Poisson process factorization for mutational signature analysis with genomic covariates

Mutational signatures are powerful summaries of the mutational processes altering the DNA of cancer cells and are increasingly relevant as biomarkers in personalized treatments. The widespread approach to mutational signature analysis consists of decomposing the matrix of mutation counts from a sample of patients via non-negative matrix factorization (NMF) algorithms. However, by working with aggregate counts, this procedure ignores the non-homogeneous patterns of occurrence of somatic mutations along the genome, as well as the tissue-specific characteristics that notoriously influence their rate of appearance. This gap is primarily due to a lack of adequate methodologies to leverage locus-specific covariates directly in the factorization. In this paper, we address these limitations by introducing a model based on Poisson point processes to infer mutational signatures and their activities as they vary across genomic regions. Using covariate-dependent factorized intensity functions, our Poisson process factorization (PPF) generalizes the baseline NMF model to include regression coefficients that capture the effect of commonly known genomic features on the mutation rates from each latent process. Furthermore, our method relies on sparsity-inducing hierarchical priors to automatically infer the number of active latent factors in the data, avoiding the need to fit multiple models for a range of plausible ranks. We present algorithms to obtain maximum a posteriori estimates and uncertainty quantification via Markov chain Monte Carlo. We test the method on simulated data and on real data from breast cancer, using covariates on alterations in chromosomal copies, histone modifications, cell replication timing, nucleosome positioning, and DNA methylation. Our results shed light on the joint effect that epigenetic marks have on the latent processes at high resolution.