Adaptive enrichment designs involve preplanned rules for modifying enrollment criteria based on accruing data in a randomized trial. Such designs have been proposed, for example, when the population of interest consists of biomarker positive and biomarker negative individuals. The goal is to learn which populations benefit from an experimental treatment. Two critical components of adaptive enrichment designs are the decision rule for modifying enrollment, and the multiple testing procedure. We provide the first general method for simultaneously optimizing both of these components for two stage, adaptive enrichment designs. We minimize expected sample size under constraints on power and the familywise Type I error rate. It is computationally infeasible to directly solve this optimization problem since it is not convex. The key to our approach is a novel representation of a discretized version of this optimization problem as a sparse linear program. We apply advanced optimization methods to solve this problem to high accuracy, revealing new, approximately optimal designs.



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