پرداختن به عدم قطعیت در تجزیه و تحلیل هزینه اثربخشی پزشکی: مفاهیم حداکثرسازی مطلوبیت مورد انتظار برای روش های انجام تجزیه و تحلیل حساسیت و استفاده از تجزیه و تحلیل هزینه اثربخشی برای تعیین اولویت ها برای پژوهش های پزشکی

This paper examines the objectives for performing sensitivity analysis in medical cost–effectiveness analysis and the implications of expected utility maximization for methods to perform such analyses. The analysis suggests specific approaches for optimal decision making under uncertainty and specifying such decisions for subgroups based on the ratio of expected costs to expected benefits, and for valuing research using value of information calculations. Though ideal value of information calculations may be difficult, certain approaches with less stringent data requirements may bound the value of information. These approaches suggest methods by which the vast cost–effectiveness literature may help inform priorities for medical research.

Despite some recent slowing in the growth of health care costs in the US, health care costs have risen substantially over the past several decades and are likely to continue rising (Smith et al., 1998). This appears to be largely due to the growth of new technology (Fuchs, 1990 and Newhouse, 1992). While improvements in health are highly valued (Cutler and Richardson, 1997 and Murphy and Topel, 1998), evidence from diverse methodological perspectives suggests that many technologies may have little value at the margin (Eddy, 1990, Brook et al., 1983 and McClellan et al., 1994). Cost–effectiveness analysis and other methods for medical technology assessment have arisen to attempt to address this important problem. One of the main challenges faced by medical cost–effectiveness analysis has been the question of how to perform these analyses in the presence of uncertainty about the benefits and costs of medical interventions. The uncertainty of primary interest in this regard is uncertainty in population level outcomes, although uncertainty in outcomes at the individual level may be present simultaneously. This uncertainty in population level outcomes may result either from limited evidence from clinical trials or the need to extrapolate based on the results of clinical trials using decision analysis and its associated uncertainties in the structure and parameters of decision models. This uncertainty concerning the benefits and costs of medical interventions has motivated much interest in sensitivity analysis within medical cost–effectiveness analysis. Yet though there have been many proposals about how to address uncertainty in cost–effectiveness analysis, there has been relatively little discussion of the objectives for performing sensitivity analysis. Without a clear understanding of these objectives, it is difficult to know by what criterion to assess the merits of the many alternative approaches to sensitivity analysis. Thus, the lack of clarity concerning the objectives for sensitivity analysis is an important reason for the continuing ambiguity about how to address uncertainty in cost–effectiveness analysis. This paper attempts to identify the objectives for sensitivity analysis within cost–effectiveness analysis and to develop methods suited to reaching those objectives. The primary objectives of sensitivity analysis are argued to be: (1) to help a decision maker make the best decision in the presence of uncertainty, (2) to identify the sources of uncertainty to guide decisions for individuals or subgroups with characteristics that differ from a base case, and (3) to set priorities for the collection of additional information. This paper studies these problems by examining the implications of an expected utility maximization model for the optimal choice of medical interventions when there is uncertainty about the costs and benefits of those interventions. The results indicate that if the objective is to maximize expected utility given available information — as is implicit, for example, in the maximization of quality-adjusted life expectancy — and if financial risk is effectively diversified through either public or private insurance, then the optimal decision is determined by the ratio of the expected cost divided by the expected benefit. Other assumptions about preferences or insurance will yield other conclusions about how to account for uncertainty (Mullahy, 1997), but also would require different models for cost–effectiveness in the absence of uncertainty at the population level. These findings also have implications for sensitivity analyses done for other purposes. If the objective of sensitivity analysis is to guide decisions for subgroups that differ from the base case, then the ratio of expected costs to expected benefits for that subgroup is the appropriate criterion. If the objective of sensitivity analysis is to set priorities for the acquisition of additional information, then the incremental increase in expected utility with additional information is the appropriate measure of benefit. Though such ideal value of information calculations may be difficult to perform, other approaches to sensitivity analysis with less stringent data requirements may provide bounds on the value of information. Together, these approaches suggest a theoretically grounded approach by which the tools of medical cost–effectiveness analysis can be used to help set priorities for medical research. Following these approaches, it may be possible to draw upon the vast literature on the cost–effectiveness of specific medical interventions (Elixhauser et al., 1998) to address crucial needs for more systematic ways to set priorities for medical research. After active discussion between Congress, the Administration, and the leadership of the National Institutes of Health (NIH) over the value of and priorities for Federal funding of biomedical research, the need for such systematic approaches to identify priorities for research at the NIH was recently highlighted in a report of the Institute of Medicine (IOM, 1998). Section 2 discusses the objectives of sensitivity analysis. Section 3 discusses the primary methods currently used to perform sensitivity analysis. Section 4 uses an expected utility maximization model to derive methods for optimal decision making in the context of uncertainty about population outcomes. Section 5 extends the basic results of Section 4 to encompass uncertainty at the individual level. Section 6 uses the model to derive methods for sensitivity analysis to guide decisions for individuals or subgroups that differ from a base case. Section 7 applies these principles to a stylized decision concerning a medical treatment of uncertain benefit. Section 8 uses the model to derive methods to use sensitivity analyses to inform priorities for the collection of additional information to guide decision making, including approaches to bound value of information calculations with limited information. Section 9 applies these ideas to a stylized model of the decision whether to treat prostate cancer and discusses some challenges in implementing these approaches to set priorities for research. Section 10 concludes.

This paper has examined the purposes for which sensitivity analysis is performed in medical cost–effectiveness analysis and the implications of an expected utility maximization model for the methods to perform such analyses. The analysis suggests specific approaches for optimal decision making under uncertainty, specifying such decisions for subgroups, and assessing the value of collecting additional information. At a theoretical level, there are several limitations of this work. First, even with certainty about costs and benefits, cost–effectiveness analysis may not maximize the welfare of individuals (Meltzer et al., 1998), or society (Arrow, 1951 and Meltzer and Johannesson, 1998). Perhaps more important are issues about how risk at the individual level may affect welfare (Kahneman and Tversky, 1979) that are essentially ignored by the assumptions of perfect insurance and expected utility maximization. Though this is an important limitation of QALYs, it is one that needs to be addressed regardless of the issues about aggregate uncertainty addressed by sensitivity analysis. Though concerns about aggregate financial and health risk may be less compelling in a social context where the aggregate risks associated with individual technologies are usually modest, the issue of how risk should be assessed in policy decisions deserves further consideration because other assumptions about preferences concerning risk or about insurance would lead to different conclusions about many methodological issues in cost–effectiveness analysis, including sensitivity analysis (e.g. Mullahy, 1997). Indeed, when a medical intervention has major financial implications that are difficult to insure against, such as lost earnings, the marginal utility of income cannot reasonably be considered constant and the results above concerning the ratio of means will no longer hold. This suggests that it may be useful to distinguish between uncertainty in insured and uninsured costs in assessing the implications of uncertainty in costs in cost–effectiveness analyses. Additionally, it suggests that further characterization of optimal decision making when insurance is not complete would be a valuable area for future work. Rather than using expected utility to incorporate preferences over uncertain outcomes, it might be argued that it would be preferable to report the joint distribution of benefits and costs. Nothing about this analysis suggests that such data should not be presented. However, using such data to make choices would still require decisions about how to incorporate risk into decision making. Unlike traditional forms of sensitivity analysis, the expected value approach provides direct guidance about how the optimal decision varies with the assumptions that are made. At an empirical level, there are important challenges in developing meaningful priors concerning the parameters of decision models (e.g. probabilities, quality of life values, discount rates, etc.). As discussed above, this may often require extensive review of existing data, primary data collection, or even analyses based on arbitrary priors. It may also be very difficult to specify how research may affect posteriors. Whether it is possible to adequately address these challenges will be resolved only through efforts to apply these ideas empirically. These approaches to assess the value of research also pose additional challenges. These include the interdependence of the benefits of related research, the possibility that the research might become less (or more) valuable over time if technological or demographic changes alter the management, frequency or natural history of a disease, and the unpredictability of how the results of research (particularly basic research) might be useful in areas outside the initial areas of inquiry (serendipity). The difficulty of these issues implies that the sort of formal analyses suggested here are more likely to be useful for evaluating clinical research than basic research. Despite these theoretical and empirical challenges, the importance of making good decisions about the allocation of resources to medical interventions and medical research suggest that work in this area be an important priority. It is encouraging in this regard that the recent IOM report on improving priority setting at the NIH recommended: “In setting priorities, NIH should strengthen its analysis and use of health data, such as burdens and costs of diseases, and on data on the impact of research on the health of the public” (IOM, 1998, p. 11). On the other hand, the limited number of cases where cost–effectiveness analysis has strongly influenced medical resource allocation and the likely resistance of medical researchers to having research proposals evaluated by formal criteria suggest that formal techniques to set priorities for research will have to prove their value. It is possible that cost–effectiveness analysis may enhance its influence if it can address key methodological challenges in measuring benefits and costs, and techniques for sensitivity analysis. There may also be less resistance to the use of cost–effectiveness analysis in policy decisions, such as allocation of research funds, than to its use in decisions to ration medical treatments. Nevertheless, formal techniques to inform priorities for research seems more likely to gain acceptance through instances where neglected areas of research can be identified through formal analysis than through instances where research is suggested to be of little value. Consistent with this, threats to increases in the NIH budget due to Congressional questions about the value of increased appropriations for research and NIH priorities in allocating research funds were an important motivation for the IOM report that encouraged efforts to use formal approaches to determine the value of research.