tissues i and j, respectively, and Ns being the number of overlapping individuals, and rp is the correlation of gene expression levels between two tissues in the overlapping sample. If i = j, then re = 1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{var}}\left( {b_i} \right) = {\mathrm{var}}( {\hat b_i} ) - {\mathrm{var}}\left( {e_i} \right)$$\end{document}varbi=var(b^i)-varei, where var(bi) is the variance of true cis-eQTL effects across genes in tissue i. We therefore can estimate the correlation of true cis-eQTL effect sizes across genes between tissues i and j as3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat r_b = \frac{{\widehat {{\mathrm{cov}}}\left( {b_i,b_j} \right)}}{{\sqrt {\widehat {{\mathrm{var}}}\left( {b_i} \right)\widehat {{\mathrm{var}}}(b_j)} }} = \frac{{\widehat {{\mathrm{cov}}}\left( {\hat b_i,\hat b_j} \right) - \hat r_e\sqrt {\widehat {{\mathrm{var}}}\left( {e_i} \right)\widehat {{\mathrm{var}}}(e_j)} }}{{\sqrt {\left[ {\widehat {{\mathrm{var}}}\left( {\hat b_i} \right) - \widehat {{\mathrm{var}}}\left( {e_i} \right)} \right]\left[ {\widehat {{\mathrm{var}}}\left( {\hat b_j} \right) - \widehat {{\mathrm{var}}}\left( {e_j} \right)} \right]} }}$$\end{document}r^b=cov^bi,bjvar^bivar^(bj)=cov^b^i,b^j-r^evar^eivar^(ej)var^b^i-var^eivar^b^j-var^ejwhere \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {{\mathrm{var}}}( {\hat b_i} )$$\end{document}var^(b^i) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {{\mathrm{var}}}( {\hat b_j} )$$\end{document}var^(b^j) (i.e., the estimates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{var}}( {\hat b_i} )$$\end{document}var(b^i) and
