Our most serious assumption is no correlation between effects on incidence βGX and direct effects on prognosis βGY, for those SNPs entering the regression of step 2. If incidence and prognosis have common biological mechanisms then this assumption may be violated and create bias in b and hence in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \beta _{GY}$$\end{document}β^GY. However, considering pleiotropy in general some authors have argued that independence of effects is likely to be the norm in complex disease25. We explore this assumption in the following simulations and return to this point in the Discussion.
