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Recent advances in biological research have seen the emergence ofhigh-throughput technologies with numerous applications that allow the study ofbiological mechanisms at an unprecedented depth and scale. A large amount ofgenomic data is now distributed through consortia like The Cancer Genome Atlas(TCGA), where specific types of biological information on specific type oftissue or cell are available. In cancer research, the challenge is now toperform integrative analyses of high-dimensional multi-omic data with the goalto better understand genomic processes that correlate with cancer outcomes,e.g. elucidate gene networks that discriminate a specific cancer subgroups(cancer sub-typing) or discovering gene networks that overlap across differentcancer types (pan-cancer studies). In this paper, we propose a novel mixedgraphical model approach to analyze multi-omic data of different types(continuous, discrete and count) and perform model selection by extending theBirth-Death MCMC (BDMCMC) algorithm initially proposed by\citet{stephens2000bayesian} and later developed by\cite{mohammadi2015bayesian}. We compare the performance of our method to theLASSO method and the standard BDMCMC method using simulations and find that ourmethod is superior in terms of both computational efficiency and the accuracyof the model selection results. Finally, an application to the TCGA breastcancer data shows that integrating genomic information at different levels(mutation and expression data) leads to better subtyping of breast cancers.

The scalable Birth-Death MCMC Algorithm for Mixed Graphical Model Learning with Application to Genomic Data Integration