The S-PrediXcan formula when only the top eQTL is used to predict the expression level of a gene can be expressed as\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{*{20}{c}} {Z_{\mathrm{S - PrediXcan}}} & { = \mathop {\sum }\limits_{l \in {\mathrm{Model}}_g} w_{lg}\frac{{\hat \sigma _l}}{{\hat \sigma _g}}\frac{{\hat \beta _l}}{{{\mathrm{se}}\left( {\beta _l} \right)}}} \\ {} & { = w_{1g}\frac{{\hat \sigma _1}}{{\sqrt {w_{1g}^2\hat \sigma _1^2} }}Z_1} \\ {} & { = Z_1} \end{array}$$\end{document}ZS-PrediXcan= ∑l∈Modelgwlgσ^lσ^gβ^lseβl=w1gσ^1w1g2σ^12Z1=Z1where Z1 is the GWAS Z-score of the top eQTL in the model for gene. Thus12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_{{\mathrm{top}}\,{\mathrm{eQTL}}\,{\mathrm{S}} - {\mathrm{PrediXcan}}}^2 = Z_{{\mathrm{GWAS}}}^2$$\end{document}ZtopeQTLS-PrediXcan2=ZGWAS2
