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

Mark van der Laan, Sandrine Dudoit and Katherine Pollard
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Mark 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 Pollard: Center for Biomolecular Science & Engineering, University of California, Santa Cruz

No 1138, U.C. Berkeley Division of Biostatistics Working Paper Series from Berkeley Electronic Press

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.

Keywords: Adjusted p-value, asymptotic control, bootstrap, consistency, cut-off, family-wise error rate, maxima of test statistics; minima of p-values, multiple testing, null distribution; null hypothesis; quantile; step-down; test statistic, Type I error rate , (search for similar items in EconPapers)
Date: 2004-09-10
Note: oai:bepress.com:ucbbiostat-1138
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Citations: View citations in EconPapers (7)

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