LAUSR

It is well known that if the hypothesis test is left unchanged, the Type I error rate may be inflated for sample size re-estimation (SSR) designs. To address this issue, three main approaches have been proposed in the literature: combination test, conditional error and conventional test with sample size increase in the allowable region (AR) only. These three seemingly different approaches are in fact connected. For each combination test, there is a corresponding conditional error function and AR. Designing adaptation rules in this AR with conventional test guarantees the Type I error rate control but at the same time always leads to smaller power comparing to the corresponding combination test (or conditional error) approach. In cases where conventional test is still preferable, step-wise adaptation rules as proposed in Liu and Hu (Liu and Hu, 2015 [46]) can be alternatively considered. This type of adaptation rule does not need to be fully contained in the AR for Type I error rate control, thus may not necessarily be less powerful. We believe controversies in the statistical community on the efficiency comparisons between group sequential (GS) and SSR design stem partially from the misalignment of performance metrics and conditional versus unconditional interpretations. We advocate summary metrics, such as median, variance or tail probabilities of the sample size in addition to expectation and that the definition of efficiency be tailored to individual sponsor. Conditional metrics by favorable, promising and unfavorable zones of the interim results provide additional insights and should always be incorporated into the decision process.