Motivation: Cancer progresses by accumulating genomic events, such as mutations and copy number alterations, whose chronological order is key to understanding the disease but difficult to observe. Instead, cancer progression models use co-occurence patterns in cross-sectional data to infer epistatic interactions between events and thereby uncover their most likely order of occurence. State-of-the-art progression models, however, are limited by mathematical tractability and only allow events to interact in directed acyclic graphs, to promote but not inhibit subsequent events, or to be mutually exclusive in distinct groups that cannot overlap.

Results: Here we propose Mutual Hazard Networks (MHN), a new Machine Learning algorithm to infer cyclic progression models from cross-sectional data. MHN model events by their spontaneous rate of fixation and by multiplicative effects they exert on the rates of successive events. MHN compared favourably to acyclic models in cross-validated model fit on four datasets tested. In application to the glioblastoma dataset from The Cancer Genome Atlas, MHN proposed a novel interaction in line with consecutive biopsies: IDH1 mutations are early events that promote subsequent fixation of TP53 mutations.
Availability Implementation and data are available at https://github.com/RudiSchill/MHN.