Two-stage adaptive enrichment design for testing an active factor

We propose an adaptive enrichment approach to test an active factor, which is a factor whose effect is non-zero in at least one subpopulation. We implement a two-stage play-the-winner design where all subjects in the second stage are enrolled from the subpopulation that has the highest observed effect in the first stage. We recommend a weighted Fisher's combination of the most powerful test for each stage, respectively: the first stage Hotelling's test and the second stage noncentral chi-square test. The test is further extended to cover binary outcomes and time-to-event outcomes.