Validity of the Hochberg procedure revisited for clinical trial applications

There is much interest in using the Hochberg procedure (HP) for statistical tests on primary endpoints of confirmatory clinical trials. The procedure is simple to use and enjoys more power than the Bonferroni and the Holm procedures. However, the HP is not assumption free like the other two procedures. It controls the familywise type I error rate when test statistics (used for statistical tests) are independent or if dependent satisfy a conditionally independent formulation. Otherwise, its properties for dependent tests at present are not fully understood. Consequently, its use for confirmatory trials, especially for their primary endpoints, remains worrisome. Confirmatory trials are typically designed with 1-2 primary endpoints. Therefore, a question was raised at the Food and Drug Administration as to whether the HP is a valid test for the simple case of performing treatment-to-control comparisons on two primary endpoints when their test statistics are not independent. Confirmatory trials for statistical tests normally use simple test statistics, such as the normal Z, student's t, and chi-square. The literature does include some work on the HP for dependent cases covering these test statistics, but concerns remain regarding its use for confirmatory trials for which endpoint tests are mostly of the dependent kind. The purpose of this paper is therefore to revisit this procedure and provide sufficient details for better understanding of its performance for dependent cases related to the aforementioned question. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.