Between-groups within-gene heterogeneity of residual variances in microarray gene expression data

The analysis of microarray gene expression data typically tries to identify differential gene expression patterns in terms of differences of the mathematical expectation between groups of arrays (e.g. treatments or biological conditions). Nevertheless, the differential expression pattern could also be characterized by group-specific dispersion patterns, although little is known about this phenomenon in microarray data. Commonly, a homogeneous gene-specific residual variance is assumed in hierarchical mixed models for gene expression data, although it could result in substantial biases if this assumption is not true.

In this manuscript, a hierarchical mixed model with within-gene heterogeneous residual variances is proposed to analyze gene expression data from non-competitive hybridized microarrays. Moreover, a straightforward Bayes factor is adapted to easily check within-gene (between groups) heterogeneity of residual variances when samples are grouped in two different treatments. This Bayes factor only requires the analysis of the complex model (hierarchical mixed model with between-groups heterogeneous residual variances for all analyzed genes) and gene-specific Bayes factors are provided from the output of a simple Markov chain Monte Carlo sampling.

This statistical development opens new research possibilities within the gene expression framework, where heterogeneity in residual variability could be viewed as an alternative and plausible characterization of differential expression patterns.