Cancer genomes accumulate a large number of somatic mutations resulting from a combination of stochastic errors in DNA processing, cancer-related aberrations of the DNA repair machinery, or carcinogenic exposures; each mutagenic process leaves a characteristic mutational signature. A key challenge is understanding the interactions between signatures, particularly as DNA repair deficiencies often modify the effects of other mutagens. Here, we introduce RepairSig, a computational method that explicitly models additive primary mutagenic processes; non-additive secondary processes, which interact with the primary processes; and a mutation opportunity, that is, the distribution of sites across the genome that are vulnerable to damage or preferentially repaired. We demonstrate that RepairSig accurately recapitulates experimentally identified signatures, identifies autonomous signatures of deficient DNA repair processes, and explains mismatch repair deficiency in breast cancer by de novo inference of both primary and secondary signatures from patient data. RepairSig is freely available for download at https://github.com/ncbi/RepairSig.
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