We applied MeCS to data from 10 brain regions in GTEx (we referred to the meta-analyzed data as GTEx-brain hereafter). There were strong sample overlaps among the ten brain regions (mean overlap = 70.4%) and the mean correlation in expression level between pairwise brain regions across all the expressed genes was moderate (mean rp = 0.33). The gain of power by the meta-analysis was demonstrated by the observation that the mean χ2 statistic for cis-eQTLs (selected from GTEx-blood at PeQTL < 5 × 10−8) in GTEx-brain was larger than that in any individual brain region (Supplementary Fig. 20c). The association test-statistic for a SNP can be written as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ^2 = 1 + n_{{\mathrm{eff}}}\frac{{q^2}}{{1 - q^2}}$$\end{document}χ2=1+neffq21-q2, where neff is the effective sample size and q2 is the variance explained by a SNP45. We therefore can approximately estimate neff of GTEx-brain assuming constant mean q2 across brain regions (Supplementary Note 2). Note that this assumption is justified by the highly consistent estimates of variance of cis-eQTL effects across genes in different brain
