Adaptive designs with arbitrary dependence structure based on Fisher’s combination test

Abstract

Adaptive designs were originally developed for independent and uniformly distributed p-values. However, in general the type I error rate of a given adaptive design depends on the true dependence structure between the stage-wise p-values. Since there are settings, where the p-values of the stages might be dependent with even unknown dependence structure, it is of interest to consider the most adverse dependence structure maximizing the type I error rate of a given adaptive design (worst case). In this paper, we explicitly study the type I error rate in the worst case for adaptive designs without futility stop based on Fisher's combination test. Potential inflation of the type I error rate is studied if the dependence structure between the p-valuesofthestagesisnottakenintoaccountadequately.Itturnsoutthatconsiderable inflation of the type I error rate can occur. This emphasizes that the examination of the true dependence structure between the stage-wise p-values and an adequate choice of the conditional error function is crucial when adaptive designs are used.