type-1 error compared with the unadjusted analysis. However this situation, if not implausible, is arguably less likely than positive genetic correlation2. Results for the family-wise error were more pronounced and followed the same pattern.Table 1Power for quantitative incidence and prognosis with non-genetic confoundingGenetic correlation000.250.250.450.45−0.25−0.25−0.45−0.45AdjustmentNoYesNoYesNoYesNoYesNoYesAll SNPs not affecting prognosis5.125.005.255.065.425.235.055.045.025.10All SNPs affecting incidence but not prognosis7.245.039.596.0612.59.155.935.655.386.85SNP with highest type-1 error33.05.761.719.187.963.720.015.010.828.5Family-wise type-1 error22.35.561.012.894.853.412.110.06.816.3All SNPs affecting prognosis19.516.718.718.016.617.219.313.818.710.9All SNPs affecting incidence and prognosis20.316.516.716.510.011.921.313.120.68.38SNP with greatest increase in power6.639.218.050.134.859.56.934.85.214.9SNP with greatest decrease in power72.319.975.041.920.412.193.619.296.122.0Estimates shown as % with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P \, < \, 0.05$$\end{document}P<0.05 over 1000 simulations of 100,000 independent SNPs. Five thousand SNPs have effects on incidence only, 5000 on prognosis only and 5000 on both incidence and prognosis. Heritability of both incidence and prognosis is 50% with the genetic correlation shown over all SNPs. Common non-genetic factors explain 40% of variation in both incidence and prognosis. Rows 2–5 show type-1 error rates. All SNPs, mean power across the relevant SNPs. Family-wise error, probability of at least one SNP with effect on incidence but not on prognosis having \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P \, < \, \frac{{0.05}}{{5000}} = 10^{ - 5}$$\end{document}P<0.055000=10-5. SNP
