We selected these two disorders because there is a high genetic correlation between them (estimate for rG between schizophrenia and bipolar disorder using ldsc: 0.72, SE: 0.03; estimated using meta-analysis of all PGC2 schizophrenia and bipolar cohorts, excluding cohorts which were used as test set in the initial PGC1 analysis), and it enabled us to draw a direct comparison between the approach described here and a previous study, which estimated multi-trait BLUP SNP effects \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{b}}_{{\mathrm{MT}} - {\mathrm{BLUP}}}} \right)$$\end{document}b^MT-BLUP from individual-level data in an approach equivalent to Eq. (9). The previous study used PGC1 data in the training set and selected four cohorts for schizophrenia and three cohorts for bipolar disorder as test sets. For schizophrenia, the training set comprised 17 cohorts (8826 cases, 6106 controls) and for bipolar disorder the training set comprised 11 cohorts (5867 cases, 3328 controls). The test set of 4 cohorts for schizophrenia contained 4068 cases and 5471 controls, and the test set of 3 cohorts for bipolar disorder contained 2029 cases and 5338 controls. The analyses on the PGC1 data were performed on 745,705 HapMap3 SNPs in common across all data sets. To have a direct comparison to our previous study, we began by re-analysing the same PGC1 training set data to estimate: (i) OLS SNP effects using Eq. (5) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{b}}_{{\mathrm{OLS}}}} \right)$$\end{document}b^OLS, (ii) BLUP SNP effects from the individual-level data using Eq. (8) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{b}}_{{\mathrm{BLUP}}}} \right)$$\end{document}b^BLUP, and (iii) approximate SBLUP effects using the OLS SNP effects from Eq. (5) and the ARIC data as a reference \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{b}}_{{\mathrm{SBLUP}}}} \right)$$\end{document}b^SBLUP using Eq. (11). For the estimation of schizophrenia SBLUP effects, λ was set to 1,100,000, corresponding roughly to 1,000,000 markers and an observed scale SNP heritability estimate of 0.47, and for the estimation of bipolar disorder SBLUP effects, lambda was set to 1,200,000, corresponding roughly to 1,000,000 markers and an observed scale SNP heritability estimate of 0.45. For the four SCZ testing cohorts and the three BIP testing cohorts used in the previous study, we created: (i) weighted multi-trait SBLUP predictors \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{wMT}} - {\mathrm{SBLUP}}}} \right)$$\end{document}g^wMT-SBLUP, (ii) weighted multi-trait BLUP predictor-based individual-level single-trait BLUP estimates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{wMT}} - {\mathrm{BLUP}}}} \right)$$\end{document}g^wMT-BLUP, and (iii) weighted multi-trait GWAS predictor based on GWAS OLS estimates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{wMT}} - {\mathrm{OLS}}}} \right)$$\end{document}g^wMT-OLS. We then compared the prediction accuracy we obtained using the weighted multi-trait SBLUP predictors to the individual-level multi-trait BLUP predictor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{MT}} - {\mathrm{BLUP}}}} \right)$$\end{document}g^MT-BLUP used in the previous study16.