A mixed Bayesian/Frequentist approach in sample size determination problem for clinical trials

In this paper we introduce a stochastic optimization method based on a mixed Bayesian/frequentist approach to a sample size determination problem in a clinical trial. The data are assumed to come from a nor- mal distribution for which both the mean and the variance are unknown. In contrast to the usual Bayesian decision theoretic methodology, which assumes a single decision maker, our method recognizes the existence of three decision makers, namely: the company conducting the trial, which decides on its size; the regulator, whose approval is necessary for the drug to be licensed for sale; and the public at large, who determine ultimate usage. Moreover, we model the subsequent usage by plausible assumptions for actual behaviour. A Monte Carlo Markov Chain is applied to nd the maximum expected utility of conducting the trial. Sample size determination problem is an important task in the planning of trials. The problem may be formulated formally in statistical terms. The most frequently used methods are based on the required size, and power of the trial for a specifed treatment efect Several authors have recognized the value of using prior distributions rather than point estimates in sample size calculations.