On the Bayes risk induced by alternative design priors for sample size choice

In a decision-theoretic framework, criteria for selecting the optimal sample size for an experiment can be based on the Bayes risk of a decision function, i.e. the expected value of the risk function with respect to a prior distribution that describes a design scenario. In the presence of uncertainty on such scenario, an entire class of parametric distributions can be taken into account. The resulting robust optimal sample size is the one yielding a su ciently small value for the largest risk over the class. In this article we illustrate this robust sample size determination approach for a one-sided testing problem on a normal mean, that is the typical set-up of a superiority clinical trial with continuous endpoints.