A Test of the Dependence Assumptions for the Simes-Test-based Multiple Test Procedures

The Hochberg procedure is known to be more powerful than the Bonferroni method but the test statistics need to satisfy certain dependence conditions. Due to the lack of validation of the positive dependence assumption in the Hochberg procedure, the U.S. Food and Drug Administration guidance on multiple endpoints in clinical trials provides conservative recommendations on the Hochberg procedure, and limits its application on a small set of standard test statistics. Based on the demand of using the Hochberg procedure in a more flexible way, we develop a test to validate the dependence assumption in the Hochberg procedure and Benjamini-Hochberg procedure. A simulation study is conducted for power analysis, and a case study in metastatic breast cancer is included to illustrate how the proposed test can be applied to validating the dependence type between the progression-free survival and overall survival.