| It has been a long-standing problem concerning how confidence intervals can be constructed following a group sequential clinical trial, in which the study duration or the number of subjects is a random variable that depends on the data collected so far, instead of being fixed in advance. After a brief review of the literature on this problem, we propose a new approach which combines an extension of Siegmund's (1978) ordering to survival data with recent developments in hybrid resampling (Chuang and Lai, 1998; 2000). We have also developed computational algorithms to implement our resampling procedure, thus providing clinicians with a practical method to construct confidence intervals following group sequential tests in clinical trials with time-to-event endpoints. Simulation studies have shown that the confidence intervals thus constructed have coverage probabilities close to the nominal values, consistent with the asymptotic theory. In this connection we also develop (i) hybrid resampling methods for confidence intervals for population means following group sequential tests with random group sizes and (ii) a general ordering scheme involving multivariate quantiles that can be applied generally when a stochastic sequence is observed up to a stopping time. |
