New results on optimal conditional error functions for adaptive two-stage designs

Unblinded interim analyses in clinical trials with adaptive designs are gaining increasing popularity. Here, the type I error rate is controlled by defining an appropriate conditional error function. Since various approaches to the selection of the conditional error function exist, the question of an optimal choice arises. In this article, we extend existing work on optimal conditional error functions by two results. Firstly, we prove that techniques from variational calculus can be applied to derive existing optimal conditional error functions. Secondly, we answer the question of optimizing the conditional error function of an optimal promising zone design and investigate the efficiency gain.