Given that causal variants are largely unknown, we propose a heuristic method that considers as a candidate causal variant, any SNP in LD (r2 > 0.45) with a GWS SNP and located within 100 kb of the latter (Supplementary Fig. 2). This heuristic is justified by a previous study by Wu et al.21 which has quantified the fine-mapping precision of GWAS and has found over multiple computer simulations that causal variants lied within 100 kb of the GWS SNPs ~90% of the time and that LD r2 between causal and GWS SNPs was >0.45. Once candidate causal variants are identified for each independent GWS included in the PGS, we approximate Eq. (1) by replacing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{jk,l}^2$$\end{document}rjk,l2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{jk,1}r_{jk,2}$$\end{document}rjk,1rjk,2 with the average of these quantities over all candidate causal variants, as shown below in Eq. (2):2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_2^2/R_1^2 \approx \frac{{\rho _b^2h_2^2}}{{h_1^2}} \times \left( {\frac{{\mathop {\sum }\nolimits_{k = 1}^{M_{\mathrm{T}}} \overline {r_{k,1}r_{k,2}} \sqrt {\frac{{p_{k,2}(1 - p_{k,2})}}{{p_{k,1}(1 - p_{k,1})}}} }}{{\mathop
