A Comparison of Two Methods for Adaptive Multi-Arm Two-Stage Design

We consider the problem of comparing multiple treatment arms to a common control arm over the two stages of a group sequential randomized clinical trial. At the end of stage one, arms may be tested and dropped for overwhelming efficacy, futility, safety, or any other arbitrary reason, and the sample sizes of the arms going forward for stage two testing may be adaptively altered. At the end of stage two, a final analysis is performed, and efficacious treatment arms are identified by a testing procedure that offers strong control of the family-wise error rate (FWER). Two testing procedures, the $p$ -value combination method and the conditional error rate method, are discussed theoretically and then compared by simulation. While both procedures control the FWER, the conditional error rate procedure is seen to provide greater power than the $p$ -value combination procedure for a wide range of scenarios and alternative hypotheses. Plausible reasons for this power differential are given.