Correlated Mixed Membership Modeling of Somatic Mutations

Recent studies of cancer somatic mutation profiles seek to identify mutations for targeted therapy in personalized medicine. Analysis of profiles, however, is not trivial, as each profile is heterogeneous and there are multiple confounding factors that influence the cause-and-effect relationships between cancer genes such as cancer (sub)type, biological processes, total number of mutations, and non-linear mutation interactions. Moreover, cancer is biologically redundant, i.e., distinct mutations can result in the alteration of similar biological processes, so it is important to identify all possible combinatorial sets of mutations for effective patient treatment. To model this phenomena, we propose the correlated zero-inflated negative binomial process to infer the inherent structure of somatic mutation profiles through latent representations. This stochastic process takes into account different, yet correlated, co-occurring mutations using profile-specific negative binomial dispersion parameters that are mixed with a correlated beta-Bernoulli process and a probability parameter to model profile heterogeneity. These model parameters are inferred by iterative optimization via amortized and stochastic variational inference using the Pan Cancer dataset from The Cancer Genomic Archive (TCGA). By examining the the latent space, we identify biologically relevant correlations between somatic mutations.