Metamats: A mechanistic software for the simulation, inference and prediction of clinical metastasis

The development of metastases is a complex process that can be better understood using mechanistic mathematical models. Our R package "Metamats" proposes a ready-to-use implementation of a semi-mechanistic model describing the time dynamics of the population of metastatic tumors through a small number of parameters ($\alpha$ the gompertz growth rate of the tumors, $\mu$ the instantaneous dissemination rate and $\gamma$ a scale parameter). "Metamats" can be used to simulate individual patients, infer parameters from individual longitudinal data or population time-to-event data, and make predictions. As an example of application, we used the model to describe the dynamics of brain metastases in a population of 103 patients with small-cell lung cancer from the Assistance publique-Hôpitaux de Marseille (AP-HM) hospital. Combining AP-HM patients with 100 patients from the CONVERT study, we used a population approach relying on a non-linear mixed-effect model coupled to our semi-mechanistic model. This population approach allowed us to describe the effects of prophylactic cerebral irradiation in SCLC patients on brain-metastases free survival through a coefficient on the metastatic dissemination parameter ($\mu$).