Risk aversion and uncertainty in cost‐effectiveness analysis: the expected‐utility, moment‐generating function approach

The availability of patient‐level data from clinical trials has spurred a lot of interest in developing methods for quantifying and presenting uncertainty in cost–effectiveness analysis (CEA). Although the majority has focused on developing methods for using sample data to estimate a confidence interval for an incremental cost–effectiveness ratio (ICER), a small strand of the literature has emphasized the importance of incorporating risk preferences and the trade‐off between the mean and the variance of returns to investment in health and medicine (mean‐variance analysis). This paper shows how the exponential utility–moment‐generating function approach is a natural extension to this branch of the literature for modelling choices from healthcare interventions with uncertain costs and effects. The paper assumes an exponential utility function, which implies constant absolute risk aversion, and is based on the fact that the expected value of this function results in a convenient expression that depends only on the moment‐generating function of the random variables. The mean‐variance approach is shown to be a special case of this more general framework. The paper characterizes the solution to the resource allocation problem using standard optimization techniques and derives the summary measure researchers need to estimate for each programme, when the assumption of risk neutrality does not hold, and compares it to the standard incremental cost–effectiveness ratio. The importance of choosing the correct distribution of costs and effects and the issues related to estimation of the parameters of the distribution are also discussed. An empirical example to illustrate the methods and concepts is provided. Copyright © 2004 John Wiley & Sons, Ltd.