Interval estimation in two-stage, drop-the-losers clinical trials with flexible treatment selection

In a two-stage, drop-the-losers clinical trial, researchers choose the 'best' among a number of treatments at an interim analysis after the first stage. The selected treatment continues to the second stage for confirmation of efficacy, and the remaining treatments (the 'losers') are dropped from the study. Wu et al. (Biometrika 2010; 97:405-418) showed how to construct confidence limits for the mean difference between the selected treatment and the control when the treatment is chosen after the first stage based on the highest efficacy in the primary clinical endpoint. In this article, we show how to construct a lower confidence limit for the mean difference when the treatment is chosen based on first-stage safety data, early endpoint efficacy data, a combination of safety and efficacy data or any other prespecified selection rule. The result extends the applicability of drop-the-losers designs, for in practice, the 'best' treatment often is not chosen for efficacy alone.