dominate the non-genetic. These are the scenarios in which our approach does best; furthermore, the type-1 errors are more consistent under different scenarios under our approach than the unadjusted analysis. Turning to power, there is again a modest reduction in general, with more substantial gains and losses possible for individual SNPs. Overall, we conclude that our approach can be preferred to an unadjusted analysis.Table 3Power for binary incidence and prognosis with non-genetic confoundingGenetic correlation000.250.250.450.45−0.25−0.25−0.45−0.45AdjustmentNoYesNoYesNoYesNoYesNoYesAll SNPs not affecting prognosis5.025.005.045.015.055.035.015.015.005.03All SNPs affecting incidence but not prognosis5.375.025.665.215.965.685.185.215.055.60SNP with highest type-1 error11.68.2013.78.518.214.68.409.208.3014.0Family-wise type-1 error5.805.607.705.2012.08.804.606.206.608.70All SNPs affecting prognosis8.998.638.328.397.496.489.288.169.297.34All SNPs affecting incidence and prognosis9.138.597.808.0010.99.609.747.819.776.33SNP with greatest increase in power36.548.124.534.623.029.97.2016.65.908.50SNP with greatest decrease in power51.433.333.027.010.99.6050.420.763.220.9Parameters are as in Table 1 with cases defined as subjects in the top 20th percentile of the incidence trait, and poor prognosis as cases in the top 50th percentile of the prognosis trait. Prognosis is analysed in cases onlyTable 4Power for binary incidence and prognosis without non-genetic confoundingGenetic correlation000.250.250.450.45−0.25−0.25−0.45−0.45AdjustmentNoYesNoYesNoYesNoYesNoYesAll SNPs not affecting prognosis5.005.005.005.015.005.035.005.015.005.03All SNPs affecting incidence but not prognosis5.005.015.025.225.105.705.035.215.115.66SNP with highest type-1 error7.307.307.708.607.7015.58.309.108.1014.4Family-wise type-1 error3.503.704.405.205.6010.14.805.505.609.10All SNPs affecting prognosis8.768.778.608.388.257.588.618.418.257.63All SNPs affecting incidence and prognosis8.718.728.388.007.666.458.398.047.666.51SNP with greatest increase in power13.614.913.918.15.907.808.4012.55.807.80SNP with greatest decrease in power44.242.553.342.648.927.751.943.443.125.8Parameters as in Table 3 except that that there are
