Ancestry-stratified meta analyses were performed using the software package rareGWAMA (see URLs for software use). Specifically, the method aggregated weighted Z-score statistics, that is,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Z}_{{\rm{META}}}=\frac{{\sum }_{k}{w}_{k}{Z}_{k}}{{({\sum }_{k}{w}_{k}^{2})}^{1/2}},$$\end{document}ZMETA=∑kwkZk(∑kwk2)1/2,where Zk is the Z-score statistic in study k. The weight wk is defined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w}_{k}=\sqrt{{N}_{k}{p}_{k}(1-{p}_{k}){R}_{k}^{2}},$$\end{document}wk=Nkpk(1−pk)Rk2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p}_{k}$$\end{document}pk is the variant allele frequency, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}_{k}^{2}$$\end{document}Rk2 is the imputation quality in study k. This method accounts for between-study heterogeneity in phenotype measures, imputation accuracy, allele frequencies and sample sizes.
