To test for a joint association between GWAS summary statistics SNPs and eQTL, the SMR method36, a Mendelian randomization approach, was used. SMR software (version 1.03) was run using the default settings. The European samples of the 1000G were used as a reference panel. Bonferroni multiple-testing correction was applied on 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 SNPs 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. Finally, gene-trait associations based on SMR-HEIDΙ were defined as the ones for which PSMR met the Bonferroni significance threshold and had PHEIDI > 0.05. We conducted a combination of SMR and HEIDI based on GTEx project latest (version 8) multi-tissue cis-eQTL databases99 from 13 brain regions and pituitary tissue that
