Since the significant SMR results could also reflect linkage model that was of less biological interest, we used the heterogeneity in dependent instruments (HEIDI) test to distinguish pleiotropy (or causality) model from linkage model. The HEIDI test considers the pattern of associations using all the SNPs that are significantly associated with gene expression (eQTLs) in the cis-eQTL region (± 250 kb from the center of the gene probe). Under Hardy-Weinberg equilibrium and LD, bXY estimated at the top associated cis-eQTL (bXY(top)) will be equal to that estimated at any of the cis-SNPs in LD that is associated with gene expression. In the HEIDI test, we excluded the SNPs in strong LD with top cis-eQTL at r2 > 0.9 which was calculated by using individual level data from the HapMap2 CEU. We also removed SNPs in the cis-eQTL region with a PeQTL > 1.6 × 10−3 (equivalent to χ2 < 10) to avoid weak instrumental variables according to the original paper [22]. The null hypothesis of the HEIDI test was that there was a single causal variant which meant that there
