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

Abstract

In this paper we introduce a stochastic optimization method based ona mixed Bayesian/frequentist approach to a sample size determinationproblem 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, whichassumes a single decision maker, our method recognizes the existence ofthree decision makers, namely: the company conducting the trial, whichdecides on its size; the regulator, whose approval is necessary for the drugto be licensed for sale; and the public at large, who determine ultimateusage. Moreover, we model the subsequent usage by plausible assumptionsfor actual behaviour. A Monte Carlo Markov Chain is applied to nd themaximum expected utility of conducting the trial.Sample size determination problem is an important task in the planning oftrials. The problem may be formulated formally in statistical terms. Themost frequently used methods are based on the required size, and power of thetrial for a specifed treatment efect Several authors haverecognized the value of using prior distributions rather than point estimatesin sample size calculations.