We carry out simulations to assess the false-positive error rate and power of the test procedure described above. For each replicate of data, we generate cases and controls from the same source population, together with additional samples from three external cohorts, not necessarily genetically matched for population. These external samples will be used to expand the control cohort, but are not phenotyped for the disease of interest. We specify the divergence between the case-control source population and each external cohort by means of FST [Weir, 1996], where FST = 0 corresponds to equal allele frequencies at any given SNP across all populations.