The proposed approach is illustrated in two oncology clinical trials with more than two analyses. We carry out a simulation study to illustrate the power gain by using the refined boundary for different choices of boundaries for the two hypotheses. The endpoints are tested in a predefined sequence, each at the significance level, until the first nonsignificant test (Maurer, Hothorn, and Lehmacher 1995. This bound suggests that the secondary boundary can be refined so that the group sequential design can be tested at a significance level greater than α while still controlling the family-wise error rate at level α. In confirmatory clinical trials, the hierarchical test (also called the fixed sequence procedure) has been frequently used to test multiple ordered endpoints. We consider this general setup and derive a sharp upper bound on the probability of rejecting the secondary hypothesis at an interim and a final analysis. The information times may also be different for a noninferiority hypothesis and a superiority hypothesis due to different analysis sets. In many event-driven trials, however, the information times are usually different because of different event rates for the two endpoints. By mainly driven, we mean that the interim analyses are planned at points in time where a certain number of. We consider the situation of testing hierarchically a (key) secondary endpoint in a group-sequential clinical trial that is mainly driven by a primary endpoint. When the information times at the interim analysis are the same for the primary and the secondary hypotheses, it has been shown in the literature that the secondary hypothesis has to be tested using a group sequential boundary at a level no more than α. Hierarchical testing of multiple endpoints in group-sequential trials. The trial uses a group sequential design with an interim and a final analysis. We consider a confirmatory clinical trial where a primary and a secondary endpoints are tested hierarchically to control the family-wise error rate at level α.
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