Semiparametric efficiency and its implication on the design and analysis of group-sequential studies

Authors have shown that the time-sequential joint distributions of many statistics used to analyze data arising from group-sequential time-to-event and longitudinal studies are multivariate normal with an independent increments covariance structure. In Theorem 1 of this article, we demonstrate that this limiting distribution arises naturally when one uses an efficient test statistic to test a single parameter in a semiparametric or parametric model. Because we are able to think of many of the statistics in the literature in this fashion, the limiting distribution under investigation is just a special case of Theorem 1. Using this general structure, we then develop an information-based design and monitoring procedure that can be applied to any type of model for any type of group-sequential study provided that there is a unique parameter of interest that can be efficiently tested.