Bayes factors in the presence of population stratification

Hidden population stratification (PS) is a main concern in the analysis of case-control genetic association studies. All methods to correct for hidden PS have been focused on classical hypothesis testing, and cannot be directly applied to Bayesian analysis. In this paper, to study the impact and the correction of hidden PS on Bayes factor (BF), we use a simple approximation of BF in terms of the maximum likelihood estimates of the odds ratio (OR) and its asymptotic variance. One advantage is that the commonly used principal components analysis method with a large panel of null markers scanned from existing genome-wide association studies can be directly employed to correct for hidden PS in estimating the OR and its asymptotic variance, through which a correction to BF for hidden PS can be achieved. Using simulations, we examine the impact of ignoring hidden PS on BF and show that the proposed method yields an appropriate correction in Bayesian analysis.