That is, MeCS uses “null” SNPs (e.g., PeQTL > 0.01) to quantify sampling correlation of the estimated SNP effects between two data sets (θ), similar to the strategy used in the latest version of METAL (method unpublished, URLs), whereas MTAG39 uses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}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^ estimated by the intercept of bivariate LD score regression41 that relies on the assumption of an infinitesimal model which is invalid in cis-eQTL regions42. Han et al.40 suggest the use of the number of overlapping individuals43 or z-statistics to compute \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^ for summary-data-based analysis. However, a meta-analysis of cis-eQTL effects from two tissues requires the correlation of expression level between the tissues (because θ = rpρ with rp being the correlation of expression level and ρ being the proportion of sample overlap44) which is not available in summary data, and \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^ 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
