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Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate

Author

Listed:
  • 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)

Abstract

The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the characterization and construction of a test statistics null distribution (rather than data generating null distribution) for deriving cut-offs for these test statistics (i.e., rejection regions) and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which the step-down maxT and minP procedures asymptotically control the Type I error rate, for arbitrary data generating distributions, without the need for conditions such as subset pivotality. Inspired by this general characterization, we then propose as an explicit null distribution the asymptotic distribution of the vector of null value shifted and scaled test statistics. Step-down procedures based on consistent estimators of the null distribution are shown to also provide asymptotic control of the Type I error rate. A general bootstrap algorithm is supplied to conveniently obtain consistent estimators of the null distribution.

Suggested Citation

  • van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-35, June.
    • Handle: RePEc:bpj:sagmbi:v:3:y:2004:i:1:n:14
    DOI: 10.2202/1544-6115.1041
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    Cited by:

    1. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version," PIER Working Paper Archive 11-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Feb 2011.
    2. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    3. Yang Yang & Victor DeGruttola, 2008. "Resampling-Based Multiple Testing Methods with Covariate Adjustment: Application to Investigation of Antiretroviral Drug Susceptibility," Biometrics, The International Biometric Society, vol. 64(2), pages 329-336, June.
    4. Alessio Farcomeni, 2009. "Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 501-517, September.
    5. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    6. Schumi Jennifer & DiRienzo A. Gregory & DeGruttola Victor, 2008. "Testing for Associations with Missing High-Dimensional Categorical Covariates," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-17, September.

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