We thus proceeded defining a way to compute partial PS (pPS), a statistic that estimates the total standardized PS using only a subset of the genome, as1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{pPS}}}_{j}=\frac{{\overline{x}}_{j}^{\prime}-{\mu }_{\overline{x}^{\prime} }}{{\sigma }_{\overline{x}^{\prime} }},$$\end{document}pPSj=x¯j′−μx¯′σx¯′,where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{x}}_{j}^{\prime}$$\end{document}x¯j′ is the raw partial PS for individual j, defined as the weighted average of associated allelic states using only a fraction p of all available SNPs. In turn, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{\overline{x}^{\prime} }$$\end{document}μx¯′ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma }_{\overline{x}^{\prime} }$$\end{document}σx¯′ are, respectively, mean and standard deviation of the raw PS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{x}^{\prime}$$\end{document}x¯′) in a population of reference. Hence, pPS is essentially a Z-score which yields the traditional standardized PS when applied to the full genome. Furthermore, we call the pPS calculated on ancestry specific portions of a given genome “ancestry-specific pPS” (aspPS). The model described above ignores entirely the problem of coupling the correct portions of the genome with
