Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Stumpf, Michael P.H.

6 Issues per year

IMPACT FACTOR 2016: 0.646
5-year IMPACT FACTOR: 1.191

CiteScore 2016: 0.94

SCImago Journal Rank (SJR) 2016: 0.625
Source Normalized Impact per Paper (SNIP) 2016: 0.596

Mathematical Citation Quotient (MCQ) 2016: 0.06

See all formats and pricing
More options …
Volume 3, Issue 1


Volume 10 (2011)

Volume 9 (2010)

Volume 6 (2007)

Volume 5 (2006)

Volume 4 (2005)

Volume 2 (2003)

Volume 1 (2002)

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

Sandrine Dudoit / Mark J. van der Laan / Katherine S. Pollard
Published Online: 2004-06-09 | DOI: https://doi.org/10.2202/1544-6115.1040

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).

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

About the article

Published Online: 2004-06-09

Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 3, Issue 1, Pages 1–69, ISSN (Online) 1544-6115, DOI: https://doi.org/10.2202/1544-6115.1040.

Export Citation

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston. Copyright Clearance Center

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Franck Chiappini, Alain Barrier, Raphaël Saffroy, Marie-Charlotte Domart, Nicolas Dagues, Daniel Azoulay, Mylène Sebagh, Brigitte Franc, Stephan Chevalier, Brigitte Debuire, Sandrine Dudoit, and Antoinette Lemoine
Laboratory Investigation, 2006, Volume 86, Number 2, Page 154
Tapan S. Mehta, Stanislav O. Zakharkin, Gary L. Gadbury, and David B. Allison
Physiological Genomics, 2006, Volume 28, Number 1, Page 24
Jean-François Chich, Olivier David, Fanny Villers, Brigitte Schaeffer, Didier Lutomski, and Sylvie Huet
Journal of Chromatography B, 2007, Volume 849, Number 1-2, Page 261
Katrina M. Waters, Jon M. Jacobs, Marina A. Gritsenko, and Norman J. Karin
Bone, 2011, Volume 48, Number 6, Page 1328
Seung Yeon Baik, Minkyung Jeong, Hyang Sook Kim, and Seung-Hwan Lee
Journal of Affective Disorders, 2017
Marcus Bantscheff, Markus Schirle, Gavain Sweetman, Jens Rick, and Bernhard Kuster
Analytical and Bioanalytical Chemistry, 2007, Volume 389, Number 4, Page 1017
Owen A Ross, Alexandra I Soto-Ortolaza, Michael G Heckman, Jan O Aasly, Nadine Abahuni, Grazia Annesi, Justin A Bacon, Soraya Bardien, Maria Bozi, Alexis Brice, Laura Brighina, Christine Van Broeckhoven, Jonathan Carr, Marie-Christine Chartier-Harlin, Efthimios Dardiotis, Dennis W Dickson, Nancy N Diehl, Alexis Elbaz, Carlo Ferrarese, Alessandro Ferraris, Brian Fiske, J Mark Gibson, Rachel Gibson, Georgios M Hadjigeorgiou, Nobutaka Hattori, John PA Ioannidis, Barbara Jasinska-Myga, Beom S Jeon, Yun Joong Kim, Christine Klein, Rejko Kruger, Elli Kyratzi, Suzanne Lesage, Chin-Hsien Lin, Timothy Lynch, Demetrius M Maraganore, George D Mellick, Eugénie Mutez, Christer Nilsson, Grzegorz Opala, Sung Sup Park, Andreas Puschmann, Aldo Quattrone, Manu Sharma, Peter A Silburn, Young Ho Sohn, Leonidas Stefanis, Vera Tadic, Jessie Theuns, Hiroyuki Tomiyama, Ryan J Uitti, Enza Maria Valente, Simone van de Loo, Demetrios K Vassilatis, Carles Vilariño-Güell, Linda R White, Karin Wirdefeldt, Zbigniew K Wszolek, Ruey-Meei Wu, and Matthew J Farrer
The Lancet Neurology, 2011, Volume 10, Number 10, Page 898
Owen A. Ross, Alexandra I. Soto-Ortolaza, Michael G. Heckman, Christophe Verbeeck, Daniel J. Serie, Sruti Rayaprolu, Stephen S. Rich, Michael A. Nalls, Andrew Singleton, Rita Guerreiro, Emma Kinsella, Zbigniew K. Wszolek, Thomas G. Brott, Robert D. Brown, Bradford B. Worrall, James F. Meschia, and Christian Wider
PLoS ONE, 2013, Volume 8, Number 9, Page e75035
Paolo Miotto, Francesca Forti, Alessandro Ambrosi, Danilo Pellin, Diogo F. Veiga, Gabor Balazsi, Maria L. Gennaro, Clelia Di Serio, Daniela Ghisotti, Daniela M. Cirillo, and Delia Goletti
PLoS ONE, 2012, Volume 7, Number 12, Page e51950
Yongchao Ge, Stuart C Sealfon, and Terence P Speed
Statistical Methods in Medical Research, 2009, Volume 18, Number 6, Page 543
Alessio Farcomeni
Statistical Methods in Medical Research, 2008, Volume 17, Number 4, Page 347
Sunil Mathur and Samuel Dolo
Statistical Methods in Medical Research, 2008, Volume 17, Number 4, Page 405
Sergey V. Malov, Alexey Antonik, Minzhong Tang, Alexandre Berred, Yi Zeng, and Stephen J. O'Brien
Biometrical Journal, 2017, Volume 59, Number 1, Page 126
Tai-Qin Huang, Min Su Lee, Eunha Oh, Byoung-Tak Zhang, Jeong-Sun Seo, and Woong-Yang Park
International Journal of Radiation Biology, 2008, Volume 84, Number 9, Page 734
Christina C. Bartenschlager and Michael Krapp
AStA Wirtschafts- und Sozialstatistisches Archiv, 2015, Volume 9, Number 2, Page 107
Scandinavian Journal of Statistics, 2007, Volume 34, Number 2, Page 275
Tsu-Hsin Howe, Ching-Fan Sheu, Tien-Ni Wang, and Yung-Wen Hsu
Research in Developmental Disabilities, 2014, Volume 35, Number 7, Page 1748
Yoshiyuki Ninomiya and Hironori Fujisawa
Biometrics, 2007, Volume 63, Number 4, Page 1135
Jeffrey C. Miecznikowski, David Gold, Lori Shepherd, and Song Liu
Statistics & Probability Letters, 2011, Volume 81, Number 11, Page 1695
David Shilane, Jarno Martikainen, Sandrine Dudoit, and Seppo J. Ovaska
Information Sciences, 2008, Volume 178, Number 14, Page 2870
Xinping Cui, Haibing Zhao, and Jason Wilson
Journal of Biopharmaceutical Statistics, 2010, Volume 20, Number 2, Page 223
Aurélie Labbe and Mary E. Thompson
Canadian Journal of Statistics, 2007, Volume 35, Number 1, Page 51

Comments (0)

Please log in or register to comment.
Log in