Association rule mining for genome-wide association studies through Gibbs sampling

Finding associations between genetic markers and a phenotypic trait such as coronary artery disease (CAD) is of primary interest in genome-wide association studies (GWAS). A major challenge in GWAS is the involved genomic data often contain large number of genetic markers and the underlying genotype-phenotype relationship is mostly complex. Current statistical and machine learning methods lack the power to tackle this challenge with effectiveness and efficiency. In this paper, we develop a stochastic search method to mine the genotype-phenotype associations from GWAS data. The new method generalizes the well-established association rule mining (ARM) framework for searching for the most important genotype-phenotype association rules, where we develop a multinomial Gibbs sampling algorithm and use it together with the Apriori algorithm to overcome the overwhelming computing complexity in ARM in GWAS. Three simulation studies based on synthetic data are used to assess the performance of our developed method, delivering the anticipated results. Finally, we illustrate the use of the developed method through a case study of CAD GWAS.