For each curated disease and quantitative trait, the Partners HealthCare Biobank sample was repeatedly and randomly split into a validation set comprising 1/3 of the data and a testing set comprising 2/3 of the data. Tuning parameters (P-value threshold in P+T, fraction of causal SNPs in LDpred, and global shrinkage parameter in PRS-CS) were selected in the validation set, and the predictive performance was evaluated in the testing set. We use the average R2 between the observed and predicted phenotypes across 100 random splits to assess the predictive performance for the quantitative traits, and report the average Nagelkerke’s R2 metric across 100 random splits for disease (case–control) phenotypes. Nagelkerke’s R2 is defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{{\mathrm{nag}}}^2 = R^2/R_{{\mathrm{max}}}^2$$\end{document}Rnag2=R2∕Rmax2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2 = 1 - ({\cal{L}}_{{\mathrm{res}}}{\mathrm{/}}{\cal{L}}_{{\mathrm{full}}})^{2/N}$$\end{document}R2=1-(Lres∕Lfull)2∕N, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{{\mathrm{max}}}^2 = 1 - {\cal{L}}_{{\mathrm{res}}}^{2{\mathrm{/}}N}$$\end{document}Rmax2=1-Lres2∕N, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal{L}}_{{\mathrm{res}}}$$\end{document}Lres is the likelihood of a restricted logistic regression model with covariates only (an intercept, current age,
