Robust Bayesian sample size determination for avoiding the range of equivalence in clinical trials

This article considers sample size determination methods based on Bayesian credible intervals for θθ, an unknown real-valued parameter of interest. We consider clinical trials and assume that θθ represents the difference in the effects of a new and a standard therapy. In this context, it is typical to identify an interval of parameter values that imply equivalence of the two treatments (range of equivalence). Then, an experiment designed to show superiority of the new treatment is successful if it yields evidence that θθ is sufficiently large, i.e. if an interval estimate of θθ lies entirely above the superior limit of the range of equivalence. Following a robust Bayesian approach, we model uncertainty on prior specification with a class ΓΓ of distributions for θθ and we assume that the data yield robust evidence   if, as the prior varies in ΓΓ, the lower bound of the credible set inferior limit is sufficiently large. Sample size criteria in the article consist in selecting the minimal number of observations such that the experiment is likely to yield robust evidence. These criteria are based on summaries of the predictive distributions of lower bounds of the random inferior limits of credible intervals. The method is developed for the conjugate normal model and applied to a trial for surgery of gastric cancer.