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

It is becoming increasingly common to study complex associations between multiple phenotypes and high-dimensional genomic features in biomedicine. However, it requires flexible and efficient joint statistical models if there are correlations between multiple response variables and between high-dimensional predictors. We propose a structured multivariate Bayesian variable selection model to identify sparse predictors associated with multiple correlated response variables. The approach makes use of known structure information between the multiple response variables and high-dimensional predictors via a Markov random field (MRF) prior for the latent indicator variables of the coefficient matrix of a sparse seemingly unrelated regressions (SSUR). The structure information included in the MRF prior can improve the model performance (i.e., variable selection and response prediction) compared to other common priors. In addition, we employ random effects to capture heterogeneity of grouped samples. The proposed approach is validated by simulation studies and applied to a pharmacogenomic study which includes pharmacological profiling and multi-omics data (i.e., gene expression, copy number variation and mutation) from in vitro anti-cancer drug sensitivity screening.