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

J. van der Laan Mark, Dudoit Sandrine and Pollard Katherine S.
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J. van der Laan Mark: 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

Statistical Applications in Genetics and Molecular Biology, 2004, vol. 3, issue 1, 35

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.

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
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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DOI: 10.2202/1544-6115.1041

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