Table 1 shows type-1 error rates for the standard unadjusted analysis and for the adjusted analysis using our procedure. For all analyses, the rate is close to the nominal level when averaged over all SNPs; however, the majority of SNPs have no index event bias. Among the SNPs with effects on incidence, the type-1 error is inflated for the unadjusted analysis while our approach achieves the correct rate when there is no genetic correlation between incidence and prognosis. Under positive genetic correlation, the type-1 error increases for all analyses, but is consistently lower for our adjusted analysis. For some individual SNPs, the type-1 error can be very high under the unadjusted analysis but is substantially reduced under our approach, and at the nominal level when there is no genetic correlation. Under strong negative genetic correlation, our approach has slightly increased 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
