The problem of testing multiple hypotheses using a group sequential procedure often arises in clinical trials. We review several group sequential Holm (GSHM) type procedures proposed in the literature and clarify the relationships between them. In particular, we show which procedures are equivalent or, if different, which are more powerful and what are their pros and cons. We propose a step-up group sequential Hochberg (GSHC) procedure as a reverse application of a particular step-down GSHM procedure. We conducted an extensive simulation study to evaluate the familywise error rate (FWER) and power properties of that GSHM procedure and the GSHC procedure and found that the GSHC procedure controls FWER more closely and is more powerful. All procedures are illustrated with a common numerical example, the data for which are chosen to bring out the differences between them. A real case study is also presented to illustrate application of these procedures. R programs for applying the proposed procedures, additional simulation results, and the proof of the FWER control of the GSHC procedure in a special case are provided in Supplementary Material.

中文翻译：

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分组顺序 Holm 和 Hochberg 过程

使用组序贯程序检验多个假设的问题经常出现在临床试验中。我们回顾了文献中提出的几个组序贯 Holm (GSHM) 类型程序，并阐明了它们之间的关系。特别是，我们展示了哪些程序是等效的，或者如果不同，哪些程序更强大，它们的优缺点是什么。我们提出了一个升压组顺序 Hochberg (GSHC) 程序作为特定降压 GSHM 程序的反向应用。我们进行了广泛的模拟研究以评估该 GSHM 程序和 GSHC 程序的全族错误率 (FWER) 和功率特性，发现 GSHC 程序更紧密地控制 FWER 并且更强大。所有程序都用一个常见的数字示例来说明，选择哪些数据以显示它们之间的差异。还提供了一个真实的案例研究来说明这些程序的应用。补充材料中提供了用于应用建议程序的 R 程序、附加模拟结果以及在特殊情况下对 GSHC 程序的 FWER 控制的证明。