Bayesian hierarchical modeling of means and covariances of gene expression data within families

We describe a hierarchical Bayes model for the influence of constitutional genotypes from a linkage scan on the expression of a large number of genes. The model comprises linear regression models for the means in relation to genotypes and for the covariances between pairs of related individuals in relation to their identity-by-descent estimates. The matrices of regression coefficients for all possible pairs of single-nucleotide polymorphisms (SNPs) by all possible expressed genes are in turn modeled as a mixture of null values and a normal distribution of non-null values, with probabilities and means given by a third-level model of SNP and trait random effects and a spatial regression on the distance between the SNP and the expressed gene. The latter provides a way of testing for cis and trans effects. The method was applied to data on 116 SNPs and 189 genes on chromosome 11, for which Morley et al. (Nature 2004, 430: 743–747) had previously reported linkage. We were able to confirm the association of the expression of HSD17B12 with a SNP in the same region reported by Morley et al., and also detected a SNP that appeared to affect the expression of many genes on this chromosome. The approach appears to be a promising way to address the huge multiple comparisons problem for relating genome-wide genotype × expression data.