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).
Funder
the Inserm PlanCancer
the Region Nouvelle Aquitaine
Publisher
Public Library of Science (PLoS)
Subject
Computational Theory and Mathematics,Cellular and Molecular Neuroscience,Genetics,Molecular Biology,Ecology,Modeling and Simulation,Ecology, Evolution, Behavior and Systematics
Reference41 articles.
1. Modelling Survival Data in Medical Research
2. Nonparametric Estimation from Incomplete Observations;EL Kaplan;Journal of the American Statistical Association,1958
3. Regression Models and Life-Tables;DR Cox;Journal of the Royal Statistical Society Series B (Methodological),1972
4. Random survival forests;H Ishwaran;The Annals of Applied Statistics,2008
5. Regularization Paths for Cox’s Proportional Hazards Model via Coordinate Descent;N Simon;J Stat Softw,2011
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献