  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.
