effects of underlying population structure. We present a simulation study to investigate the false-positive error rate of this procedure, and provide evidence that we can correct for substantial population structure between cases and controls from the original study and the diverse external reference samples used to expand the control cohort, certainly to the extent of allele frequency differences we expect between European populations. We also demonstrate that the use of an expanded control group with adjustment for axes of genetic variation can be more powerful than analysis of the samples from the original GWA study alone.