M. Prague(1) and G. Sotton(1) and V. Rondeau (2)
(1) Inria Bordeaux, Inserm U1219 Bordeaux Public Health, SISTM Team, Bordeaux France (2) Inserm U1219 Bordeaux Public Health, Biostatistic Team, Bordeaux France
Background: Evaluation of cancer treatments is based on the evaluation of the physiological response of tumors of patients included in a trial. The assessment is often based on the anatomical tumor change in size. However, it is often difficult to account for the longitudinal trajectory. Other outcome of interest are the time to death and the time to relapse, a progression being either an increase of target lesions, the appearance of new lesions or a non-equivocal progression according to non-target lesions. These outcomes are naturally analyzed using survival and joint survival models with frailty terms to account for inter-individual variabilities [1]. Sometimes, in a two-step approach, predicted tumor size is included as a covariate in survival models [2]. In this work, we want to propose a new implementation for a trivariate joint frailty model to capture the tumors nonlinear growth and to model it simultaneously with recurrent progresions and overall survival.
Methods: Mathematical mechanistic modeling of tumor growth has become an important tool in evaluating anticancer treatments in population analyses. In particular, Ordinary Differential Equations (ODE) provide a wide range of potential descriptions of changes in tumor size, see Ribba et al. 2017 for a review. Krol et al. (2017) [3] proposed a multivariate non-linear mechanistic joint frailty model for longitudinal data, recurrent events, and a terminal event. In this work, the tumor growth is modeled by the analytic solution of an ODE model, which resumes to a mixed effect model. It has been implemented in the R package frailtypack [4]. An intuitive extension of this is to use a more complex ODE model for the tumor growth that does not have an analytic solution and thus rely on an ODE equation solver. Here, we evaluate the capability of a new feature of the Stochastic Approximation Expectation-Maximization algorithm in Monolix [6] to estimate the parameters of a joint frailty model, where tumor kinetics is defined by a mechanistic ODE mixed-effect model.
Results: We focus on an application to colorectal cancer. We simulate data such that they mimic the data collected on the GERCOR study, which is a two arm phase III clinical trial of 220 patients with metastatic colorectal cancer. We perform a simulation study to validate the method. Using the same exact setting as in Krol et al. (2017), with an ODE description of the tumor growth that has an analytic solution, we compare the results of our implementation in Monolix with those obtained with frailtypack. We demonstrate that there is no inconsistency and both software give similar results. Of note, Monolix implementation is faster in term of computation time. In both cases, all parameter are estimated without bias with satisfactory confidence intervals, the most difficult parameter to estimate being the shared frailty variances.
Conclusion: We propose an implementation in Monolix of a multivariate mechanistic joint frailty model for the analysis of a nonlinear longitudinal biomarker (possibly left censored), recurrent events, and a terminal event. The propose program improves existing tools since the application of an ODE on the biomarker dynamics provides a better understanding of the underlying biological process. Indeed, the ODE model can be as complex as needed providing that parameters of the model are identifiability, which is still a requirement for inference.
Keywords: cancer, joint modeling, longitudinal data, monolix, ordinary differential equation, survival analysis, tumor size
References:
[1] A. Krol, A. Mauguen, Y. Mazroui, A. Laurent, S. Michiels, and V. Rondeau. Tutorial in joint modeling and prediction : A statistical software for correlated longitudinal out-comes, recurrent events and a terminal event.Journal of Statistical Software, 81(3),2017.
[2] Desmée, S., Mentré, F., Veyrat-Follet, C., & Guedj, J. (2015). Nonlinear mixed-effect models for prostate-specific antigen kinetics and link with survival in the context of metastatic prostate cancer: a comparison by simulation of two-stage and joint approaches. The AAPS journal, 17(3), 691-699.
[3] Ribba, B., Holford, N. H., Magni, P., Trocóniz, I., Gueorguieva, I., Girard, P., … & Friberg, L. E. (2014). A review of mixed‐effects models of tumor growth and effects of anticancer drug treatment used in population analysis. CPT: pharmacometrics & systems pharmacology, 3(5), 1-10.
[4] Król, A., Tournigand, C., Michiels, S., & Rondeau, V. (2018). Multivariate joint frailty model for the analysis of nonlinear tumor kinetics and dynamic predictions of death. Statistics in medicine, 37(13), 2148-2161.
[5] Rondeau, V., Mazroui, Y., & Gonzalez, J. R. (2012). frailtypack: an R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametrical estimation. J Stat Softw, 47(4), 1-28.
[6] Monolix version 2019R2. http://lixoft.com/products/monolix/ Antony, France: Lixoft SAS, 2018.
Reference: PAGE () Abstr 9309 [www.page-meeting.org/?abstract=9309]
Poster: Oral: Methodology - New Tools