The final per-GRS log odds γ1, …, γ19 were converted to an equivalent per-SNP score via a weighted sum1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{*{20}{c}} {{\mathrm{GRS}}_i^{{\mathrm{meta}}} \propto \mathop {\sum}\limits_{j = 1}^m {x_{ij}} \left( {\frac{{\gamma _1}}{{\sigma _1}}\alpha _{j1} + \ldots + \frac{{\gamma _{19}}}{{\sigma _{19}}}\alpha _{j19}} \right), } \end{array}$$\end{document}GRSimeta∝∑j=1mxijγ1σ1αj1+…+γ19σ19αj19,where m is the total number of SNPs, σ1, …, σ19 are the empirical standard deviations of each of the 19 GRSs in the derivation data, αj1, …, αj19 are the SNP effect sizes (from the GWAS summary statistics) for the jth SNP in each of the GRSs, respectively, and xij is the genotype {0, 1, 2} for the ith individual’s jth SNP. A SNP’s effect size αjk was considered to be zero for the kth score if the SNP was not included in that score. This resulted in 3.6 million SNPs for inclusion in the metaGRS.
