Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates

Sandrine Dudoit, Mark van der Laan and Katherine Pollard
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Sandrine Dudoit: Division of Biostatistics, School of Public Health, University of California, Berkeley
Mark van der Laan: Division of Biostatistics, School of Public Health, University of California, Berkeley
Katherine Pollard: Center for Biomolecular Science & Engineering, University of California, Santa Cruz

No 1137, U.C. Berkeley Division of Biostatistics Working Paper Series from Berkeley Electronic Press

Abstract: The present article proposes general single-step multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors, such as the generalized family-wise error rate. 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 single-step common-quantile and common-cut-off 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. In the special case of family-wise error rate (FWER) control, our method yields the single-step minP and maxT procedures based on minima of unadjusted p-values and maxima of test statistics, respectively, with the important distinction in the choice of null distribution. Single-step 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. The special cases of t- and F-statistics are discussed in detail. The companion articles focus on step-down multiple testing procedures for control of the FWER (van der Laan et al., 2003a) and on augmentations of FWER-controlling methods to control error rates such as the generalized family-wise error rate and the proportion of false positives among the rejected hypotheses (van der Laan et al., 2003b). The proposed bootstrap multiple testing procedures are evaluated by a simulation study and applied to gene expression microarray data in the fourth article of the series (Pollard et al., 2004).

Keywords: Adjusted p-value, asymptotic control, bootstrap; consistency; cut-off, F-statistic, generalized family-wise error rate, multiple testing, null distribution, null hypothesis, quantile, single-step, test statistic, t-statistic, Type I error rate, (search for similar items in EconPapers)
Date: 2004-09-10
Note: oai:bepress.com:ucbbiostat-1137
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Citations: View citations in EconPapers (12)

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