Optimal Sample Size for Multiple Testing

We consider the choice of an optimal sample size for multiple-comparison problems. The motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression. However, the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests. We discuss two decision problems in the context of this setup: the sample size selection and the decision about the multiple comparisons. We adopt a decision-theoretic approach, using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible, while keeping the number of false discoveries manageable. For consistency, we use the same loss function for both decisions. The decision rule that emerges for the multiple-comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate. For the sample size selection, we combine the expe...