Topics in Gatekeeping and Group Sequential Procedures for Multiple Endpoints

In many clinical trials, multiple hypotheses are routinely tested. Multiplicity problems occur in clinical trials through many sources or dimensions, e.g., multiple endpoints (efficacy and safety), multiple treatment arms or doses of a drug, multiple patient populations, etc. Examples of multidimensional multiplicity problems include trials in which an investigational drug is compared to a control on a primary and a secondary endpoints at several dose levels in a group sequential trial. In this case, the first dimension of multiplicity includes the multiple endpoints while the multiple dose-control tests introduce the second dimension with multiple patient groups defining the third. The familywise error rate (FWER) is generally controlled in such problems using multiple testing procedures (MTPs).;This dissertation makes contributions to multiplicity problems in the following aspects. First, gatekeeping procedures are introduced to handle the multiple testing problems in which logically dependent structures exist among ordered families of hypotheses. For instance, in a multiple endpoint problem, the secondary endpoint can be validly tested after establishing significance on the primary endpoint. A serial gatekeeping procedure requires that hypotheses in a family be tested if and only if (iff) all hypotheses in the preceding family are rejected. A parallel gatekeeping procedure allows the testing on the next family only if at least one hypothesis in the preceding family is rejected. In Chapter 2, we investigate the connection between the serial and the parallel gatekeeping and propose a general framework that we call k-out-of-ngatekeeping and propose a multistage procedure. The general paradigm allows the testing on secondary hypotheses only if at least k (1