A mathematical model of the metastatic bottleneck predicts patient outcome and response to cancer treatment
Fig 3
a,b Fit and validation of our model on the SEER data, exemplary for three cancers, for which we obtained the best, intermediate, and worse fit, respectively, and for which validation data was available (see S2 Fig for remaining ten cancers). Black points represent data records, blue lines show fitted, and red lines predicted curves. a Metastasis detection probability (left panel) is compared to cancer death probability (right). For cancer death probability, up and down-oriented triangles present the upper and lower estimates of that variable from the data, respectively, while the black dots represent a Kaplan-Meier (KM) derived estimate (S1 Text). The predictions stay within the range of the estimators. b The median time to death data for all patients, (left panel) was used for model fitting and is tumor-size dependent. For a validation cohort of patients with metastases detected at diagnosis, the model correctly predicts a much shorter median time to death and that this time is almost constant across tumor diameters (right). c Independent validation on survival data for two pancreatic cancer cohorts: Autopsy and Adjuvant, analyzed by Haeno et al. [30] (black, with gray confidence bands). We predict their survival function using our pancreas cancer model, fit solely to SEER data, and accessing only information about tumor diameters of patients in the cohorts. For both cohorts, our predictions (red) are as close to the data as predictions obtained from the the Haeno et al. model (orange).