This equation has the same form as the TWAS expression if we use the scaled weight vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde{\mathbf W}}_g$$\end{document}W~g instead of Wg. Summary-TWAS imputes the Z-score for the gene-level result assuming that under the null hypothesis, the Z-scores are normally distributed with the same correlation structure as the SNPs; whereas in S-PrediXcan we compute the results of PrediXcan using summary statistics. Thus, S-TWAS and S-PrediXcan yield equivalent mathematical expressions (after setting the factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt {\frac{{(1 - R_l^2)}}{{(1 - R_g^2)}}} \approx 1$$\end{document}(1-Rl2)(1-Rg2)≈1).
