Bayesian Modeling of Differential Gene Expression

Abstract

We present a Bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects, and show how to use the output for choosing lists of genes for further investigation. We give empirical evidence that expression-level dependent array effects are needed, and explore different nonlinear functions as part of our model-based approach to normalization. The model includes gene-specific variances but imposes some necessary shrinkage through a hierarchical structure. Model criticism via posterior predictive checks is discussed. Modeling the array effects (normalization) simultaneously with differential expression gives fewer false positive results. To choose a list of genes, we propose to combine various criteria (for instance, fold change and overall expression) into a single indicator variable for each gene. The posterior distribution of these variables is used to pick the list of genes, thereby taking into account uncertainty in parameter estimates. In an application to mouse knockout data, Gene Ontology annotations over- and underrepresented among the genes on the chosen list are consistent with biological expectations.

Bayesian Robust Inference for Differential Gene Expression in cDNA Microarrays with Multiple Samples

“…We use a Bayesian linear model (Lindley and Smith 1972) with t-distributed sampling errors to allow for outliers (Besag and Higdon 1999). We also explicitly model the non-constant variances by using an exchangeable prior for the gene precisions (Lewin et al 2003). Our model includes design effects that deal with normalization issues (Kerr, Martin, and Churchill 2000).…”

Bayesian Methods for Microarray Data

“…Both of these include a constant term in a linear model, estimated in a fully Bayesian manner. Bhattacharjee et al (2004) and Lewin et al (2006) model normalization as a nonlinear function of expression level. Bhattacharjee et al (2004) use a normalization term γ gcr , which is modeled as a piecewise linear function of gene expression level.…”

Coherent Frequentism: A Decision Theory Based on Confidence Sets

“…Consider the null hypothesis − ≤ ≤ + , where the non negative scalar is a minimal degree of practical or scientific significance in a particular application. For instance, researchers developing methods of analyzing microarray data are increasingly calling for specification of a minimal level of biological significance when testing null hypotheses of equivalent gene expression against alternative hypotheses of differential gene expression (Bickel, 2011c;Bochkina and Richardson, 2007;Lewin et al, 2006;Van De Wiel and Kim, 2007). Bickel (2004) and McCarthy and Smyth (2009) for every ∈ and for every that is an element of but not of the boundary of By the usual concept of statistical power, the Type II error rate of p ± associated with testing the false null hypothesis that = at significance level is…”