In contrast, the WTCCC example represents a very different situation where the approximations may be expected to yield accurate test statistics. This is because there is relatively little population stratification in these data (the individuals are all from the UK, and the relatedness matrix is approximately diagonal), and the effect sizes of the most strongly associated SNPs for Crohn's disease are small compared with the effect sizes in the HMDP data above14. Both conditions favor the approximation assumptions in EMMAX and GRAMMAR. Empirical comparisons (Figure 1d) show that, for this particular data set, the p values from EMMAX differ negligibly from the exact values. However, the p values from GRAMMAR still depart notably from the exact values.
