The scalable birth–death MCMC algorithm for mixed graphical model learning with application to genomic data integration

Abstract

Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is now distributed through consortia like The Cancer Genome Atlas (TCGA), where specific types of biological information on specific type of tissue or cell are available. In cancer research the challenge is now to perform integrative analyses of high-dimensional multiomic data with the goal to better understand genomic processes that correlate with cancer outcomes, for example, elucidate gene networks that discriminate a specific cancer subgroups (cancer subtyping) or discovering gene networks that overlap across different cancer types (pan-cancer studies). In this paper we propose a novel mixed graphical model approach to analyze multiomic data of different types (continuous, discrete and count) and perform model selection by extending the birth–death MCMC (BDMCMC) algorithm initially proposed by Stephens (Ann. Statist. 28 (2000) 40–74) and later developed by Mohammadi and Wit (Bayesian Anal. 10 (2015) 109–138). Using simulations, we compare the performance of our method to the LASSO method and the standard BDMCMC method and find that our method is superior in terms of both computational efficiency and the accuracy of the model selection results. Finally, an application to the TCGA breast cancer data shows that integrating genomic information at different levels (mutation and expression data) leads to better subtyping of breast cancers.