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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.

Suggested Citation

  • Richard M. Bittman & Joseph P. Romano & Carlos Vallarino & Michael Wolf, 2009. "Optimal testing of multiple hypotheses with common effect direction," Biometrika, Biometrika Trust, vol. 96(2), pages 399-410.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:399-410
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    File URL: http://hdl.handle.net/10.1093/biomet/asp006
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    References listed on IDEAS

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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. Romano Joseph P. & Shaikh Azeem & Wolf Michael, 2011. "Consonance and the Closure Method in Multiple Testing," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-25, February.
    2. Ruth Heller & Abba Krieger & Saharon Rosset, 2023. "Optimal multiple testing and design in clinical trials," Biometrics, The International Biometric Society, vol. 79(3), pages 1908-1919, September.
    3. Penney, Jeffrey, 2013. "Hypothesis testing for arbitrary bounds," Economics Letters, Elsevier, vol. 121(3), pages 492-494.
    4. Zeng-Hua Lu, 2016. "Extended MaxT Tests of One-Sided Hypotheses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 423-437, March.
    5. Zeng-Hua Lu, 2019. "Extended MinP Tests for Global and Multiple testing," Papers 1911.04696, arXiv.org, revised Aug 2024.
    6. Christian Ritz & Rikke Pilmann Laursen & Camilla Trab Damsgaard, 2017. "Simultaneous inference for multilevel linear mixed models—with an application to a large-scale school meal study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 295-311, February.
    7. Saharon Rosset & Ruth Heller & Amichai Painsky & Ehud Aharoni, 2022. "Optimal and maximin procedures for multiple testing problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1105-1128, September.
    8. Taddesse Kassahun & Eshetu Wencheko & Arne C. Bathke, 2023. "Nonparametric directional testing for multivariate problems in conjunction with a closed testing principle," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 349-363, June.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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