Multiple testing in adaptive designs–a review

Abstract

During the course of a study it would be desirable to take advantage of new internal or external information in order to modify design features laid down in the study protocol. However, for conventional controlled experiments this does not seem feasible without casting doubt on the statistical validity of the whole experiment. In contrast, modifications pertaining to treatment arms, endpoints, hypotheses, statistical methods etc. are possible within adaptive designs, thus enabling the conduct of complex controlled experiments which may still be tailored after onset to meet ethical and scientific as well as economic requirements.

This article briefly reviews recent statistical methods for adaptive study design, particularly those built from $p$-value combination rules or, equivalently, conditional error functions. Its main focus, however, is on the application of adaptive testing methods to clinical experiments with multiple objectives, e.g., multiple treatment arms or endpoints. The authors demonstrate in this overview that as a consequence of using an adaptive interim analysis, null hypotheses may be dropped or added, and test statistics may be exchanged, whilst the studywise type I error rate remains under (strong) control. Moreover, adaptive designs may be applied to experiments aiming to establish doseresponse relationships, or to demonstrate non-inferiority, superiority or equivalence of multiple treatment arms. An example from the literature, which has not previously been discussed from an adaptive viewpoint, is provided as a worked illustration.