Adaptive and non-adaptive group sequential tests

Methods have been proposed to re-design a clinical trial at an interim stage in order to increase power. In order to preserve the type I error rate, methods for unplanned design-change have to be defined in terms of non-sufficient statistics and this calls into question their efficiency and the credibility of conclusions reached. We evaluate schemes for adaptive re-design, extending the theoretical arguments for use of sufficient statistics of Tsiatis & Mehta (2003) and assessing the possible benefits of pre-planned adaptive designs by numerical computation of optimal tests; these optimal adaptive designs are concrete examples of optimal sequentially-planned sequential tests proposed by Schmitz (1993). We conclude that the flexibility of unplanned adaptive designs comes at a price and we recommend that the appropriate power for a study should be determined as thoroughly as possible at the outset. Then, standard error-spending tests, possibly with unevenly-spaced analyses, provide efficient designs, but it is still possible to fall back on flexible methods for re-design should study objectives change unexpectedly once the trial is under way.