Structured Bayesian variable selection for multiple related response variables and high-dimensional predictors

It is becoming increasingly common to study the complex association between multiple outcomes and high-dimensional predictors in biomedicine. However, the related multiple outcomes and related high-dimensional predictors require flexible and efficient joint statistical models. We propose a multivariate structured Bayesian variable selection model to identify sparse predictors associated with multiple outcomes. The approach uses a known structure prior between the multiple outcomes and predictors via a Markov random field (MRF) prior for the latent indicator variables of the coefficient matrix of a sparse seemingly unrelated regression. The prior knowledge in the MRF prior has the potential to generate new structure knowledge. In addition, we employ random effects to capture sample heterogeneity of grouped data. The proposed approach is validated by simulation studies and a large-scale pharmacogenomic study which includes a pharmacological profiling and multi-omics data from in vitro anti-cancer drug screening.