Finally, we have considered analyses with only genotype G and incidence X as predictors. In practice, further covariates will be included, such as principal components of ancestry. Analytic equivalents of Eq. (3) are more complicated in this case, but one can often treat the conditional SNP effects as approximately equal to those on the residuals from a first-stage regression on the further covariates. With this justification we can apply our procedure to conditional SNP effects on incidence and prognosis.
