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