Test procedures for multiple hypotheses in a group sequential clinical trial that control the family-wise error rate are considered. Several graphical group sequential tests suggested in the literature, which are special cases of Bonferroni-closure tests, are discussed. The focus is on the question of whether to consider at the current stage only the evidence of the current repeated p-value or the evidence over all repeated p-values from the previous stages. A new test strategy controlling the family-wise error rate is introduced that consistently works across all hypotheses, with the evidence (i.e., repeated p-value) from the current stage. The strategy is more powerful than similar previously suggested test procedures. This is achieved by using the evidence from previous stages to increase the significance levels. For the test procedures, corresponding compatible simultaneous confidence intervals are presented, having the disadvantage of often not providing additional information on the treatment effects. For this reason, we extend previous work about informative simultaneous confidence intervals for one-stage graphical tests to graphical group sequential trials. Iterative algorithms are introduced that calculate these informative bounds that have a small power loss compared to the original graphical group sequential test. The boundaries can be calculated after each stage. In addition, previous work is extended by a criterion to estimate the accuracy of the numerically calculated boundaries. The suggested informative bounds can be used to provide median-conservative, i.e., reliable estimators, for estimating the treatment effects in a group sequential test with multiple hypotheses.

翻译：考虑在分组序贯临床试验中控制族系误差率的多重假设检验程序。本文讨论了文献中提出的几种图形分组序贯检验方法，这些方法是Bonferroni闭包检验的特例。重点聚焦于当前阶段仅考虑当前重复p值的证据，还是考虑来自前一阶段所有重复p值的证据问题。本文提出一种新的控制族系误差率的检验策略，该策略在所有假设中一致地使用当前阶段的证据（即重复p值）。该策略比先前建议的类似检验程序更具统计功效，这是通过利用先前阶段的证据来提高显著性水平实现的。针对这些检验程序，给出了相应的兼容同时置信区间，但其缺点是通常无法提供关于治疗效果的额外信息。为此，我们将先前关于单阶段图形检验信息性同时置信区间的工作扩展至图形分组序贯试验。引入迭代算法计算这些信息性边界，与原始图形分组序贯检验相比仅产生较小的功效损失。这些边界可在每个阶段后计算。此外，通过引入评估数值计算边界精度的准则，扩展了先前工作。建议的信息性边界可用于提供中位数保守（即可靠）的估计量，以在具有多重假设的分组序贯检验中估计治疗效果。