Optimal healthcare decisions: Comparing medical treatments on a cost-effectiveness basis

This paper deals with medical treatments comparison from the cost-effectiveness viewpoint. A decision theory scheme is considered, where the decision space is the set of treatments involved, the space of states of nature consists of the respective net benefits of the treatments, and the utility function is one of two possible candidates. A first candidate is the one typically used in the literature on cost-effectiveness analysis, for which the utility of a decision is proportional to the net benefit gain, and a second one is of the type 0–1, which penalizes the wrong decisions with a fixed quantity. Their associated optimal decision rules, both frequentist and Bayesian, are analyzed and compared via frequentist evaluation of their performance, and the conclusion is that the latter beats the former in the sense of choosing the optimal treatment more often than any other, thus minimizing the proportion of wrong decisions. Illustrations with simulated and real data are provided.