Bayesian average error-based approach to sample size calculations for hypothesis testing

Under the classical statistical framework, sample size calculations for a hypothesis test of interest maintain prespecified type I and type II error rates. These methods often suffer from several practical limitations. We propose a framework for hypothesis testing and sample size determination using Bayesian average errors. We consider rejecting the null hypothesis, in favor of the alternative, when a test statistic exceeds a cutoff. We choose the cutoff to minimize a weighted sum of Bayesian average errors and choose the sample size to bound the total error for the hypothesis test. We apply this methodology to several designs common in medical studies.