Adjusted Inference for Multiple Testing Procedure in Group-Sequential Designs

Adjustment of statistical significance levels for repeated analysis in group-sequential trials has been understood for some time. Adjustment accounting for testing multiple hypotheses is also well understood. There is limited research on simultaneously adjusting for both multiple hypothesis testing and repeated analyses of one or more hypotheses. We address this gap by proposing adjusted-sequential p-values that reject when they are less than or equal to the family-wise Type I error rate (FWER). We also propose sequential $p$ -values for intersection hypotheses to compute adjusted-sequential $p$ -values for elementary hypotheses. We demonstrate the application using weighted Bonferroni tests and weighted parametric tests for inference on each elementary hypothesis tested.