A Fully Bayesian Approach to Calculating Sample Sizes for Clinical Trials with Binary Responses

Abstract

In this paper we discuss a behavioral Bayes approach to the sample size question in clinical trials with binary responses for which the central limit theorem cannot be applied to provide an adequate approximation of the size of a trial. A fully Bayesian framework is considered. The optimal sample size is obtained by maximizing the expected net benefit, which is the benefit from subsequent use of the new treatment under consideration minus the cost of the trial. The regulatory requirements for granting a licence to the new treatment are discussed. It is shown, not surprisingly, that the optimal sample size depends strongly on the expected benefit from a conclusively favorable outcome, and on the strength of the evidence required by the regulator. Conventional approaches to the question ignore the trade-off between costs and benefits.