspective once the costs of the last year of life are considered. Indeed, the costs of the last year of life make up a large fraction of lifetime medical expenditures (Hogan et al., 2001; Stooker et al., 2001; Brockmann, 2002; Hoover et al., 2002). Increasing life expectancy, the reasoning goes, simply postpones the expensive last year of life adding little to lifetime costs. This assumption is in line with the “compression-of-morbidity” hypothesis, which states that changes in life style will compress the period of senescence near the end of life (Fries, 1980). Prevention might actually decrease lifetime costs if we considered the fact that the costs of the last year of life decrease with age (Levinsky et al., 2001; Yang et al., 2003). The main reason is less aggressive care at higher age resulting in a decrease in expenditures for hospital care (Levinsky et al., 2001). Lifetime costs would decrease even further if future health care costs and the expensive last year of life were discounted to present value. The farther the costs ahead in the future, the smaller their present value. The rationale behind discounting is that we prefer a dollar today to a dollar tomorrow because it allows to increase our consumption of goods (Lipscomb et al., 1996). Most studies analyzing the impact of aging on health care costs have used average expenditure data, which do not separate between the costs of survivors and decedents. Only a few studies on the effect of population aging on national health care expenditures have analyzed the impact of using separate expenditure data as opposed to average expenditure data (Roos et al., 1987; Madsen et al., 2002). Little is known, however, how using expenditure data on the last year of life affects societal costs when we consider treatment of an individual. Therefore, the goal of our study was to analyze how the cost-effectiveness ratio of preventive care would change if expenditures for the last year of life were explicitly considered. To this end, we analyzed clinical preventive measures in the general population. Our study differs from the ones by Roos et al. (1987) as well as Madsen et al. (2002) in focusing on individual aging as opposed to population aging. Population aging is not only the result of an increase in life expectancy (i.e., individual aging), but also of a decrease in the fertility rate.
1. Methods 1.1. Data We obtained U.S. expenditure data on survivors and decedents at each age between the ages 65 and 100 years from Yang et al. (2003) who had analyzed the Medicare current beneficiary survey (MCBS) Cost and Use files for the years 1992–1998 (Fig. 1). The MCBS files carry data from a representative sample of more than 10,000 Medicare beneficiaries per year (Adler, 1994). The Cost and Use files include all health care services whether covered by Medicare or not. The two most prominent health care services not covered by Medicare, prescription drugs and long-term facility care, are thus included. Expenditures are in 1998 dollars. In addition, we used a U.S. life table (Social Security Online, 1999).
A. Gandjour, K.W. Lauterbach / Journal of Health Economics 24 (2005) 715–724
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Fig. 1. Medicare expenditures by age and time to death (Yang et al., 2003, Copyright ©. The Gerontological Society of America. Reproduced by permission of the publisher).
1.2. Model We built a deterministic model with a societal perspective. The target population consisted of 65-year-old males and females with an average risk of death. We calculated how the cost-effectiveness ratio of prevention would change if we used separate expenditure data for survivors and decedents, i.e., last year of life data. The comparator was an average-cost analysis using average-cost data of survivors and decedents. Assuming that previous costeffectiveness analyses on prevention have all used the average-cost method, the comparator had a median cost-effectiveness ratio of US$ 14,000 per QALY in 1998 dollars (Stone et al., 2000). In order to isolate the impact of using separate expenditure data for survivors and decedents, we kept all other cost and benefit components typically considered in a cost-effectiveness analysis constant. Therefore, our primary calculation did not directly use the median cost-effectiveness ratio as an input factor, but determined only its change when using last year of life data. It was not until the last step of the analysis that we explicitly used the median cost-effectiveness ratio in order to subtract the savings by using last year of life data, thus estimating the median cost-effectiveness ratio based on last year of life data. The impact of using last year of life data was measured in terms of costs per life year gained. In detail, we took the following steps: (1) From the life table we took probabilities of death at each age and transformed them into probabilities of death under preventive care. (2) For each cost-analysis method we determined lifetime costs and life expectancy of preventive care compared to no preventive care. Thus, we performed a marginal analysis for each method. (3) We determined the incremental cost-effectiveness ratio of using one cost-analysis method compared to the other.
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(4) We subtracted the incremental savings by using last year of life data from the median cost-effectiveness ratio of preventive care (US$ 14,000 per QALY). 1.2.1. Determining mortality rates under prevention As a measure of the effectiveness of prevention, we took the hazard ratio of prevention as compared to no prevention. The hazard ratio is the ratio of the hazard rates of prevention and no prevention and approximates the relative risk of death. Assuming a constant hazard rate h over lifetime, the probability that an event occurs during the following year is expressed by an exponential function (Kuntz and Weinstein, 2002): p(d) = 1 − exp(−h)
(1)
where p(d) is the probability of death. If we know p(d) , we are able to calculate the hazard rate h by rearranging equation (1) (Kuntz and Weinstein, 2002): h = − ln(1 − p(d) )
(2)
Therefore, if we take the probabilities of death at each age from the life table, we are able to calculate the average hazard rate of the general population at each age. The hazard rate of prevention hP can be calculated by multiplying the population’s average hazard rate by the hazard ratio of prevention HRP : hP = − ln(1 − p(d) ) × HRP
(3)
If we want to calculate the probability of death under prevention (p(d)P ), we need to transform back the hazard rate of prevention (hP ) by using equation (1): p(d)P,i = 1 − exp(ln(1 − p(d)P,i ) × HRP )
(4)
where i is an index for age. The probability of survival under prevention p(s)P is then calculated as follows: p(s)P,i = 1 − p(d)P,i = exp(ln(1 − p(d)P,i ) × HRP )
(5)
1.2.2. Determining marginal costs and life years gained Multiplying the probabilities of survival as calculated from equation (5) yields the cumulative survival probability at each age. If we then multiply cumulative survival probabilities with the probability of survival and the expenditures for survivors at each age, repeat the calculation with the probability of death and the expenditures for decedents, add up costs for all ages, then we get lifetime costs of 65-year-old (target population): k 100 100 C = Ck = p(s)P,65 × C(s)65 + p(d)P,65 × C(d)65 + p(s)P,i−1 k=65
k=66
i=66
× [p(s)P,i × C(s)i + p(d)P,i × C(d)i ] where C is the cost; i, k the age; C(s) the cost of survivors; C(d) the cost of decedents.
(6)
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The discounted expected value of lifetime costs (EV) is calculated as follows: EV = p(s)P,65 × C(s)65 + p(d)P,65 × C(d)65
k p(s)P,i−1 × [p(s)P,i × C(s)i + p(d)P,i × C(d)i ] 100 i=66 + k−65 (1 + r) k=66
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(7)
where r is the annual discount rate. If we want to determine how a given hazard ratio affects the expected value, we need to insert the right side of equations (4) and (5) into equation (7): EV = exp(ln(1 − p(d)P,65 ) × HRP ) × C(s)65 + (1 − exp(ln(1 − p(d)P,65 ) × HRP ))
100 exp(ln(1 − p(d)P,i−1 ) × HRP ) i=66 × [exp(ln(1 − p(d)P,i ) × HRP ) × C(s)i 100 + (1 − exp(ln(1 − p(d)P,i ) × HRP )) × C(d)i ] (8) × C(d)65 + k−65 (1 + r) k=66 If we want to compare prevention with no prevention, we first need to calculate the expected value of lifetime costs based on the hazard ratio of interest (absence of prevention has a hazard ratio of 1.0) and then determine the difference:
EVP = EVP − EVP¯
(9)
where EVP is the expected value of prevention, EVP¯ is the expected value of no prevention, and EVP is the change in the expected value or the marginal discounted lifetime cost of prevention. In order to calculate the number of discounted life years (LYs) with and without prevention, we need to determine the cumulative survival probabilities at each age, discount them, and add them up: k p (s)P,i 100 i=65 (10) LYs = k−65 (1 + r) k=65
If we want to determine how a particular hazard ratio affects the number of discounted life years, we need to insert the right side of equation (5) into equation (10): k exp(ln(1 − p ) × HR ) P (d)P,i 100 i=65 (11) LYs = (1 + r)k−65 k=65
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1.2.3. Determining the incremental cost-effectiveness of using last year of life data We determined marginal lifetime costs (Eq. (9)) both for the last year of life and the average-cost method. In order to assess the magnitude of the cost difference between both methods, we divided it by the number of life years gained through prevention ( LYs) (Eq. (11)):
EVP(LYOL-AC)
EVP − EVP(AC) =
LYs LYs(P) − LYs(P) ¯
(12)
where EVP(LYOL) is the marginal lifetime cost of prevention using last year of life data,
EVP(AC) is the marginal lifetime cost of prevention using average-cost data, LYs(P) are the life years with prevention, and LYs(P) ¯ are the life years without prevention. Usually, cost savings are not divided by an effectiveness gain because a negative cost-effectiveness ratio may not be interpreted properly given that it may result from cost savings or lower effectiveness. Yet we performed the division because in our analysis the negative sign was clearly attributable to cost savings. In the base case analysis we discounted costs and life years at an annual rate of 3% (Lipscomb et al., 1996). 1.3. Ancillary analyses In a two-way analysis we examined how changing the discount rate and the hazard ratio affected the cost difference between both approaches divided by the number of life years gained. In another two-way analysis, we assessed the impact of the hazard ratio together with an extension of the model up to the age of 119. Due to the lack of expenditure data beyond the age 100, we varied the change of age-related expenditures for decedents and survivors compared to the previous age.
2. Results Fig. 2 shows the relationship between the hazard ratio and marginal lifetime costs of prevention compared to no prevention. Marginal lifetime costs were calculated by the last year of life and average-cost method, respectively. Lowering the hazard ratio increases lifetime costs based on both methods, but less so for the last year of life method: the last year of life method accounts for the fact that the high costs of those who die dominate age-specific costs. Hence, when the last year of life is postponed, average age-specific costs fall. In contrast, the average-cost method, which does not distinguish between survivors and decedents, overestimates average age-specific costs by not accounting for a decrease in the proportion of decedents. In order to assess the magnitude of cost savings from using the last year of life method (as shown as the difference between the two graphs in Fig. 2), we divided cost savings by the number of life years gained. Fig. 3 shows that the ratio of lifetime savings to life years gained is in the range of US$ 4900–6600 per life year gained and increases slightly with a decreasing hazard ratio of prevention. The reason for the fairly constant ratio is that a decrease in the hazard ratio increases life expectancy almost proportionally to savings.
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Fig. 2. Relationship between the hazard ratio of prevention and marginal lifetime costs of prevention compared to no prevention (=hazard ratio of 1.0). Lifetime costs were calculated by considering expenditures for survivors and decedents (last year of life analysis) or average expenditures (average-cost analysis).
Fig. 3. Relationship between the hazard ratio of prevention and the reduction in the cost-effectiveness ratio of prevention by using last year of life data as opposed to average-cost data.
2.1. Ancillary analyses A two-way analysis simultaneously varying the discount rate (0–10%) and the hazard ratio (0.01–0.99) showed that even the most extreme case yielded a cost per life year gained ratio above US$ 4800. Another two-way analysis varying the rate of change of age-related expenditures for decedents and survivors between the ages of 101 and 119 together with the hazard ratio had little impact on the results: a change in age-related expenditures for decedents (survivors) from −10% to +10% yielded a cost difference per life year gained between US$ 5000 and US$ 13,700 (US$ 5000 and US$ 9300).
3. Discussion The model shows that the cost-effectiveness ratio of prevention improves by US$ 4900–6600 per life year saved once we use expenditure data on the last year life as op-
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posed to average-cost data. The result was very robust to changes in the discount rate and hazard ratio as well as extrapolation of age-related expenditures beyond the age of 100. As an example of the impact of using last year of life expenditure data, consider vigorous exercise in males at average risk, which reduces the hazard rate by 10% thus leading to a hazard ratio of 0.9 (Lee et al., 1995). In this example, use of last year of life expenditure data decreases the cost per life year gained ratio by US$ 5033. In other words, using average-cost data overestimates the cost-effectiveness ratio of vigorous exercise by US$ 5033 per life year gained. The reduction in the cost-effectiveness ratio of prevention would be even larger if we calculated the cost per QALY ratio. Taking into consideration that elderly people have on average a 30% reduction in health-related quality of life (Johannesson et al., 1997; Sisk et al., 1997), the overestimation in terms of costs per additional QALY is between US$ 7000 and US$ 9500. Hence, the model is able to explain more than half of the median cost increase of published cost-effectiveness analyses on clinical preventive services, which show that an additional QALY comes at a median price of US$ 14,000 (Stone et al., 2000). Converting results in 2004 dollars by the Consumer Price Index increases the degree of overestimation even further, to between US$ 8200 and US$ 11,000 per additional QALY. The model is not without limitations yet. An important limitation is its generalizability to preventive services for target groups other than the general population (which, of course, also contains sick individuals). The absolute cost difference between survivors and deceased as well as between deceased of different ages is probably disease-dependent. In our analysis we considered the average expenditure pattern across all diseases. Thus, our results hold for the average disease pattern, but might not apply to each disease. As a further limitation, one may question transferability of our results to preventive services starting before the age of 65. Due the lack of cost data on survivors and decedents before the age of 65, our model was confined to prevention starting at age 65. Given our finding, however, that the marginal cost-effectiveness ratio was stable independent from the gain in life expectancy it seems unlikely that a further delay of death (which is the result of earlier prevention) changes the marginal cost-effectiveness ratio considerably. Relatively minor limitations concern the assumptions of our model. While our exponential distribution of survival data is probably the most frequently used distribution, there are alternatives such as the Weibull or the Gamma distribution. Further, we used a multiplicative model, which assumes that prevention decreases the baseline hazard rate by a fixed relative rate. In contrast, an additive model presumes that prevention reduces the baseline hazard rate by a fixed absolute rate (Kuntz and Weinstein, 2002). The appropriateness of a model depends on the disease. Finally, one may argue that in line with the “compression-of-morbidity” hypothesis (Fries, 1980) we not only need to consider the preventive effect on postponing death, but also on reducing morbidity. The argument goes that leaving out a morbidity reduction underestimates the cost-saving potential of prevention. However, our analysis built on previous ones in that we kept all other cost and benefit components typically considered in a costeffectiveness analysis constant (which, of course, includes the avoidance of disease due to prevention) and only analyzed how the cost-effectiveness ratio changed when considering the expenditures of the last year of life.
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For future research, we recommend to collect data on the costs of survivors and deceased for different target groups and ages before 65. These data would help to analyze whether or not our results can be transferred to specific groups and earlier prevention.
Acknowledgements The authors would like to thank for Zhou Yang, Edward Norton, and Sally Stearns for providing Medicare expenditure data and two anonymous reviewers for helpful comments.
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