Multi-stage enrichment and basket trial designs with population selection.

As biomarker information from early-phase trials can be unreliable due to high variability, it is logical to take a prospective two-stage approach when designing a late-phase confirmatory trial, ie, refining the target population at the first stage and performing the hypothesis testing at the second stage. The use of a reliable intermediate endpoint at the first stage can further improve the trial efficiency from both time and cost perspectives. Nevertheless, there are needs for expanding such two-stage confirmatory designs to more stages for monitoring efficacy on the refined population. There is limited literature on this matter, particularly for two popular designs with population selection midway, ie, the biomarker enrichment design and the basket design. In this manuscript, we focus on these two popular designs and discuss how to implement the interim efficacy analyses after population refinement while controlling type I error. Power and stopping probability are also explored for the two designs.