SNPs were simulated independently under Hardy–Weinberg equilibrium with minor allele frequencies drawn uniformly from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0.01,0.49)$$\end{document}(0.01,0.49). SNP effects, confounders and residual variation in incidence and prognosis were drawn independently from normal distributions. For heritability of 50% distributed among 10,000 SNPs with effects on prognosis, each SNP explains, on average, 0.005% of variation. As half of SNPs affecting prognosis also have effects on incidence, and the total non-genetic confounder variance is 40%, index event bias arises from confounders that together explain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{0.5}}{2} + 0.4 = 65\%$$\end{document}0.52+0.4=65% of variation in prognosis. Estimates of SNP effects on incidence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \beta _{GX}$$\end{document}β^GX were obtained from linear regression of incidence on genotype, and unadjusted estimates of SNP effects on prognosis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \beta _{GY}^\prime$$\end{document}β^GY′ from linear regression of prognosis on genotype and incidence.
