We ran computer simulations to evaluate the performances of Eqs. (1) and (2) under various genetic architectures. We also assessed the performances of a naive approach that assumes GWS SNPs to be the causal variants. In this case the expected RA explained by allele frequencies and LD differences between populations would approximately equal to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{{M_{\mathrm{T}}}}\left( {\mathop {\sum }\limits_{k = 1}^{M_{\mathrm{T}}} \sqrt {\frac{{p_{k,2}(1 - p_{k,2})}}{{p_{k,1}(1 - p_{k,1})}}} } \right)^2 \times \frac{{{\mathrm{var}}({\mathrm{PGS}}_1)}}{{{\mathrm{var}}({\mathrm{PGS}}_2)}}$$\end{document}1MT∑k=1MTpk,2(1−pk,2)pk,1(1−pk,1)2×var(PGS1)var(PGS2). When PGS-SNPs are independent and given that SNP effect sizes from GWAS are typically small and of similar magnitude, this naive approach can be further considered as a function of the ratio of heterozygosity at GWS SNPs between ancestries.
