We then repeated the simulation with no non-genetic confounding, so that bias only arises through genetic correlation violating our independence assumption. Table 2 shows that type-1 error for our approach is similar to that when non-genetic confounding is present, but for the unadjusted analysis the errors are reduced and generally closer to the nominal level than for our approach. Again there is a slight decrease in power under our approach, with considerable increases and decreases possible for individual SNPs. Supplementary Tables 3 and 4 show similar patterns for absolute bias and mean square error.Table 2Power for quantitative incidence and prognosis without non-genetic confoundingGenetic correlation000.250.250.450.45−0.25−0.25−0.45−0.45AdjustmentNoYesNoYesNoYesNoYesNoYesAll SNPs not affecting prognosis5.005.005.015.045.035.135.015.035.035.12All SNPs affecting incidence but not prognosis5.005.015.175.725.617.305.185.645.617.20SNP with highest type-1 error8.028.028.5015.213.035.68.3013.713.433.7Family-wise type-1 error4.503.904.908.808.0024.75.309.207.8022.1All SNPs affecting prognosis16.616.616.215.615.113.316.215.615.113.3All SNPs affecting incidence and prognosis16.416.415.414.413.09.7515.414.512.99.86SNP with greatest increase in power31.233.325.136.49.2013.918.629.46.7010.7SNP with greatest decrease in power20.117.953.935.462.026.246.131.956.626.2Parameters are as in Table 1 except that there are no common non-genetic factors of incidence and prognosis
