We created LD-pruned sets of SNPs using PLINK 1.940 with R2 threshold of 0.1 within 250 SNP windows. To assess the effect of imputation quality on our procedure, we created separate pruned sets for SNPs with imputation R2 greater than 0.9, 0.98 and 0.99 in both incidence and survival GWAS. These sets contained 245,913, 154,095 and 140,092 SNPs, respectively, and the regression of survival log hazard ratios on incidence log odds ratios gave coefficients of 0.048, −0.022 and −0.025, respectively. We were surprised to observe the change in sign of the coefficient as imputation R2 increased from 0.9 to 0.98, because the coefficient should be the same regardless of which SNPs are used for its estimation. Imputation introduces genotyping errors that do not follow a classical measurement error model because allele dosage is bounded in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,2]$$\end{document}[0,2]. Furthermore, standard imputation methods do not take phenotype into account. As a result, effect sizes for imputed SNPs are biased in ways that have not been well characterised. While such biases must be small for
