Gatekeeping Multiple Testing Procedures for Sequential Families of Hypotheses

• Activity Number: 5
• Type: Invited
• Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Peter H. Westfall*+
• Companies: Texas Tech University
• Keywords: Bonferroni ; dose response ; multiple endpoints ; multiple comparisons ; resampling ; Simes' test

Abstract

Sequential testing involves testing hypotheses in a pre-selected order, all at the 0.05 level. This method can be extended to "gatekeeping" methods, where a single primary hypothesis (the gatekeeper) is tested at the 0.05 level, and then a collection of secondaries is tested using a familywise error rate (FWE) controlling method only if the primary is significant. The primary concern of this talk is the case where a "gate" contains multiple hypotheses. It is known that one can test hypotheses within each gate using an FWE-controlling method specific to the given gate, and proceed when all of the hypotheses in the gate are rejected. It is also known that if one proceeds to the next gate when only at least one of the hypotheses in a gate is found significant, then the method fails to control the FWE. Nevertheless, it is desirable to proceed to test secondary endpoints when one or more primary endpoints is found significant. I present methods for controlling the FWE with sequential families of hypotheses; these include weighted resampling-based and weighted Simes-based closed tests. The methods are illustrated using a multiple dose, multiple endpoint clinical trial.