PRS summarizes genetic liability from many variants into a single number as a weighted sum of per-loci risk allele dosage21. More precisely, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{PRS}}_{tj} = \mathop {\sum }\nolimits_{{\mathrm{i}} \in {\mathrm{S}}} \hat \beta _{ti}x_{ij},$$\end{document}PRStj= ∑i∈Sβ^tixij, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{ij} \in \left\{ {0,1,2} \right\}$$\end{document}xij∈0,1,2 is the additively coded allele frequency of the ith marker for the jth individual, S is a set of SNP’s that survived the clumping and thresholding steps, t is one of the two traits studied as base phenotypes, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \beta _{ti}$$\end{document}β^ti is estimated effect-size (log odds ratio or regression coefficient) obtained from GWAS summary statistics on the base phenotype, which may be genetically correlated, but not necessarily the same as the target phenotype. In our case, the base phenotype is either PTSD or schizophrenia, depending on the discovery data set used in the analyses (PGC-PTSD or PGC-schizophrenia), whereas the target phenotype is PTSD diagnosis.
