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.

翻译：对于组序贯试验中重复分析的统计显著性水平调整已有所理解。同样，针对多重假设检验的调整方法也较为常见。然而，同时调整多重假设检验与单一或多个假设的多次分析的研究仍有限。为填补这一空白，我们提出调整序贯p值，当组序贯设计中基本假设的调整序贯p值小于或等于族系型I错误率（FWER）时，拒绝该假设。我们还提出交集假设的序贯p值，作为计算基本假设调整序贯p值的工具。通过加权Bonferroni检验和加权参数检验的应用实例，我们将调整序贯p值与期望的FWER进行比较，以对每个被检验的基本假设进行推断。