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.

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

A survey is given of differential expression analyses using the linear modeling features of the limma package. The chapter starts with the simplest replicated designs and progresses through experiments with two or more groups, direct designs, factorial designs and time course experiments. Experiments with technical as well as biological replication are considered. Empirical Bayes test statistics are explained. The use of quality weights, adaptive background correction and control spots in conjunction with linear modelling is illustrated on the β7 data.

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limma: Linear Models for Microarray Data

New normal linear modeling strategies are presented for analyzing read counts from RNA-seq experiments. The voom method estimates the mean-variance relationship of the log-counts, generates a precision weight for each observation and enters these into the limma empirical Bayes analysis pipeline. This opens access for RNA-seq analysts to a large body of methodology developed for microarrays. Simulation studies show that voom performs as well or better than count-based RNA-seq methods even when the data are generated according to the assumptions of the earlier methods. Two case studies illustrate the use of linear modeling and gene set testing methods.

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voom: precision weights unlock linear model analysis tools for RNA-seq read counts

A flexible statistical framework is developed for the analysis of read counts from RNA-Seq gene expression studies. It provides the ability to analyse complex experiments involving multiple treatment conditions and blocking variables while still taking full account of biological variation. Biological variation between RNA samples is estimated separately from the technical variation associated with sequencing technologies. Novel empirical Bayes methods allow each gene to have its own specific variability, even when there are relatively few biological replicates from which to estimate such variability. The pipeline is implemented in the edgeR package of the Bioconductor project. A case study analysis of carcinoma data demonstrates the ability of generalized linear model methods (GLMs) to detect differential expression in a paired design, and even to detect tumour-specific expression changes. The case study demonstrates the need to allow for gene-specific variability, rather than assuming a common dispersion across genes or a fixed relationship between abundance and variability. Genewise dispersions de-prioritize genes with inconsistent results and allow the main analysis to focus on changes that are consistent between biological replicates. Parallel computational approaches are developed to make non-linear model fitting faster and more reliable, making the application of GLMs to genomic data more convenient and practical. Simulations demonstrate the ability of adjusted profile likelihood estimators to return accurate estimators of biological variability in complex situations. When variation is gene-specific, empirical Bayes estimators provide an advantageous compromise between the extremes of assuming common dispersion or separate genewise dispersion. The methods developed here can also be applied to count data arising from DNA-Seq applications, including ChIP-Seq for epigenetic marks and DNA methylation analyses.

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Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation

The ovarian hormones oestrogen and progesterone profoundly influence breast cancer risk, underpinning the benefit of endocrine therapies in the treatment of breast cancer. Modulation of their effects through ovarian ablation or chemoprevention strategies also significantly decreases breast cancer incidence. Conversely, there is an increased risk of breast cancer associated with pregnancy in the short term. The cellular mechanisms underlying these observations, however, are poorly defined. Here we demonstrate that mouse mammary stem cells (MaSCs) are highly responsive to steroid hormone signalling, despite lacking the oestrogen and progesterone receptors. Ovariectomy markedly diminished MaSC number and outgrowth potential in vivo, whereas MaSC activity increased in mice treated with oestrogen plus progesterone. Notably, even three weeks of treatment with the aromatase inhibitor letrozole was sufficient to reduce the MaSC pool. In contrast, pregnancy led to a transient 11-fold increase in MaSC numbers, probably mediated through paracrine signalling from RANK ligand. The augmented MaSC pool indicates a cellular basis for the short-term increase in breast cancer incidence that accompanies pregnancy. These findings further indicate that breast cancer chemoprevention may be achieved, in part, through suppression of MaSC function.

Control of mammary stem cell function by steroid hormone signalling

Assessment of array quality is an essential step in the analysis of data from microarray experiments. Once detected, less reliable arrays are typically excluded or "filtered" from further analysis to avoid misleading results. In this article, a graduated approach to array quality is considered based on empirical reproducibility of the gene expression measures from replicate arrays. Weights are assigned to each microarray by fitting a heteroscedastic linear model with shared array variance terms. A novel gene-by-gene update algorithm is used to efficiently estimate the array variances. The inverse variances are used as weights in the linear model analysis to identify differentially expressed genes. The method successfully assigns lower weights to less reproducible arrays from different experiments. Down-weighting the observations from suspect arrays increases the power to detect differential expression. In smaller experiments, this approach outperforms the usual method of filtering the data. The method is available in the limma software package which is implemented in the R software environment. This method complements existing normalisation and spot quality procedures, and allows poorer quality arrays, which would otherwise be discarded, to be included in an analysis. It is applicable to microarray data from experiments with some level of replication.

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Jody Neilson

Papers

Empirical array quality weights in the analysis of microarray data