The conditional GWAS analysis usually requires individual-level genotype and phenotype data, which are not always available. Here, we propose a method to perform an approximate multi-trait-based conditional GWAS analysis that only requires summary data. Since GWAS summary data for risk factors and disease are often from multiple independent studies, the analysis has to be performed conditioning on the genetic values of the covariate risk factors (denoted by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{g}}_x = \{ g_{x_1},g_{x_2}, \ldots, g_{x_t}\}$$\end{document}gx={gx1,gx2,…,gxt}), where the genetic value is defined as the aggregated effect of all SNPs on a phenotype accounting for LD. Following the method that uses GWAS summary data to perform a multi-SNP-based conditional and joint analysis (GCTA-COJO)53, the SNP effect on the disease accounting for gx 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}$$\hat b_{zy}|{\hat{\mathbf b}}_{xy} = \hat b_{zy} - {\hat{\mathbf b}}_{zx}^t{\hat{\bf b}}_{xy},$$\end{document}b^zy∣b^xy=b^zy-b^zxtb^xy,where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{zy}$$\end{document}b^zy is the SNP effect on the disease on the logit scale (i.e., logOR), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}
