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Group sequential design (GSD) is widely used in clinical trials in whichcorrelated tests of multiple hypotheses are used. Multiple primary objectivesresulting in tests with known correlations include evaluating 1) multipleexperimental treatment arms, 2) multiple populations, 3) the combination ofmultiple arms and multiple populations, or 4) any asymptotically multivariatenormal tests. In this paper, we focus on the first 3 of these and extend theframework of the weighted parametric multiple test procedure from fixed designswith a single analysis per objective to a GSD setting where differentobjectives may be assessed at the same or different times, each in a groupsequential fashion. Pragmatic methods for design and analysis of weightedparametric group sequential design(WPGSD) under closed testing procedures areproposed to maintain the strong control of familywise Type I error rate (FWER)when correlations between tests are incorporated. This results in the abilityto relax testing bounds compared to designs not fully adjusting for knowncorrelations, increasing power or allowing decreased sample size. We illustratethe proposed methods using clinical trial examples and conduct a simulationstudy to evaluate the operating characteristics.

A unified framework for weighted parametric group sequential design (WPGSD)