a considerable number of highly ranked SNPs differ between the methods (Fig. 4 and Supplementary Table 2). In general, EMMAX results are similar to uncorrected analysis when the inflation of test statistics is small, but they become more similar to the PCA as the inflation increases. Notably, the PCA consistently shows larger departures from the uncorrected analysis than EMMAX does across all ten phenotypes. For example, when the overdispersion of test statistics was negligible, such as in the CRP phenotype, only 66% of the top 2,000 hits were concordant between the principal component and the uncorrected analysis, whereas 89% were concordant between EMMAX and the uncorrected analysis.