We illustrate the use of marginal proportional hazards models and other survival models with various group sequential methods to test multiple survival endpoints at K interim analyses. The Stage 1 data allows three decisions (1) stop and declare significance, (2) stop for futility, and (3) continue the study with sample size for the second stage based on the first stage data. This research gives methods for sequential monitoring of survival data in clinical trials with multiple endpoints. These methods partition the study into two stages. Next, we discuss the Bauer–KÖhne and Proschan–Hunsberger two-stage adaptive methods which bound the Type I error rate. We discuss adjustments when the Brownian motion model assumption does not hold, and estimation and confidence intervals after stopping early. The landmark paper of Lan & DeMets (1983) provided the theory behind the alpha spending functionapproach to group sequential testing. Being quicker at stopping tests in case they are either performing better or worse than expected (group sequential testing). Flexible versions of these methods are developed using alpha spending function approach, where the decision to perform an interim analysis may be based on information independent of the study up to that point. Group sequential design 1 and 2 are test statistics at the interim and final analyses, respectively E. When repeated significance testing occurs on the same data, adjustments have to be made to the hypothesis testing procedure to maintain overall significance and power levels. We compare two methods for group sequential analysis with equally spaced looks, the Pocock and the O’Brien–Fleming methods, both based on the Brownian motion model. This chapter first describes group sequential methods, where interim tests of a study are done and the study may be stopped either for efficacy (if a large enough early treatment effect is seen) or for futility (if it is unlikely that a treatment effect will be significant if the study goes to completion).
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