To address this assertion, we have also investigated the sensitivity of our approach to the number of axes of genetic variation, by adjusting only for those axes of genetic variation, this time amongst the first ten, which are correlated with disease status using P <0.05. Supplementary Table V presents the false-positive error rate of the trend test for association, T_Fmds, adjusting for up to three or up to ten axes of genetic variation. Results are presented over 5,000 replicates for a range of FST, for a significance level of 5%. Also presented is the proportion of replicates of simulated data in which more than the first three axes of genetic variation were selected to adjust for population structure. The choice of the number of axes of genetic variation used for adjustment has little impact on the false-positive error rate, with less than 10% of replicates of data utilizing more than the first three axes. There is also little effect on power, demonstrated in supplementary Table VI for a SNP with minor allele frequency of 20% frequency in the source population, and a heterozygous genotype relative risk of 1.5.
