Flexible model-based non-negative matrix factorization with application to mutational signatures.

Somatic mutations in cancer can be viewed as a mixture distribution of several mutational signatures, which can be inferred using non-negative matrix factorization (NMF). Mutational signatures have previously been parametrized using either simple mono-nucleotide interaction models or general tri-nucleotide interaction models. We describe a flexible and novel framework for identifying biologically plausible parametrizations of mutational signatures, and in particular for estimating di-nucleotide interaction models. Our novel estimation procedure is based on the expectation-maximization (EM) algorithm and regression in the log-linear quasi-Poisson model. We show that di-nucleotide interaction signatures are statistically stable and sufficiently complex to fit the mutational patterns. Di-nucleotide interaction signatures often strike the right balance between appropriately fitting the data and avoiding over-fitting. They provide a better fit to data and are biologically more plausible than mono-nucleotide interaction signatures, and the parametrization is more stable than the parameter-rich tri-nucleotide interaction signatures. We illustrate our framework in a large simulation study where we compare to state of the art methods, and show results for three data sets of somatic mutation counts from patients with cancer in the breast, Liver and urinary tract.

Model selection and robust inference of mutational signatures using Negative Binomial non-negative matrix factorization.

BACKGROUND: The spectrum of mutations in a collection of cancer genomes can be described by a mixture of a few mutational signatures. The mutational signatures can be found using non-negative matrix factorization (NMF). To extract the mutational signatures we have to assume a distribution for the observed mutational counts and a number of mutational signatures. In most applications, the mutational counts are assumed to be Poisson distributed, and the rank is chosen by comparing the fit of several models with the same underlying distribution and different values for the rank using classical model selection procedures. However, the counts are often overdispersed, and thus the Negative Binomial distribution is more appropriate. RESULTS: We propose a Negative Binomial NMF with a patient specific dispersion parameter to capture the variation across patients and derive the corresponding update rules for parameter estimation. We also introduce a novel model selection procedure inspired by cross-validation to determine the number of signatures. Using simulations, we study the influence of the distributional assumption on our method together with other classical model selection procedures. We also present a simulation study with a method comparison where we show that state-of-the-art methods are highly overestimating the number of signatures when overdispersion is present. We apply our proposed analysis on a wide range of simulated data and on two real data sets from breast and prostate cancer patients. On the real data we describe a residual analysis to investigate and validate the model choice. CONCLUSIONS: With our results on simulated and real data we show that our model selection procedure is more robust at determining the correct number of signatures under model misspecification. We also show that our model selection procedure is more accurate than the available methods in the literature for finding the true number of signatures. Lastly, the residual analysis clearly emphasizes the overdispersion in the mutational count data. The code for our model selection procedure and Negative Binomial NMF is available in the R package SigMoS and can be found at https://github.com/MartaPelizzola/SigMoS .