To estimate the average heritability at cis regions a modification of the Haseman-Elston regression method was used that analyzes the data of several traits in a single linear regression 16. Briefly, ygi represents the expression for gene g and individual i, normalized to have mean 0 and variance 1 across all the individuals. Ygij = (ygi * ygj) is a measure of phenotypic similarity between twins i and j in gene g and πgij is the IBD sharing between the DZ pair (i,j) at gene g calculated as described above. Ygij was regressed on the IBD sharing πgij over all genes and all DZ twin pairs. The coefficient of this regression is an estimate of the average variance explained in cis. The quotient of this value with the average of total heritability for the same set of transcripts represents a measure of the proportion of the heritability that is explained by variants in cis. Next, each gene’s expression value was corrected by the cis-eQTL effects and calculated as the residuals of the linear regression of the original gene expression levels
