Optimal choice of the number of treatments to be included in a clinical trial.

It is common for a number of potentially effective treatments to be available for clinical evaluation. Limitations on resources mean that this inevitably leads to a decision as to how many, and which, treatments should be considered for inclusion in a clinical trial. This paper considers the problem of selection of possible treatments for inclusion in a phase III clinical trial. We assume that treatments will be compared using a standard frequentist hypothesis test, and propose a Bayesian decision-theoretic approach that leads to minimization of the total sample size of the trial subject to controlling the familywise type I error rate and the expected probability of rejecting at least one null hypothesis. The method is illustrated in the simplest situation, in which two experimental treatments could be included in the clinical trial, exploring the levels of evidence that are required to lead to an optimal trial that includes one or both of these treatments.