Design and analysis of drop-the-losers studies using binary endpoints in the rare disease setting.

The drop-the-losers design combines a phase 2 trial of k treatments and a confirmatory phase 3 trial under a single adaptive protocol, thereby gaining efficiency over a traditional clinical development approach. Such designs may be particularly useful in the rare disease setting, where conserving sample size is paramount, and control arms may not be feasible. We propose an unconditional exact likelihood (UEL) testing and inference procedure for these designs for a binary endpoint using small sample sizes, comparing its operating characteristics to existing methods. Additional practical considerations are evaluated, including the choice of stagewise sample sizes and effect of ties.