We also tested if the normalized effect size of each SNP was different for SBP versus DBP. Suppose that Y is SBP normalized to a standard normal (mean centered, then divided by the standard deviation) and Z is normalized DBP, and X is the SNP dosage. Then we model Y=aX+E and Z=bX+F, where a is the regression coefficient for Y on X and similarly b for Z; E and F are the residual errors, respectively. Since Var(Y)=Var(Z)=1, assuming a and b have the same sign (which is generally the case since the phenotypes are correlated), testing the equality of a and b is also a test of effect difference between SBP and DBP. Now, consider the difference Y-Z=(a-b)X+(E-F). Regressing Y-Z on X tests the difference between a and b; in this analysis, we additionally adjust for the same covariates as discussed previously.
