A Bayesian semiparametric approach to learning about gene–gene interactions in case-control studies

Gene–gene interactions are often regarded as playing significant roles in influencing variabilities of complex traits. Although much research has been devoted to this area, to date a comprehensive statistical model that addresses the various sources of uncertainties, seem to be lacking. In this paper, we propose and develop a novel Bayesian semiparametric approach composed of finite mixtures based on Dirichlet processes and a hierarchical matrix-normal distribution that can comprehensively account for the unknown number of sub-populations and gene–gene interactions. Then, by formulating novel and suitable Bayesian tests of hypotheses we attempt to single out the roles of the genes, individually, and in interaction with other genes, in case-control studies. We also attempt to identify the significant loci associated with the disease. Our model facilitates a highly efficient parallel computing methodology, combining Gibbs sampling and Transformation-based MCMC (TMCMC). Application of our ideas to biologically realistic data sets revealed quite encouraging performance. We also applied our ideas to a real, myocardial infarction dataset, and obtained interesting results that partly agree with, and also complement, the existing works in this area, to reveal the importance of sophisticated and realistic modeling of gene–gene interactions.