Optimal Testing of Multiple Hypotheses with Common Effect Direction

We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role of consonant procedures, from an interpretive as well as a theoretical viewpoint, and introduce a new procedure, which is consonant and has a maximin property under the normal model. The results are then applied to PROactive, a clinical trial designed to investigate the effectiveness of a glucose-lowering drug on macrovascular outcomes among patients with type 2 diabetes. Optimal Testing of Multiple Hypotheses With Common Effect Direction Richard M. Bittman Bittman Biostat, Inc. 766 Grove Street, Suite 600 Glencoe, IL 60022 rmb@bittmanbiostat.com Joseph P. Romano Department of Statistics Stanford University Stanford, CA 94305 romano@stanford.edu Carlos Vallarino Medical Outcomes Research Takeda Pharmaceuticals Deerfield, IL 60015 cvallarino@tpna.com Michael Wolf Institute for Empirical Research in Economics University of Zurich CH-8006 Zurich, Switzerland mwolf@iew.uzh.ch Summary. We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role of consonant procedures, from an interpretive as well as a theoretical viewpoint, and introduce a new procedure, which is consonant and has a maximin property under the normal model. The results are then applied to PROactive, a clinical trial designed to investigate the effectiveness of a glucose-lowering drug on macrovascular outcomes among patients with type 2 diabetes.

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