It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes to the population sampled, care must be taken to ensure strong control of the familywise Type I error rate.

Our main contribution is a general method for constructing randomized trial designs that (1) allow changes (based on a prespecified decision rule) to the population enrolled based on interim data, (2) make no parametric model assumptions, and (3) guarantee the asymptotic, familywise Type I error rate is strongly controlled at a specified level. As a demonstration of our method, we prove new, sharp results for a simple, two-stage enrichment design. We then compare this design to a fixed design, focusing on each design's ability to determine overall and subpopulation specific treatment effects.