Causal associations between risk factors and common diseases inferred from GWAS summary data.

Leveraging multiple independent genetic instruments (z) to test for causality. Shown in panel a is a schematic example that if an exposure (x) has an effect on an outcome (y), any instruments (SNPs) causally associated with x will have an effect on y, and the effect of x on y (bxy) at any of the SNPs is expected to be identical. This is further illustrated in a toy example in panel b that under a causal model, for the SNPs associated with x, the estimated effect of z on y (\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) should be linearly proportional to the estimated effect of z on x (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{zx}$$\end{document}b^zx) and the ratio between the two is an estimate of the mediation effect of x on y, i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy} = \hat b_{zy}/\hat b_{zx}$$\end{document}b^xy=b^zy∕b^zx

Putative causal associations between seven modifiable risk factors and common diseases. Shown are the results from GSMR analyses with disease data a from a meta-analysis of two community-based studies (GERA and UKB) and b from published independent case–control studies. Colors represent the effect sizes (as measured by odds ratios, ORs) of risk factors on diseases, red for risk effects and blue for protective effects. The significant effects after correcting for 231 tests (PGSMR < 2.2 × 10−4) are labeled with ORs (P-values). The nominally significant effects (PGSMR < 0.05) are labeled with “*”

GSMR analysis to test for the effect of BMI on T2D with and without filtering the pleiotropic outliers. Shown in a and b are the plots of effect sizes and association P-values of all the genetic instruments from GWAS for BMI vs. those for T2D. Shown in c is the plot of bxy vs. GWAS P-value of BMI at each genetic variant. Shown in d, e, and f are the plots for the instruments after the pleiotropic outliers being removed by the HEIDI-outlier approach (see Methods for details of the HEIDI-outlier approach). Error bars in a and d represent the standard errors. The dashed lines in b and e represent the GWAS threshold P-value of 5 × 10−8. The coordinates in b, c, e, and f are truncated at 50 for better graphic presentation

GSMR analysis to test for the effect of LDL-c on Alzheimer’s disease (AD) with and without pleiotropic outliers. Shown in a and b are the plots of effect sizes and association P-values of the original set of instruments from GWAS for LDL-c vs. those for AD. Shown in c is the plot of bxy vs. GWAS P-value of LDL-c at each genetic variant. Shown in d, e, and f are the plots for the instruments after the pleiotropic outliers being removed by the HEIDI-outlier approach (see Methods for details of the HEIDI-outlier approach). Error bars in a and d represent the standard errors. The dashed lines in b and e represent the GWAS threshold P-value of 5 × 10−8. The coordinates in b, c, e, and f are truncated at 50 for better graphic presentation

GSMR vs. conditional GSMR. Shown are the results from the GSMR analyses compared with those from the conditional GSMR analyses. In the conditional GSMR analysis, the effect size of each risk factor on disease was estimated conditioning on the other risk factors (see Methods for details of the conditional method). “Community”: disease GWAS data from a meta-analysis of the two community-based studies. “Case–control”: disease GWAS data from independent published case–control studies. In gray are the associations that do not pass the P-value threshold 2.2 × 10−4 in the conditional analysis

Effects of height and educational attainment on common diseases. Shown are the results from GSMR analyses with disease data a from a meta-analysis of the GERA and UKB studies and b from published independent case–control studies. Colors represent the effect sizes (as measured by odds ratios, ORs) of risk factors on diseases, red for risk effects and blue for protective effects. The significant effects after correcting for multiple testing (PGSMR < 7.6×10−4) are labeled with ORs (P-values). The nominally significant effects (PGSMR < 0.05) are labeled with “*”