EMMAX prevents the overdispersion of test statistics using a statistical model that explicitly takes into account sample structure, rather than correcting the overdispersed test statistics caused by not taking into account genetic relatedness in the statistical model. Consequently, EMMAX can also prevent the overcorrection that would remove true positive associations. We identified 15 genome-wide significant loci with at least one of the uncorrected, 100 principal components–corrected, or EMMAX, analyses after genomic control at the suggested P threshold32 of 7.2 × 10−8 across the ten phenotypes (Table 2). In 13 of the 15 loci, EMMAX P values become smaller than the uncorrected analysis. The two-sided binomial P value of the observed asymmetry is 9.8 × 10−4 if two methods have the same statistical power. With the 100 principal components–corrected analysis, 10 of the 15 loci show smaller P values than the uncorrected analysis (binomial P value of 0.12). Although 12 of the 15 loci are found by all methods to be genome-wide significant at P < 7.2 × 10−8, two known loci33, APOB (with triglyceride) and HNF4A (with HDL), pass the
