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Optimal testing of multiple hypotheses with common effect direction

RICHARD M. BITTMAN, JOSEPH P. ROMANO, CARLOS VALLARINO and MICHAEL WOLF
Biometrika
Vol. 96, No. 2 (JUNE 2009), pp. 399-410
Published by: Oxford University Press on behalf of Biometrika Trust
Stable URL: http://www.jstor.org/stable/27798832
Page Count: 12
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Optimal testing of multiple hypotheses with common effect direction
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Abstract

We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, but not 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. Surprisingly, even if each intersection test has an optimality property, the overall procedure obtained by applying closure to these tests may be inadmissible. We 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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