marginal effects (βxy), i.e.,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{b}}_{xy} = {\mathbf{D}}^{ - \frac{1}{2}}{\mathbf{R}}_x^{ - 1}{\mathbf{D}}^{\frac{1}{2}}{\boldsymbol{\beta}}_{xy},$$\end{document}bxy=D-12Rx-1D12βxy,where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{R}}_x = \{ r_{g(x_i,x_j)}\}$$\end{document}Rx={rg(xi,xj)} is a t×t matrix with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{g(x_i,x_j)}$$\end{document}rg(xi,xj) being the genetic correlation between covariates i and j, D is a t×t diagonal matrix with the i-th diagonal element \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{{\rm {SNP}}(x_i)}^2$$\end{document}hSNP(xi)2 being the SNP-based heritability for the i-th covariate. We can estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{{\rm{SNP}}(x_j)}^2$$\end{document}hSNP(xj)2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{g(x_i,x_j)}$$\end{document}rg(xi,xj) from GWAS summary data using the LDSC approaches30,54, and estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta_{x_iy}$$\end{document}βxiy by GSMR.
