Practical identifiability analysis of a mechanistic model for the time to distant metastatic relapse and its application to renal cell carcinoma

Distant metastasis-free survival (DMFS) curves are widely used in oncology. They are classically analyzed using the Kaplan-Meier estimator or agnostic statistical models from survival analysis. Here we report on a method to extract more information from DMFS curves using a mathematical model of primary tumor growth and metastatic dissemination. The model depends on two parameters, alpha and mu, respectively quantifying tumor growth and dissemination. We assumed these to be lognormally distributed in a patient population. We propose a method for identification of the parameters of these distributions based on least-squares minimization between the data and the simulated survival curve. We studied the practical identifiability of these parameters and found that including the percentage of patients with metastasis at diagnosis was critical to ensure robust estimation. We also studied the impact and identifiability of covariates and their coefficients in alpha and mu, either categorical or continuous, including various functional forms for the latter (threshold, linear or a combination of both). We found that both the functional form and the coefficients could be determined from DMFS curves. We then applied our model to a clinical dataset of metastatic relapse from kidney cancer with individual data of 105 patients. We show that the model was able to describe the data and illustrate our method to disentangle the impact of three covariates on DMFS: a categorical one (Fuhrman grade) and two continuous ones (gene expressions of the macrophage mannose receptor 1 (MMR) and the G Protein-Coupled Receptor Class C Group 5 Member A (GPRC5a)gene). We found that all had an influence in metastasis dissemination (mu), but not on growth (alpha).

Automated summary

This article presents a method to extract more information from distant metastasis-free survival (DMFS) curves using a mathematical model. The model depends on parameters that quantify tumor growth and metastatic dissemination, and the parameters are determined using least-squares minimization. The study found that including the percentage of patients with metastasis at diagnosis was critical to the robust estimation of the parameters. The impact and identifiability of covariates and their coefficients in the model were also studied.