Bayesian models for pooling microarray studies with multiple sources of replications

Abstract

Background: Biologists often conduct multiple but different cDNA microarray studies that all target the same biological system or pathway. Within each study, replicate slides within repeated identical experiments are often produced. Pooling information across studies can help more accurately identify true target genes. Here, we introduce a method to integrate multiple independent studies efficiently.

A Bayesian Model for Pooling Gene Expression Studies That Incorporates Co-Regulation Information

“…The following model combines studies from two different platforms, spotted and oligonucleotide arrays, and assumes that the average expression of a gene is independent of other genes. It is similar to the model introduced by Conlon et al [19]; the spotted array study consists of replicate slides within repeated experiments, and the oligonucleotide array study contains multiple probes, slides and experiments. We specify Model (1) as follows.…”

“…These are the log-ratios of fluorescent intensity levels for the mRNA of the control and treatment samples, which are labelled green and red (Cy3 and Cy5). The y jgse values are standardized so that each slide had zero mean and unit standard deviation (see also Shen et al [17]; Conlon et al [19], [20]). This model takes into account that the y jgse are influenced by slide and experiment variance.…”

“…For parameters common to both Models (1) and (2), we assigned conjugate scaled inverse chi-squared prior distributions to the experiment, slide and probe variance parameters, , , and , respectively. The scale parameters are derived from the data, by pooling information from all genes (similar to Tseng et al [5]; Lönnstedt and Speed [8]; Gottardo et al [10]; Conlon et al [19], [20]). For Model (2), the prior distribution of operon variability was assigned an inverse chi-squared distribution, with scale parameter equivalent to the variability within operons of each study.…”

“…A common goal of gene expression studies is to identify genes that are differentially expressed between two conditions, such as wildtype versus mutant or treatment versus control. Bayesian and empirical Bayesian models have been developed extensively for individual microarray studies (Baldi and Long [1]; Efron et al [2]; Newton et al [3], [4]; Tseng et al [5]; Broët et al [6]; Ibrahim et al [7]; Lönnstedt and Speed [8]; Townsend and Hartl [9]; Gottardo et al [10]; Ishwaran and Rao [11], [12]; Kendziorski et al [13]; Do et al [14]; Lönnstedt and Britton [15]), and several Bayesian approaches have recently been introduced to combine multiple microarray studies (Choi et al [16]; Shen et al [17]; Jung et al [18]; Conlon et al [19], [20]; Scharpf et al [21]; see also Tseng et al [22] for a comprehensive review of meta-analysis methods). Choi et al [16] introduced the first Bayesian meta-analysis model to detect differentially expressed genes between two experimental conditions.…”

“…Similar to Choi et al [17], Jung et al [18] pooled standardized gene effect size estimates into an overall mean effect across studies, and included a parameter of inter-study variability in the model. Unlike these previous methods, Conlon et al ([19], [20]) introduced a Bayesian meta-analysis model that treated each study separately, combining only probabilities of differential expression without integrating expression values. In a comparative study of Bayesian meta-analysis models, Conlon et al [20] found that combining only probabilities of differential expression outperformed pooling expression measures across studies, for their data sets.…”