Beyond RECIST: mathematical modeling and Bayesian inference reveal the importance of immune parameters in metastatic breast cancer

Immunotherapies that target the host immune system to mount effective responses hold great promise. Yet, overcoming patient- and organ-specific tumor heterogeneities remains a significant challenge. In order to quantify individual patient responses, we fit a tumor-immune mathematical model to patient and site-specific dynamics during combination therapy (nivolumab + ipilimumab + entinostat) informed by RECIST measurements of the tumor dynamics and immune markers measured by spatial proteomics. Bayesian parameter inference of site-specific patient responses revealed that only the immunosuppression parameters were predictive of response; parameters controlling cytotoxicity were uninformative. Via comparison of a large cohort of fitted tumors, we quantified the variability in tumor-immune dynamics to reveal controllable parameter regimes. We developed methods that employed posterior parameter sampling and simulation to create virtual tumor populations, enabling extrapolation beyond the data to predict probabilities of response in metastatic lesions, even when no data exist at a site. We also showed that scans in the week immediately following treatment are particularly valuable to identify the tumor dynamics. Our modeling and inference framework can thus be used to overcome sample size limitations to create virtual patient cohorts that give new insights into mechanisms of disease progression.