PC covariates33, EMMAX with PC covariates33, and ROADTRIPS37 (see Web Resources). All PC runs used only one PC, but the additional inclusion of random PCs has little effect on results21. Power to detect causal variants may vary between methods, but our focus here was on correcting false positive associations. We did not simulate the approach described in ref. 30 as this method is completely immune from stratification, ensuring a value of 1.00 in all entries of the table; this approach has appealing properties, but may have reduced power in some instances (see above). We note that the method of ref. 37 with PC covariates incorporated is an approach of potentially high interest, but not currently implemented in ROADTRIPS software.
