Modeling Nonlinear Gene Interactions Using Bayesian MARS

Abstract

DNA microarray technology enables us to monitor the expression levels of thousands of genes simultaneously, and hence helps to obtain a better picture of the interactions between the genes. In order to understand the biological structure underlying these gene interactions, we present here a statistical approach to model the functional relationship between genes and also between genes and disease status. We suggest a hierarchical Bayesian model based on multivariate adaptive regression splines (MARS) to model these complex nonlinear interaction functions. The novelty of the approach lies in the fact that we attempt to capture the complex nonlinear dependencies between the genes which otherwise would have been missed by linear approaches. Owing to the large number of genes (variables) and the complexity of the data, we use Markov Chain Monte Carlo (MCMC) based stochastic search algorithms to choose among models. The Bayesian model is flexible enough to identify significant genes as well as model the functional relationships between them. The effectiveness of the proposed methodology is illustrated using two publicly available microarray data sets: leukemia and hereditary breast cancer.