Cost-effectiveness analysis is a statistical decision problem in which, for a given disease, there is a finite set of alternative medical treatments and the problem consists of choosing the optimal treatment based on its random cost and effectiveness. This chapter introduces the elements of this decision problem, the utility functions commonly used, and the procedure for characterizing the optimal treatment.

This is done by assuming a utility function of the cost and the effectiveness of the treatments and the optimal decision is the one having the largest utility with respect to the reward distributions. Therefore, the optimal treatment strongly depends on the utility function we adopt for the decision problem.

Further, the reward distributions typically depend on an unknown parameter, and the elimination of this parameter is carried out using samples of the cost and effectiveness. We present both the Bayesian and the frequentist methods for doing that. Illustrations of the methods for choosing optimal treatments on simulated and real data are presented.

The classical cost-effectiveness acceptability curve for the utility functions considered is discussed.