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Full-Text Articles in Statistics and Probability
Test Statistics Null Distributions In Multiple Testing: Simulation Studies And Applications To Genomics, Katherine S. Pollard, Merrill D. Birkner, Mark J. Van Der Laan, Sandrine Dudoit
Test Statistics Null Distributions In Multiple Testing: Simulation Studies And Applications To Genomics, Katherine S. Pollard, Merrill D. Birkner, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
Multiple hypothesis testing problems arise frequently in biomedical and genomic research, for instance, when identifying differentially expressed or co-expressed genes in microarray experiments. We have developed generally applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for control of a broad class of Type I error rates, defined as tail probabilities and expected values for arbitrary functions of the numbers of false positives and rejected hypotheses (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; Pollard and van der Laan, 2004; van der Laan et al., 2005, 2004a,b). As argued in the early article of Pollard and van der …
Resampling Based Multiple Testing Procedure Controlling Tail Probability Of The Proportion Of False Positives, Mark J. Van Der Laan, Merrill D. Birkner, Alan E. Hubbard
Resampling Based Multiple Testing Procedure Controlling Tail Probability Of The Proportion Of False Positives, Mark J. Van Der Laan, Merrill D. Birkner, Alan E. Hubbard
U.C. Berkeley Division of Biostatistics Working Paper Series
Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. In this article we propose a new resampling based multiple testing procedure asymptotically controlling the probability that the proportion of false positives among the set of rejections exceeds q at level alpha, where q and alpha are user supplied numbers. The procedure involves 1) specifying a conditional distribution for a guessed set of true null hypotheses, given the data, which asymptotically is degenerate at the true set of …
Multiple Testing Procedures And Applications To Genomics, Merrill D. Birkner, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit
Multiple Testing Procedures And Applications To Genomics, Merrill D. Birkner, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit
U.C. Berkeley Division of Biostatistics Working Paper Series
This chapter proposes widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; van der Laan et al., 2004a,b; Pollard and van der Laan, 2004; Pollard et al., 2005). Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of Type I errors, V_n, and rejected hypotheses, R_n. These error rates include: …
Multiple Testing Procedures For Controlling Tail Probability Error Rates, Sandrine Dudoit, Mark J. Van Der Laan, Merrill D. Birkner
Multiple Testing Procedures For Controlling Tail Probability Error Rates, Sandrine Dudoit, Mark J. Van Der Laan, Merrill D. Birkner
U.C. Berkeley Division of Biostatistics Working Paper Series
The present article discusses and compares multiple testing procedures (MTP) for controlling Type I error rates defined as tail probabilities for the number (gFWER) and proportion (TPPFP) of false positives among the rejected hypotheses. Specifically, we consider the gFWER- and TPPFP-controlling MTPs proposed recently by Lehmann & Romano (2004) and in a series of four articles by Dudoit et al. (2004), van der Laan et al. (2004b,a), and Pollard & van der Laan (2004). The former Lehmann & Romano (2004) procedures are marginal, in the sense that they are based solely on the marginal distributions of the test statistics, i.e., …
Multiple Testing Procedures: R Multtest Package And Applications To Genomics, Katherine S. Pollard, Sandrine Dudoit, Mark J. Van Der Laan
Multiple Testing Procedures: R Multtest Package And Applications To Genomics, Katherine S. Pollard, Sandrine Dudoit, Mark J. Van Der Laan
U.C. Berkeley Division of Biostatistics Working Paper Series
The Bioconductor R package multtest implements widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The current version of multtest provides MTPs for tests concerning means, differences in means, and regression parameters in linear and Cox proportional hazards models. Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of false positives and rejected hypotheses. These error rates include tail probabilities …
Multiple Testing. Part Iii. Procedures For Control Of The Generalized Family-Wise Error Rate And Proportion Of False Positives, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
Multiple Testing. Part Iii. Procedures For Control Of The Generalized Family-Wise Error Rate And Proportion Of False Positives, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
U.C. Berkeley Division of Biostatistics Working Paper Series
The accompanying articles by Dudoit et al. (2003b) and van der Laan et al. (2003) provide single-step and step-down resampling-based multiple testing procedures that asymptotically control the family-wise error rate (FWER) for general null hypotheses and test statistics. The proposed procedures fundamentally differ from existing approaches in the choice of null distribution for deriving cut-offs for the test statistics and are shown to provide asymptotic control of the FWER under general data generating distributions, without the need for conditions such as subset pivotality. In this article, we show that any multiple testing procedure (asymptotically) controlling the FWER at level alpha …
Multiple Testing. Part Ii. Step-Down Procedures For Control Of The Family-Wise Error Rate, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
Multiple Testing. Part Ii. Step-Down Procedures For Control Of The Family-Wise Error Rate, Mark J. Van Der Laan, Sandrine Dudoit, Katherine S. Pollard
U.C. Berkeley Division of Biostatistics Working Paper Series
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 …
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
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
U.C. Berkeley Division of Biostatistics Working Paper Series
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 …