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Optimal testing of multiple hypotheses with common effect direction

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  • Richard M. Bittman
  • Joseph P. Romano
  • Carlos Vallarino
  • Michael Wolf

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. Copyright 2009, Oxford University Press.

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Bibliographic Info

Article provided by Biometrika Trust in its journal Biometrika.

Volume (Year): 96 (2009)
Issue (Month): 2 ()
Pages: 399-410

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Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:399-410

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  1. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
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Cited by:
  1. Jeffrey Penney, 2013. "Hypothesis Testing for Arbitrary Bounds," Working Papers 1319, Queen's University, Department of Economics.

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