Because EMMAX estimates the variance parameters under the null hypothesis, one may suspect that it is underpowered compared to the full mixed model, which estimates the variance parameters under the alternative hypothesis. This is comparable to the difference between the score statistic and the efficient score statistic25,34,35. As most genetic variants associated to date with human complex traits are estimated to explain only a small fraction of phenotypic variance20, the difference between the two approaches will be negligible in most cases. To assess the seriousness of this concern, we ran the original EMMA, which uses a full mixed effect model, on the 15 peak SNPs and compared the resulting P values to those estimated with EMMAX using GLS. Overall, as expected, the P values from the full mixed effect model tended to be smaller than the P value from the GLS model, but the magnitude of the difference was very small (Supplementary Fig. 3a). However, the running times for EMMA were substantially longer. Because the original EMMA re-estimates the variance parameters at each marker, given the size of the NFBC
