Optimal, two-stage, adaptive enrichment designs for randomized trials, using sparse linear programming

Adaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. 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 enrolment, and the multiple-testing procedure. We provide a general method for simultaneously optimizing these components for two-stage, adaptive enrichment designs. We minimize the expected sample size under constraints on power and the familywise type I error rate. It is computationally infeasible to solve this optimization problem directly because of its non-convexity. The key to our approach is a novel, discrete representation of this optimization problem as a sparse linear program, which is large but computationally feasible to solve by using modern optimization techniques. We provide an R package that implements our method and is compatible with linear program solvers in several software languages. Our approach produces new, approximately optimal trial designs.