Correcting for population structure in the expanded control group by adjustment for axes of genetic variation controls the false-positive error rate of T_Fmds, remaining consistent with the significance level even for the most extreme population structure. There is some evidence of inflation of the false-positive error rate for moderate levels of population structure. For example, for an FST of 0.01, the false-positive error rate is 6.3 ± 0.35% at a significance level of 5%. We hypothesized that with fine-scale population structure, this could be as a result of insufficient SNPs, genome-wide, used to assess the IBS relationships between samples. We thus repeated the simulation using 100,000 uncorrelated SNPs for this calculation, as opposed to 10,000 (supplementary Table I). Based on 5,000 replicates of data, the false-positive error rate dropped to 4.8 ± 0.30% at a significance level of 5%, adequately correcting for the fine scale structure between samples in the expanded control cohort.
