Firstly, we simulated 100,000 independent SNPs of which 5000 (5%) had effects on incidence only, 5000 had effects on prognosis only and 5000 had effects on both incidence and prognosis. Incidence and prognosis were simulated as quantitative traits under additive models with 50% heritability (Methods), with a non-genetic confounder (representing the combined effects of all such factors) simulated to explain 40% of variation in both incidence and prognosis. No direct effect of incidence on prognosis was simulated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\beta _{XY} = 0} \right)$$\end{document}βXY=0. Data were simulated for 20,000 unrelated individuals. Incidence and prognosis were analysed as quantitative traits using linear regression, with the prognosis model adjusting for incidence as a covariate. This simulation, which reflects the scenario discussed by Aschard et al.11, satisfies the assumptions of our procedure while creating a high degree of index event bias (Methods).
