Group sequential Holm and Hochberg procedures

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.