A Bayesian hierarchical gene model on latent genotypes for genome-wide association studies

The primary goal of genome-wide association studies is to determine which genetic markers are associated with genetic traits, most commonly human diseases. As a result of the "large p, small n" nature of genome-wide association study data sets, and especially because of the collinearity due to linkage disequilibrium, multivariate regression results in an ill-posed problem. To overcome these obstacles, we propose preprocessing single-nucleotide polymorphisms to adjust for linkage disequilibrium, and a novel Bayesian statistical model that exploits a hierarchical structure between single-nucleotide polymorphisms and genes. We obtain posterior samples using a hybrid Metropolis-within-Gibbs sampler, and further conduct inference on single-nucleotide polymorphism and gene associations using centroid estimation. Finally, we illustrate the proposed model and estimation procedure and discuss results obtained on the data provided for the Genetic Analysis Workshop 18.