SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.

/pdf/controlling-the-false-discovery-rate-a-practical-and-431ouqffk6.pdf

Controlling the false discovery rate: a practical and powerful approach to multiple testing

In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html
 .

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-3ywnbkcan0.pdf

Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2

Whole-genome association studies (WGAS) bring new computational, as well as analytic, challenges to researchers. Many existing genetic-analysis tools are not designed to handle such large data sets in a convenient manner and do not necessarily exploit the new opportunities that whole-genome data bring. To address these issues, we developed PLINK, an open-source C/C++ WGAS tool set. With PLINK, large data sets comprising hundreds of thousands of markers genotyped for thousands of individuals can be rapidly manipulated and analyzed in their entirety. As well as providing tools to make the basic analytic steps computationally efficient, PLINK also supports some novel approaches to whole-genome data that take advantage of whole-genome coverage. We introduce PLINK and describe the five main domains of function: data management, summary statistics, population stratification, association analysis, and identity-by-descent estimation. In particular, we focus on the estimation and use of identity-by-state and identity-by-descent information in the context of population-based whole-genome studies. This information can be used to detect and correct for population stratification and to identify extended chromosomal segments that are shared identical by descent between very distantly related individuals. Analysis of the patterns of segmental sharing has the potential to map disease loci that contain multiple rare variants in a population-based linkage analysis.

http://ibgwww.colorado.edu/cdrom2009/ScriptsA/purcell/GWAS/boulder_09_plink_intro.pdf

PLINK: A Tool Set for Whole-Genome Association and Population-Based Linkage Analyses

limma is an R/Bioconductor software package that provides an integrated solution for analysing data from gene expression experiments. It contains rich features for handling complex experimental designs and for information borrowing to overcome the problem of small sample sizes. Over the past decade, limma has been a popular choice for gene discovery through differential expression analyses of microarray and high-throughput PCR data. The package contains particularly strong facilities for reading, normalizing and exploring such data. Recently, the capabilities of limma have been significantly expanded in two important directions. First, the package can now perform both differential expression and differential splicing analyses of RNA sequencing (RNA-seq) data. All the downstream analysis tools previously restricted to microarray data are now available for RNA-seq as well. These capabilities allow users to analyse both RNA-seq and microarray data with very similar pipelines. Second, the package is now able to go past the traditional gene-wise expression analyses in a variety of ways, analysing expression profiles in terms of co-regulated sets of genes or in terms of higher-order expression signatures. This provides enhanced possibilities for biological interpretation of gene expression differences. This article reviews the philosophy and design of the limma package, summarizing both new and historical features, with an emphasis on recent enhancements and features that have not been previously described.

/pdf/limma-powers-differential-expression-analyses-for-rna-4yl7ae3arh.pdf

limma powers differential expression analyses for RNA-sequencing and microarray studies

In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-Seq data, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data. DESeq2 uses shrinkage estimation for dispersions and fold changes to improve stability and interpretability of the estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression and facilitates downstream tasks such as gene ranking and visualization. DESeq2 is available as an R/Bioconductor package.

/pdf/moderated-estimation-of-fold-change-and-dispersion-for-rna-59glcgpwlk.pdf

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffe two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

https://www.jstor.org/stable/pdfplus/2285452.pdf

One-Sided Simultaneous Confidence Bounds on Regression Surfaces with Intercepts

Procedures for multiple comparisons among treatment means, in analysis of covariance with a random concomitant, are considered. A Tukey-Kramer (TK)-type procedure is introduced for a conditional analysis and is compared with Thigpen and Paulson's (1974) unconditional procedure. It is first established (by simulation) that the TK procedure controls the unconditional familywise error rate at the nominal level set for the conditional procedure. In the second part of this work, the confidence interval lengths obtained by the two procedures are compared. It is found that the expected ratio of the confidence interval length obtained by the conditional method to that obtained by the unconditional method is generally less than 1. Moreover, the probability that the length of a TK interval will be larger than that of the Thigpen and Paulson procedure is (roughly) between .2 and .3.

Yosef Hochberg

Papers

One-Sided Simultaneous Confidence Bounds on Regression Surfaces with Intercepts

On Simultaneous Pairwise Comparisons in Analysis of Covariance

Distribution‐Free and Robust Procedures

Analysis of multivariate categorical data with misclassification errors by triple sampling schemes

Photoresistivity of the cuticle in the gaster segments in the ant species cataglyphis bicolor, messor arenarius and messor semirufus