1. Practical identifiability analysis of a mechanistic model for the time to distant metastatic relapse and its application to renal cell carcinoma
- Author
-
Arturo Álvarez-Arenas, Wilfried Souleyreau, Andrea Emanuelli, Lindsay S. Cooley, Jean-Christophe Bernhard, Andreas Bikfalvi, Sebastien Benzekry, Modélisation Mathématique pour l'Oncologie (MONC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Angiogenèse et Micro-environnement des Cancers (LAMC), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM), service d'urologie [CHU Bordeaux], CHU Bordeaux [Bordeaux], Méthodes computationnelles pour la prise en charge thérapeutique en oncologie : Optimisation des stratégies par modélisation mécaniste et statistique (COMPO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Cancérologie de Marseille (CRCM), Aix Marseille Université (AMU)-Institut Paoli-Calmettes, Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Institut Paoli-Calmettes, Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Fédération nationale des Centres de lutte contre le Cancer (FNCLCC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), and Centre de Recherche en Cancérologie de Marseille (CRCM)
- Subjects
[STAT.AP]Statistics [stat]/Applications [stat.AP] ,Ecology ,[SDV.CAN]Life Sciences [q-bio]/Cancer ,Survival Analysis ,[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation ,Kidney Neoplasms ,Receptors, G-Protein-Coupled ,Cellular and Molecular Neuroscience ,Computational Theory and Mathematics ,Modeling and Simulation ,Genetics ,[SDV.SP.PHARMA]Life Sciences [q-bio]/Pharmaceutical sciences/Pharmacology ,Humans ,[SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie ,Neoplasm Recurrence, Local ,Carcinoma, Renal Cell ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,[PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an] - Abstract
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, α and μ, 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 α and μ, 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 (Führman 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 (μ), but not on growth (α).
- Published
- 2022