Optimizing subgroup selection in two-stage adaptive enrichment and umbrella designs

We design two-stage confirmatory clinical trials that use adaptation to find the subgroup of patients who will benefit from a new treatment, testing for a treatment effect in each of two disjoint subgroups. Our proposal allows aspects of the trial, such as recruitment probabilities of each group, to be altered at an interim analysis. We use the conditional error rate approach to implement these adaptations with protection of overall error rates. Applying a Bayesian decision-theoretic framework, we optimize design parameters by maximizing a utility function that takes the population prevalence of the subgroups into account. We show results for traditional trials with familywise error rate control (using a closed testing procedure) as well as for umbrella trials in which only the per-comparison type 1 error rate is controlled. We present numerical examples to illustrate the optimization process and the effectiveness of the proposed designs.