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Chunk #102 — Methods — Comparison with TWAS

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Exploring the phenotypic consequences of tissue specific gene expression variation inferred from GWAS summary statistics.
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Formal similarity with TWAS can be made more explicit by rewriting S-PrediXcan formula in matrix form. With the following notation and definitions\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{*{20}{c}} {{\tilde{\bf W}}_g} & = & {\left( {\sigma _1w_{1g}, \ldots ,\sigma _pw_{pg}} \right)^\prime } \\ {{\bf{Z}}_{\mathrm{SNPs}}} & = & {\left( {Z_1, \ldots ,Z_p} \right)^\prime } \\ {} & = & {\left( {\frac{{\hat \beta _1}}{{se(\hat \beta _1)}}, \ldots ,\frac{{\hat \beta _p}}{{se(\hat \beta _p)}}} \right)\prime } \end{array}$$\end{document}W~g=σ1w1g,…,σpwpg′ZSNPs=Z1,…,Zp′=β^1se(β^1),…,β^pse(β^p)′and correlation matrix of SNPs in the model for gene g