Information Growth in a Family of Weighted Logrank Statistics Under Repeated Analyses

Abstract

The use of group sequential methods has become standard practice in the clinical-trial setting. Because patients are not all generally entered into a clinical trial at the same time and due to delayed outcomes, interim analyses are typically planned with respect to statistical-information time rather than calender time. In many cases it is sufficient for interim testing to be based upon the number of responses observed, e.g., the number of patients for whom a post-randomization blood pressure had been measured or the number of patients surviving past a given time period. In the case of censored survival data, the logrank statistic is a commonly used tool for comparing the survival experience of two or more groups. Assuming equal randomization and the null-hypothesis of no difference in survival, it is well know that statistical information grows in proportion to the number of events observed, making analysis planning on the information scale trivial. However, when weighted versions of the logrank statistic are used, the number of censored observations at each analysis time is affected by both the enrollment rate and the timing of interim analyses. We describe how statistical information grows when testing of censored survival data is based upon selected members of the G ρ, γ family of weighted logrank statistics under various enrollment scenarios that may be encountered in the clinical-trial setting. In addition, we consider the impact on estimation of treatment effects when performing an interim analysis at less than maximal information in the setting of nonproportional hazards survival data. A reweighting of the G ρ, γ statistic is proposed that reapportions unused weight at interim analyses to a subset of the last observed events, thereby providing estimates of treatment effect obtained at interim analyses that are more comparable to those that would have been obtained had estimation been performed under full support.