These results underscore how correcting the test statistics using a single inflation factor may be inappropriate, possibly reducing power and not sufficiently controlling for false positives. To further demonstrate this point, we ran a simple simulation using the variance component model on which EMMAX is based. Although simulating data under this model puts our method at an advantage, and the approach is therefore less suited for comparison to other models, it does demonstrate that under some circumstances uniformly deflating P values may be inappropriate. We randomly simulated 100 sets of phenotypes solely from the sample structure with no SNP effects and examined the quantile-quantile plots across different methods. Although the inflation for most of the SNPs is corrected by genomic control as expected, we observed substantial fluctuations of the test statistics at the tail of the distribution (Supplementary Fig. 4a,b).
