Comments on ‘Delta-Centralization Fails to Control for Population Stratification in Genetic Association Studies’

sible under the BN simulation model, where subpopulation allele frequencies are generated according to a beta distribution. DC depends on choosing ‘null’ loci whose allele frequencies in the controls match that at the candidate locus. Under the BN model, extra variability is allowed in the allele frequencies at the null loci. It is then possible for the allele frequencies at several null loci to match that at the candidate locus and yet some null loci will have a  -estimate opposite in sign to that at the candidate locus. In this case, the overall  will be under-estimated, yielding high type I error rates, as shown by Dadd et al. [1] . Our preliminary simulations under the BN model show that when null loci that match are all assigned the ‘correct’ sign, DC maintains proper type I error rates. We are in the process of fully investigating the power of such a procedure, and a full paper describing this adjustment and its ramifications will be forthcoming.