An improved closed procedure for testing multiple hypotheses

Clinical trials routinely involve multiple hypothesis testing. The closed testing procedure (CTP) is a fundamental principle in testing multiple hypotheses. This article presents an improved CTP in which intersection hypotheses can be tested at a level greater than $$ such that the control of the familywise error rate at level $$ remains. Consequently, our method uniformly improves the power of discovering false hypotheses over the original CTP. We illustrate that an improvement by our method exists for many commonly used tests. An empirical study on the effectiveness of a glucose-lowering drug is provided.