# Optimizing Group Sequential Designs that Allow Pre-planned Changes to the Population Sampled Based on Interim Data

vendredi 26 mars 2010, 10h00 - 10h55

We consider randomized trials in which the composition of the population sampled may be changed during the course of the trial, in response to data already collected. Such designs can have greater probability of demonstrating effectiveness of a treatment, compared to static designs, when it is initially uncertain in which subpopulations a treatment will be most effective. However, in allowing such data-dependent changes to the population sampled, care must be taken to ensure familywise Type I error is controlled. Our main contribution is to give a general method for constructing trial designs that (1) allow for changes (based on a prespecified decision rule) to the population sampled based on interim data, (2) make no model assumptions, and (3) guarantee asymptotically correct, familywise Type I error at a specified level $\alpha$. Our method allows the computation of optimal cutoffs defining rejection regions in such designs. The crux of the method involves reducing the computation of familywise Type I error to an optimization problem that can be solved using numerical integration. In one of our examples, we prove new, sharp results for a simple, two-stage enrichment design, and compare its power to a static design. A special case of our method yields new results for multiple hypothesis testing in static designs as well.