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Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate
U.C. Berkeley Division of Biostatistics Working Paper Series
  • Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
  • Sandrine Dudoit, Division of Biostatistics, School of Public Health, University of California, Berkeley
  • Katherine S. Pollard, Center for Biomolecular Science & Engineering, University of California, Santa Cruz
Date of this Version
12-16-2003
Comments
Published 2004 in Statistical Applications in Genetics and Molecular Biology 3(1), article 14.
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 test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rejection regions) for these test statistics 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 of a null distribution, 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.

Citation Information
Mark J. van der Laan, Sandrine Dudoit and Katherine S. Pollard. "Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate" (2003)
Available at: http://works.bepress.com/sandrine_dudoit/21/