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Chunk #33 — Methods — Computing pPS

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Ancestry deconvolution and partial polygenic score can improve susceptibility predictions in recently admixed individuals.
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common:5\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}$${\mu }_{\overline{x}^{\prime} }$$\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 \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¯′ statistic, computed across all NI individuals of a reference population and using only a subset of variants of the genome, with size NS. The traditional standardized PS is a limit case of such formula where NS = NV. We independently computed PS for phased haplotypes, using their own local ancestry pattern in case of aspPS, and subsequently merged the results from the two haplotypes of the same individual.