A note on P-values under group sequential testing and nonproportional hazards

Group sequential designs are often used for periodically assessing treatment efficacy during the course of a clinical trial. Following a group sequential test, P-values computed under the assumption that the data were gathered according to a fixed sample design are no longer uniformly distributed under the null hypothesis of no treatment effect. Various sample space orderings have been proposed for computing proper P-values following a group sequential test. Although many of the proposed orderings have been compared in the setting of time-invariant treatment effects, little attention has been given to their performance when the effect of treatment within an individual varies over time. Our interest here is to compare two of the most commonly used methods for computing proper P-values following a group sequential test, based upon the analysis time (AT) and Z-statistic orderings, with respect to resulting power functions when treatment effects on survival are delayed. Power under the AT ordering is shown to be heavily influenced by the presence of a delayed treatment effect, while power functions corresponding to the Z-statistic ordering remain robust under time-varying treatment effects.