A full Bayesian hierarchical mixture model for the variance of gene differential expression

Background  

In many laboratory-based high throughput microarray experiments, there are very few replicates of gene expression levels. Thus, estimates of gene variances are inaccurate. Visual inspection of graphical summaries of these data usually reveals that heteroscedasticity is present, and the standard approach to address this is to take a log₂ transformation. In such circumstances, it is then common to assume that gene variability is constant when an analysis of these data is undertaken. However, this is perhaps too stringent an assumption. More careful inspection reveals that the simple log₂ transformation does not remove the problem of heteroscedasticity. An alternative strategy is to assume independent gene-specific variances; although again this is problematic as variance estimates based on few replications are highly unstable. More meaningful and reliable comparisons of gene expression might be achieved, for different conditions or different tissue samples, where the test statistics are based on accurate estimates of gene variability; a crucial step in the identification of differentially expressed genes.