Effects of Gene-Environment and Gene-Gene Interactions in Case-Control   Studies: A Novel Bayesian Semiparametric Approach
  Cognizance of gene-environment interactions may help prevent or detain the onset of complex diseases like cardiovascular disease, cancer, type2 diabetes, autism or asthma by adjustments to lifestyle. In this regard, we extend the Bayesian semiparametric gene-gene interaction model of Bhattacharya & Bhattacharya (2015) to include the possibility of influencing gene-gene interactions by environmental variables and possible mutations caused by the environment. Our model accounts for the unknown number of genetic sub-populations via finite mixtures composed of Dirichlet processes, which are related to each other through a hierarchical matrix normal structure responsible for inducing gene-gene interactions and possible mutations in association with environmental variables. We also extend the Bayesian hypotheses testing procedures of Bhattacharya & Bhattacharya (2015) to detect the roles of genes and their interactions, environment and the influence of environment on gene-gene interactions, in case-control studies. We develop an effective parallel computing methodology, which harnesses the power of parallel processing technology to the efficiencies of our conditionally independent Gibbs sampling and Transformation based MCMC (TMCMC) methods.Applications of our model and methods to simulation studies with biologically realistic case-control genotype datasets obtained under five distinct set-ups yield encouraging results in each case. We followed these up by application of our ideas to a real, case-control based genotype dataset on early onset of myocardial infarction. Beside being in broad agreement with the reported literature on this dataset, the results obtained give some interesting insights to the differential effect of gender on MI. 
Durba Bhattacharya and Sourabh Bhattacharya
stat.AP