A two‐phase Bayesian methodology for the analysis of binary phenotypes in genome‐wide association studies

Recent advances in sequencing and genotyping technologies are contributing to a data revolution in genome-wide association studies that is characterized by the challenging large p small n problem in statistics. That is, given these advances, many such studies now consider evaluating an extremely large number of genetic markers (p) genotyped on a small number of subjects (n). Given the dimension of the data, a joint analysis of the markers is often fraught with many challenges, while a marginal analysis is not sufficient. To overcome these obstacles, herein, we propose a Bayesian two-phase methodology that can be used to jointly relate genetic markers to binary traits while controlling for confounding. The first phase of our approach makes use of a marginal scan to identify a reduced set of candidate markers that are then evaluated jointly via a hierarchical model in the second phase. Final marker selection is accomplished through identifying a sparse estimator via a novel and computationally efficient maximum a posteriori estimation technique. We evaluate the performance of the proposed approach through extensive numerical studies, and consider a genome-wide application involving colorectal cancer.