A simple Bayesian mixture model with a hybrid procedure for genome-wide association studies

Genome-wide association studies often face the undesirable result of either failing to detect any influential markers at all because of a stringent level for testing error corrections or encountering difficulty in quantifying the importance of markers by their P-values. Advocates of estimation procedures prefer to estimate the proportion of association rather than test significance to avoid overinterpretation. Here, we adopt a Bayesian hierarchical mixture model to estimate directly the proportion of influential markers, and then proceed to a selection procedure based on the Bayes factor (BF). This mixture model is able to accommodate different sources of dependence in the data through only a few parameters. Specifically, we focus on a standardized risk measure of unit variance so that fewer parameters are involved in inference. The expected value of this measure follows a mixture distribution with a mixing probability of association, and it is robust to minor allele frequencies. Furthermore, to select promising markers, we use the magnitude of the BF to represent the strength of evidence in support of the association between markers and disease. We demonstrate this procedure both with simulations and with SNP data from studies on rheumatoid arthritis, coronary artery disease, and Crohn's disease obtained from the Wellcome Trust Case–Control Consortium. This Bayesian procedure outperforms other existing methods in terms of accuracy, power, and computational efficiency. The R code that implements this method is available at http://homepage.ntu.edu.tw/~ckhsiao/Bmix/Bmix.htm.