Main description:

Current statistical inference problems in areas such as astronomy, genomics, and marketing routinely involve the simultaneous test of thousands, or even millions, of null hypotheses. These hypotheses concern a wide range of par- eters, for high-dimensional multivariate distributions, with complex and - known dependence structures among variables. Motivated by these applications and the limitations of existing multiple testingmethods,wehavedevelopedandimplementedresampling-basedsing- step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, de?ned as tail probabilities and expected values for arbitrary functionsg(V,R ) of the numbers of Type I errorsV and - n n n jected hypothesesR (Birkner et al. , 2005a,b,c, 2006, 2007; Dudoit et al. , n 2004a,b, 2006; Kele¸ s et al. , 2006; van der Laan et al. , 2004a,b, 2005; van der Laan and Hubbard, 2006; Pollard et al. , 2005a,b; Pollard and van der Laan, 2004; Rubinetal. ,2006). Ourproposedprocedurestake intoaccountthejoint distribution of the test statistics and provide Type I error control in testing problems involving general data generating distributions (with arbitrary - pendence structures among variables), null hypotheses (de?ned in terms of submodels for the data generating distribution), and test statistics (e. g. ,t- 2 statistics,? -statistics,F-statistics). A key ingredient of the procedures is the null distribution used in place of the unknown joint distribution of the test statistics. TheresultsofagivenMTParereportedintermsofrejectionregions (i. e. , cut-o?s) for the test statistics, con?dence regions for the parameters of interest, and adjustedp-values.

Feature:

This book provides a detailed account of the theoretical foundations of proposed multiple testing methods and illustrates their application to a range of testing problems in genomics

Back cover:

This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. The methods are applied to a range of testing problems in biomedical and genomic research, including the identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments, such as microarray experiments; tests of association between gene expression measures and biological annotation metadata (e.g., Gene Ontology); sequence analysis; and the genetic mapping of complex traits using single nucleotide polymorphisms.

The book is aimed at both statisticians interested in multiple testing theory and applied scientists encountering high-dimensional testing problems in their subject matter area. Specifically, the book proposes resampling-based single-step and stepwise multiple testing procedures for controlling a broad class of Type I error rates, defined as tail probabilities and expected values for arbitrary functions of the numbers of Type I errors and rejected hypotheses (e.g., false discovery rate). Unlike existing approaches, the procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The multiple testing results are reported in terms of rejection regions, parameter confidence regions, and adjusted p-values.

Sandrine Dudoit is Associate Professor of Biostatistics and Statistics at the University of California, Berkeley (www.stat.berkeley.edu/~sandrine). Her research and teaching activities concern the development and application of statistical and computational methods for the analysis of high-dimensional biomedical and genomic data. She is a founding core developer of the Bioconductor Project and is an Associate Editor for six journals, including the Annals of Applied Statistics and Statistical Applications in Genetics and Molecular Biology.

Mark J. van der Laan is Hsu/Peace Professor of Biostatistics and Statistics at the University of California, Berkeley (www.stat.berkeley.edu/~laan). His research concerns causal inference, adjusting for missing and censored data, and simultaneous estimation and testing based on high-dimensional observational and experimental biomedical and genomic data. He is co-author with James Robins of Unified Methods for Censored Longitudinal Data and Causality (Springer, 2003). He is a recipient of the 2005 COPSS Presidents' and Snedecor Awards and is an active Associate Editor for five journals, including the Annals of Statistics and the International Journal of Biostatistics.

Contents:

Multiple Hypothesis Testing.- Test Statistics Null Distribution.- Overview of Multiple Testing Procedures.- Single-Step Multiple Testing Procedures for Controlling General Type I Error Rates, ?(Fvn).- Step-Down Multiple Testing Procedures for Controlling the Family-Wise Error Rate.- Augmentation Multiple Testing Procedures for Controlling Generalized Tail Probability Error Rates.- Resampling-Based Empirical Bayes multiple Testing Procedures for Controlling Generalized Tail Probability Error Rates.- Simulation Studies: Assessment of Test Statistics Null Distributions.- Identification of Differentially Expressed and Co-Expressed Genes in High-Throughput Gene Expression Experiments.- Multiple Tests of Association with Biological Annotation Metadata.- HIV-1 Sequence Variation and Viral Replication Capacity.- Genetic Mapping of Complex Human Traits Using Single Nucleotide Polymorphisms: The ObeLinks Project.- Software Implementation.