A unified framework for weighted parametric group sequential design

Group sequential design (GSD) is widely used in clinical trials in which correlated tests of multiple hypotheses are used. Multiple primary objectives resulting in tests with known correlations include evaluating (1) multiple experimental treatment arms, (2) multiple populations, (3) the combination of multiple arms and multiple populations, or (4) any asymptotically multivariate normal tests. In this paper, we focus on the first three of these and extend the framework of the weighted parametric multiple test procedure from fixed designs with a single analysis per objective to a GSD setting where different objectives may be assessed at the same or different times, each in a group sequential fashion. Pragmatic methods for design and analysis of weighted parametric group sequential design under closed testing procedures are proposed to maintain the strong control of the family-wise Type I error rate when correlations between tests are incorporated. This results in the ability to relax testing bounds compared to designs not fully adjusting for known correlations, increasing power, or allowing decreased sample size. We illustrate the proposed methods using clinical trial examples and conduct a simulation study to evaluate the operating characteristics.