Group sequential methods have been widely described and implemented in the clinical trial setting when the treatment effect of interest is assumed to remain constant over time (eg. A constant difference in slopes or a constant hazard ratio with respect to time). In these situations, the design and monitoring of trials via the use of group sequential stopping rules remains relatively straightforward. However, when the effect of treatment within an individual varies with time the evaluation and implementation of stopping rules is not a trivial task because interim testing inherently changes the support of observed data. I will discuss the use of weighted logrank statistics for periodically testing survival differences under nonproportional hazards as data are accrued. By viewing the logrank statistic as a weighted difference in hazards over time, it is easy to demonstrate the dependence of the statistic on the underlying support of the survival distribution. This implies that under nonproportional hazards the null hypothesis being tested by the logrank statistic is dependent upon the length of support sampled which changes with each interim analysis. I will describe a procedure for re-weighting the logrank statistic at interim analyses which attempts to minimize the influence of changing support resulting from periodic analyses of accruing data and examine the operating characteristics of the proposed re-weighting procedure. I will also discuss a Bayesian random walk approach to putting bounds on future survival differences that may be used for guiding stopping decisions when the support of the survival distribution is prematurely truncated.
