caa a22 4500 378926039 CHVBK 20180305123617.0 cr unu---uuuuu 161128e20040609xx s 000 0 eng 10.2202/1544-6115.1040 doi (NATIONALLICENCE)gruyter-10.2202/1544-6115.1040 Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates [Elektronische Daten] [Sandrine Dudoit, Mark J. van der Laan, Katherine S. Pollard] 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., 2004b) and on augmentations of FWER-controlling methods to control error rates such as tail probabilities for the number of false positives and for the proportion of false positives among the rejected hypotheses (van der Laan et al., 2004a). The proposed bootstrap multiple testing procedures are evaluated by a simulation study and applied to genomic data in the fourth article of the series (Pollard et al., 2004). ©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston Statistical Theory and Methods nationallicence Adjusted p-value nationallicence asymptotic control nationallicence bootstrap nationallicence consistency nationallicence cut-off nationallicence F-statistic nationallicence generalized family-wise error rate nationallicence multiple testing nationallicence null distribution nationallicence null hypothesis nationallicence quantile nationallicence single-step nationallicence test statistic nationallicence t-statistic nationallicence Type I error rate nationallicence Dudoit Sandrine Division of Biostatistics, School of Public Health, University of California, Berkeley aut van der Laan Mark J. Division of Biostatistics, School of Public Health, University of California, Berkeley aut Pollard Katherine S. University of California, Santa Cruz aut Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-06-09), 1-69 3:1<1 2004 3 sagmb https://doi.org/10.2202/1544-6115.1040 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2202/1544-6115.1040 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dudoit Sandrine Division of Biostatistics, School of Public Health, University of California, Berkeley aut NATIONALLICENCE 700 1- van der Laan Mark J. Division of Biostatistics, School of Public Health, University of California, Berkeley aut NATIONALLICENCE 700 1- Pollard Katherine S. University of California, Santa Cruz aut NATIONALLICENCE 773 0- Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-06-09), 1-69 3:1<1 2004 3 sagmb CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter