Two Bayesian methods for sample size determination in clinical trials

Abstract Sample size determination is very important part in clinical trials because it inu-ences the time and the cost of the experimental studies. In this article, we consider theBayesian methods for sample size determination based on hypothesis testing. Specif-ically we compare the usual Bayesian method using Bayes factor with the decisiontheoretic method using Bayesian reference criterion in mean di erence problem for thenormal case with known variances. We illustrate two procedures numerically as well asgraphically.Keywords: Bayes factor, Bayesian reference criterion, clinical trial, hypothesis testing,normal case, sample size. 1. Introduction Sample size determination would be one of the most general tasks in clinical trials. Thereare two approaches in sample size determination problem. One is the frequentist one and theother is the Bayesian one. We can determine the sample size based on con dence interval,hypothesis test, and many others. The frequentist approach is seeking the smallest samplesize that is sucient to achieve a desired power at a speci ed signi cance level. The Bayesianapproach is nding the smallest sample size that is necessary to obtain a desired rate of