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 a scenario, an entire class of parametric distributions can be taken into account. The resulting robust optimal sample size is the one yielding a sufficiently 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.