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Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives

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Author Info

  • van der Laan Mark J.

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Dudoit Sandrine

    (Division of Biostatistics, School of Public Health, University of California, Berkeley)

  • Pollard Katherine S.

    (University of California, Santa Cruz)

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    Abstract

    This article shows that any single-step or stepwise multiple testing procedure (asymptotically) controlling the family-wise error rate (FWER) can be augmented into procedures that (asymptotically) control tail probabilities for the number of false positives and the proportion of false positives among the rejected hypotheses. Specifically, given any procedure that (asymptotically) controls the FWER at level alpha, we propose simple augmentation procedures that provide (asymptotic) level-alpha control of: (i) the generalized family-wise error rate, i.e., the tail probability, gFWER(k), that the number of Type I errors exceeds a user-supplied integer k, and (ii) the tail probability, TPPFP(q), that the proportion of Type I errors among the rejected hypotheses exceeds a user-supplied value 0

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    File URL: http://www.degruyter.com/view/j/sagmb.2004.3.1/sagmb.2004.3.1.1042/sagmb.2004.3.1.1042.xml?format=INT
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    Bibliographic Info

    Article provided by De Gruyter in its journal Statistical Applications in Genetics and Molecular Biology.

    Volume (Year): 3 (2004)
    Issue (Month): 1 (June)
    Pages: 1-27

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    Handle: RePEc:bpj:sagmbi:v:3:y:2004:i:1:n:15

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    Web page: http://www.degruyter.com

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    Web: http://www.degruyter.com/view/j/sagmb

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    Cited by:
    1. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2008. "Control of the False Discovery Rate under Dependence using the Bootstrap and Subsampling," IEW - Working Papers 337, Institute for Empirical Research in Economics - University of Zurich.
    2. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    3. Merrill Birkner & Sandra Sinisi & Mark van der Laan, 2004. "Multiple Testing and Data Adaptive Regression: An Application to HIV-1 Sequence Data," U.C. Berkeley Division of Biostatistics Working Paper Series 1161, Berkeley Electronic Press.
    4. Wang, Li & Xu, Xingzhong, 2012. "Step-up procedure controlling generalized family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 775-782.
    5. Fink, Günther & McConnell, Margaret & Vollmer, Sebastian, 2011. "Testing for Heterogeneous Treatment Effects in Experimental Data: False Discovery Risks and Correction Procedures," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-477, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods and Applications, Springer, vol. 20(2), pages 141-170, June.
    7. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "Hypothesis Testing in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 75-104, 09.
    8. Joseph P. Romano & Michael Wolf, 2008. "Balanced Control of Generalized Error Rates," IEW - Working Papers 379, Institute for Empirical Research in Economics - University of Zurich.
    9. Somerville, Paul N. & Hemmelmann, Claudia, 2008. "Step-up and step-down procedures controlling the number and proportion of false positives," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1323-1334, January.
    10. Gordon, Alexander Y., 2009. "Inequalities between generalized familywise error rates of a multiple testing procedure," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1996-2004, October.

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