Pleiotropy is an important potential confounding factor that could bias the estimate and often results in an inflated test-statistic in a MR analysis9,10,13,19. We propose a method (called HEIDI-outlier) to detect pleiotropic SNPs at which the estimates of bxy are significantly different from expected under a causal model, and remove them from the GSMR analysis (Methods). The power of detecting a pleiotropic SNP depends on the sample sizes of the GWAS data sets and the deviation of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy}$$\end{document}b^xy estimated at the pleiotropic SNP from the causal model. We have demonstrated by simulation based on a causal model with pleiotropy that the power of HEIDI-outlier is high especially when the pleiotropic effects are large (Supplementary Fig. 4a). There are certainly pleiotropic outliers (e.g., those with very small effects) not detected by HEIDI-outlier. Nevertheless, these undetected pleiotropic effects do not seem to bias the GSMR estimate (Supplementary Fig. 4b), in contrast to a small bias in the estimate from Egger regression (MR-Egger) which is thought to be free of confounding from pleiotropy13.
