Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments

Abstract

The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.

A point mutation in the Ncr1 signal peptide impairs the development of innate lymphoid cell subsets

“…52,53 A linear model was fitted to each gene, and empirical Bayes moderated t-statistics were used to assess differences in expression. 54 A false discovery rate cut-off of 0.15 was applied for calling differentially expressed genes. Gene Ontology and gene enrichment analyses were performed using Metascape (http://metascape.org).…”

Transcriptome analysis of porcine PBMCs after in vitro stimulation by LPS or PMA/ionomycin using an expression array targeting the pig immune response

“…To identify any significant differential expression, the microarray data were analyzed using Limma (Linear Models for Microarray Data) [68] from the Bioconductor open-source project running under R [69,70]. After data pre-processing using within-array global loess normalization, the empirical eBayes method in Limma, which computes moderated t-statistics, moderated F-statistics, and log-odds of differential expression, was applied to identify the significance of differential expression in each culture condition.…”

Microarray Analysis Reveals Distinct Gene Expression Profiles Among Different Tumor Histology, Stage and Disease Outcomes in Endometrial Adenocarcinoma

“…We used the Limma program in the R-based Bioconductor package to calculate the level of differential expression [49]. Briefly, a linear model was fit to the data (with cell means corresponding to the different conditions and a random effect for array), and the list of differentially expressed genes (DEGs) with Pvalue <0.01 were obtained by performing the following comparisons based on collected patients' characteristics: USC stage (late vs. early), EAC stage (late vs. early), USC prognosis (good vs. poor), and EAC prognosis (good vs. poor).…”