November, 2005

Tech Report

This article considers sample size determination methods based on Bayesian credible intervals for \(\theta\), an unknown real-valued parameter of interest. We assume that credible intervals are used to establish whether \(\theta\) belongs to an indifference region. This problem is typical in clinical trials, where \(\theta\) represents the effect-difference of two alternative treatments and experiments are judged conclusive only if one is able to exclude that \(\theta\) belongs to a range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification by a class \(\Gamma\) of distributions for \(\theta\) and we assume that the data yield robust evidence if, as the prior varies in \(\Gamma\), either the lower bound of the inferior limit of the credible set is sufficiently large or the upper bound of the superior limit is sufficiently small. Sample size determination criteria proposed in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria require computations of summaries of the predictive distributions of upper and lower bounds of the random limits of credible intervals. The method is developed assuming a normal mean as the parameter of interest and using conjugate priors. An application to the determination of sample size for a trial of surgery for gastric cancer is also illustrated.