Adaptive extensions of a two-stage group sequential procedure for testing primary and secondary endpoints (II): Sample size re-estimation

In this partII of the paper on adaptive extensions of a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints, we focus on the second stage sample size re-estimation based on the first stage data. First, we show that if we use the Cui-Huang-Wang statistics at the second stage, then we can use the same primary and secondary boundaries as for the original procedure (without sample size re-estimation) and still control the type I familywise error rate. This extends their result for the single endpoint case. We further show that the secondary boundary can be sharpened in this case by taking the unknown correlation coefficient ρ between the primary and secondary endpoints into account through the use of the confidence limit method proposed in partI of this paper. If we use the sufficient statistics instead of the CHW statistics, then we need to modify both the primary and secondary boundaries; otherwise, the error rate can get inflated. We show how to modify the boundaries of the original group sequential procedure to control the familywise error rate. We provide power comparisons between competing procedures. We illustrate the procedures with a clinical trial example.