Chunk #113 — Methods — Comparison with SMR

Source

Exploring the phenotypic consequences of tissue specific gene expression variation inferred from GWAS summary statistics.

Embedded

yes

Text

If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Z_{{\mathrm{eQTL}}} \gg Z_{{\mathrm{GWAS}}}$$\end{document}ZeQTL≫ZGWAS, i.e., the eQTL association is much more significant than the GWAS association,14\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{SMR}} = \frac{{Z_{{\mathrm{GWAS}}}^2}}{{1 + \frac{{Z_{{\mathrm{GWAS}}}^2}}{{Z_{{\mathrm{eQTL}}}^2}}}} \approx Z_{{\mathrm{GWAS}}}^2\left( {1 - \frac{{Z_{{\mathrm{GWAS}}}^2}}{{Z_{{\mathrm{eQTL}}}^2}}} \right)$$\end{document}TSMR=ZGWAS21+ZGWAS2ZeQTL2≈ZGWAS21-ZGWAS2ZeQTL2