An improved delta-centralization method for population stratification.

Dadd et al. [Hum Hered 2010;69:285-294] recently criticized our delta-centralization (DC) method of controlling for population stratification (PS) and concluded that DC does not work. To explore our method, the authors simulated data under the Balding-Nichols (BN) model, which is more general than the model we had used in our simulations. They determined that the DC method underestimated the PS parameter (δ) and inflated the type I error rates when applied to BN-simulated data, and from this they concluded that the DC method is invalid. However, we argue that this conclusion is premature. In this paper, we (1) show why δ is underestimated and type I error rates are inflated when BN-simulated data are used, and (2) present a simple adjustment to DC that works reasonably well for data from both kinds of simulations. We also show that the adjusted DC method has appropriate power under a range of scenarios.