General Covering Principle: a New Approach to Address Multiplicity in Hypothesis Testing

• Activity Number: 483 - Multiplicity
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Huajiang Li* and Hong Zhou
• Companies: Avanir Pharmaceuticals and Arkansas State University
• Keywords: Multiplicity; Familywise error rate; Covering Principle; General Covering Principle

Abstract

Recently the covering principle was proposed to address the multiplicity issue when the decision order of testing individual null hypotheses implied coverage relations and constraints in multiple testing problems. The covering principle was based on the sample space partitioning instead of the parameter space partitioning as classical closed testing and partitioning principle did. Our current research extended the covering principle to a very general form that could simultaneously deal with multiple coverage relations in testing null hypotheses. We proposed a concept called maximum constrained class and decomposed the whole family of individual null hypotheses into a few overlapped sub-families. We proved that any multiple testing procedure constructed based on the proposed principle strongly controls the familywise error rate as long as the multiple tests for each sub-family strongly control the type I error rate in the corresponding sub-family. Several examples from clinical trials were provided for the illustration purpose.