\setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \theta$$\end{document}θ^ estimated by the correlation of z-statistics in the cis-region could be biased by the strong local genetic correlation14. We showed by simulations that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \theta$$\end{document}θ^ could be estimated with high accuracy from summary data of the “null SNPs” in cis-region using a simple correlation approach (Supplementary Note 1, Supplementary Figs. 16 and 17), that the MeCS test-statistics were well calibrated under the null hypothesis (Supplementary Fig. 16), and that the MeCS estimates of meta-analysis effect sizes were well estimated under the alternative hypothesis (Supplementary Fig. 17). We compared MeCS to a univariate analysis of the mean expression phenotype across tissues and found that the estimates of effect size and SE from the two approaches were highly consistent (Supplementary Fig. 18). Note that in comparison with the separate analysis in individual tissues, the gain of power for MeCS increased with the decrease of correlation in expression phenotype between tissues, more so for meta-analysis using individual-level data (Supplementary Fig. 19).
