Confidence intervals in group sequential trials with random group sizes and applications to survival analysis

A new ordering scheme for defining quantiles of the multivariate distribution of a stopping time and a stopped stochastic process is introduced. This ordering scheme is used in conjunction with resampling methods to construct confidence intervals for a population mean following a group sequential test with random group sizes, and for the regression parameter of a proportional hazards model following a time-sequential clinical trial with censored survival data. It is shown that this approach resolves the long-standing difficulties in inference due to two different time scales in time-sequential trials, and that the confidence intervals thus constructed have coverage probabilities close to the nominal values and provide marked improvements over those based on alternative ordering schemes and normal approximations. Copyright 2006, Oxford University Press.