estimates of reverse effects were highly significant (Supplementary Table 13), it is unlikely that the large difference in the estimated effect size between the forward and reverse analyses is due to the lack of power in the reverse analysis. We further confirmed by simulation that the GSMR estimate of bxy is unbiased irrespective of the sample size for the exposure (Supplementary Fig. 20). Interestingly, there were two cases where the estimated forward and reverse effects were in opposite directions, i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy({\mathrm{BMI}} \to {\mathrm{T}}2{\mathrm{D}})} = 1.19$$\end{document}b^xy(BMI→T2D)=1.19 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy({\mathrm{T}}2{\mathrm{D}} \to {\mathrm{BMI}})}{\mathrm{=}} -0.07\left( {P = 3.6 \times 10^{ - 26}} \right)$$\end{document}b^xy(T2D→BMI)=-0.07P=3.6×10-26; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy({\mathrm{BMI}} \to {\mathrm{dyslipidemia}})} = 0.32$$\end{document}b^xy(BMI→dyslipidemia)=0.32 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat b_{xy({\mathrm{dyslipidemia}} \to {\mathrm{BMI}})} = - 0.03$$\end{document}b^xy(dyslipidemia→BMI)=-0.03 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {P = 2.0 \times 10^{ - 10}} \right)$$\end{document}P=2.0×10-10, meaning that although BMI is risk factor for the two diseases, patients who have developed the diseases may tend to lose weight.
