Next, we used the summary-data-based Mendelian randomization (SMR) method to test for a joint association between GWAS summary statistics SNPs and eQTL, using the default settings in the SMR software [65] and the 1000G European ancestries reference panel. We again applied a Bonferroni correction for multiple-testing on the SMR P-value (PSMR). Moreover, a post-filtering step was applied by conducting heterogeneity in dependent instruments (HEIDI) test. The HEIDI test distinguishes the causality and pleiotropy models from the linkage model by considering the pattern of associations using all the SNPs that are significantly associated with gene expression in the cis-eQTL region. The null hypothesis is that a single variant is associated with both trait and gene expression, while the alternative hypothesis is that trait and gene expression are associated with two distinct variants. We defined significant hits based on SMR-HEIDΙ as those for which PSMR met the Bonferroni significance threshold and had PHEIDI>0.05.
