Joint Bayesian additive regression trees for multiple nonlinear dependency networks

Identifying protein–protein interaction networks can reveal therapeutic targets in cancer; however, for heterogeneous cancers such as colorectal cancer (CRC), a pooled analysis of the entire dataset may miss subtype-specific mechanisms, whereas separate analyses of each subgroup’s data may reduce the power to identify shared relations. To address this limitation, we propose a hierarchical Bayesian model for the inference of dependency networks that encourages the common selection of edges across subgroups while allowing subtype-specific connections. To allow for nonlinear dependence relations, we rely on Bayesian Additive Regression Trees (BART) to characterize the key mechanisms for each subgroup. Because BART is a flexible model that allows nonlinear effects and interactions, it is more suitable for genomic data than classical models that assume linearity. To connect the subgroups, we place a Markov random field prior on the probability of utilizing a feature in a splitting rule; this allows us to borrow strength across subgroups in identifying shared dependence relations. We illustrate the model using both simulated data and a real data application on the estimation of protein–protein interaction networks across CRC subtypes.