Mixture modeling of microarray gene expression data

About 28% of genes appear to have an expression pattern that follows a mixture distribution. We use first- and second-order partial correlation coefficients to identify trios and quartets of non-sex-linked genes that are highly associated and that are also mixtures. We identified 18 trio and 35 quartet mixtures and evaluated their mixture distribution concordance. Concordance was defined as the proportion of observations that simultaneously fall in the component with the higher mean or simultaneously in the component with the lower mean based on their Bayesian posterior probabilities. These trios and quartets have a concordance rate greater than 80%. There are 33 genes involved in these trios and quartets. A factor analysis with varimax rotation identifies three gene groups based on their factor loadings. One group of 18 genes has a concordance rate of 56.7%, another group of 8 genes has a concordance rate of 60.8%, and a third group of 7 genes has a concordance rate of 69.6%. Each of these rates is highly significant, suggesting that there may be strong biological underpinnings for the mixture mechanisms of these genes. Bayesian factor screening confirms this hypothesis by identifying six single-nucleotide polymorphisms that are significantly associated with the expression phenotypes of the five most concordant genes in the first group.