Robustness of case-control studies of genetic factors to population stratification: magnitude of bias and type I error.

Case-control studies of genetic factors are prone to a special form of confounding called population stratification, whenever the existence of one or more subpopulations may lead to a false association, be it positive or negative. We quantify both the bias (in terms of confounding risk ratio) and the probability of false association (type I error) in the most unfavorable situation in which only one high-risk subpopulation is hidden within the studied population, considering different scenarios of population structuring and varying sample sizes. In accord with previous work, we find that the bias is likely to be small in most cases. In addition, we show that the same applies to the associated type I error whenever the subpopulation is small in proportion. For instance, when the hidden subpopulation makes up 5% of the entire population, with an allelic frequency of 0.25 (versus 0.10) and a disease rate that is double, then the estimated bias is 1.07 and the type I error associated with a sample of 500 cases and 500 controls is 8% (instead of 5%). We also show that the type I error is substantially greater for a rare allele (frequency of 0.1) than for a common allele (frequency of 0.5) and analyze the pattern of increase of vulnerability to stratification bias with sample size. Based on our findings, we may therefore conclude that with moderate sample sizes the type I error associated with population stratification remains very limited in most realistic scenarios.