Hybrid Bayes factors for genome-wide association studies when a robust test is used

Bayes factor (BF) is often used to measure evidence against the null hypothesis in Bayesian hypothesis testing. In the analysis of genome-wide association (GWA) studies, extreme BF values support the associations detected based on significant pp-values. Results from recent GWA studies are presented, which show that existing BFs may not be consistent withpp-values when a robust test is used due to using different genetic models in the BF and pp-value approaches and this may result in misleading conclusions. Two hybrid BFs, which combine the advantages of both the frequentist and Bayesian methods, are then proposed for the markers showing at least moderate associations (pp-value <10−5<10−5) based on a robust test. One is Bayesian model averaging using a posterior weighted likelihood and the other is the maximum BF using a profile likelihood. The proposed hybrid BFs and pp-values of robust tests do not depend on a single genetic model, but instead, consolidate information over a set of models. We compare the hybrid BFs with two existing BF approaches, including an existing Bayesian model averaging method, in terms of false and true positive rates by simulations. The results show that, for markers showing at least moderate associations, both the hybrid BFs have higher true positive rates than the two existing BFs, while all false positive rates are similar. Applications of the two hybrid BFs to the markers associated with bipolar disorder, type 2 diabetes and age-related macular degeneration are presented. Our hybrid BFs provide better and more robust measures to compare significantly associated markers within and across GWA studies.