Bayesian Multi-Study Non-Negative Matrix Factorization for Mutational Signatures

Mutational signatures shed insight into the range of mutational processes giving rise to tumors and allow a better understanding of cancer origin. They are typically identified from high-throughput sequencing data of cancer genomes using non-negative matrix factorization (NMF), and many such techniques have been developed towards this aim. However, it is often of particular interest to compare mutational signatures across multiple conditions, e.g. to understand which signatures are present across different treatments, or to identify signatures that are shared or specific across cancer types. Existing techniques within the NMF context only allow decomposition within a single dataset, so that integrating results across multiple conditions requires running separate analyses on each dataset, followed by subjective and manual comparisons of the identified signatures. To address this issue, we propose a Bayesian multi-study NMF method that jointly decomposes multiple studies or conditions to identify signatures that are common, specific, or partially shared by any subset. We propose two models: a "discovery-only" model that estimates de novo signatures in a completely unsupervised manner, and a "recovery-discovery" model that builds informative priors from previously known signatures to both update the estimates of these signatures and identify any novel signatures. We then further extend these models to estimate the effects of sample-level covariates on the exposures to each signature, enforcing sparsity through a non-local spike-and-slab prior. We demonstrate our approach on a range of simulations, and apply our method to colorectal cancer samples to show its utility. ### Competing Interest Statement The authors have declared no competing interest.