Romain Zakrajsek 1, Linh Nguyen Phuong 1, Célestin Bigarré 1, Andrea Vaglio 1, Pascal-Alexandre Thomas 2, Xavier-Benoit D'journo 2, Paul Habert 2, David Taieb 2, Alexis Jacquier 2, David Boulate 1,2, Sébastien Benzekry 1
1 COMPO - CRCM, Inserm UMR1068, CNRS UMR7258 (Marseille, France), 2 Assistance Publique - Hôpitaux de Marseille (Marseille, France)
Objectives
Surgical resection is the standard of care for patients with early-stage non-small lung cancer (NSCLC)1. However, 5 to 10% of patients develops metastatic recurrence1,2. Current management of early-stage patients relies only on surveillance, with no systemic adjuvant treatment. Statistical analysis for identification of relapse risk factors traditionally relies on classical survival analysis.
In this work, we propose a novel approach based on a mechanistic model of primary tumor growth and metastatic dissemination.
Methods
Data were extracted from the Epithor (“EPIdémiologie en chirurgie THORacique”) French national thoracic surgery registry. Among 1913 patients treated at Hôpital Nord (Marseille, France) between 2011 and 2024, 896 stage I NSCLC patients treated with surgery alone were included. Pre-surgical longitudinal tumor size measurements from computed tomography scans were available for 307 patients (mean = 2.22 scans per patients, volume range = 5.3 – 71,271 mm3). Distant metastatic-free survival was defined as the time until a distant metastasis appeared after surgery. Patients experienced either distant recurrence or death, or were right-censored at last follow-up.
The mechanistic model was derived from initial work by Iwata et al.3, further developed by our team4–6. Briefly, the size dynamics of the primary tumor (PT, volume V_p (t), assumed to be proportional to the number of cells) is assumed Gompertzian:
(dV_p)/dt= (α-β ln(V_p ) ) V_p, (1)
with α the initial proliferation rate parameter. The carrying capacity K=e^(α/β) is assumed constant to 1012 cells, allowing determination of β from α. The dissemination rate of the PT is given by:
d(V_p )=μV_p,
where μ is the per day probability for a PT cell to disseminate and establish a distant metastatic colony. Metastases and PT are assumed to grow according to the same growth law. The population of metastases is described by a tumor size density function ρ, such that the integral of ρ(t,V_p) between V_1 and V_2 represents the number of metastases with a size between V_1 and V_2 at time t. Assuming a minimum tumor size for detection at imaging of 5 mm (≃ 65 mm3), the individual time to relapse is given by
〖T^i〗_meta (α^i,μ^i 〖; V_diag〗^i )=”min” {t≥0 ├|∫_0^65▒〖ρ(V,t | α^i,μ^i;〖V_diag〗^i ┤)〗 ┤≥1},
where 〖V_diag〗^i is the PT size at diagnosis, a covariate required to give an initial condition to equation (1). The observation model was given by:
“log” (T^i )=”log” (〖T^i〗_meta (α^i,μ^i ;V_diag^i ))+ε^i,
where ε^i∼N(0,σ^2 ). Model parameters were estimated using nonlinear mixed-effects modeling implemented in saemix, relying on the Stochastic Approximation Expectation–Maximization (SAEM) algorithm. Inter-individual variability was estimated on α and μ assuming log-normal distributions.
Among a total of 231 variables, a selection of pre-, peri- and post-operative features (p = 16), including patient available clinical (e.g., age, sex, or smoking exposure), biological (e.g., PDL1 status, angioinvasion), and functional imaging (e.g., maximum Standardized Uptake Value, SUVmax) features were included in the analysis. These features were explored as covariates on the model parameters using backward selection.
Results
Metastatic cancer recurrence occurred in 9.69% of patients with a mean follow-up of 46.2 months (95% confidence interval: 43.2-49.1).
In a first step, parameters of the model were fitted to the data without covariate. The base model adequately reproduced the population metastasis-free survival curve compared with the Kaplan–Meier estimator. Parameter estimates were obtained with relative standard errors below 15%.
Smoking exposure (pack-years) and SUVmax were significant covariates for the tumor growth parameter α, while smoking exposure was also significant on the dissemination parameter μ. Inclusion of these covariates improved individual predictions of time to relapse, although population-level fit was not substantially modified.
Conclusion
The model could adequately describe metastasis-free real-world stage I NSCLC data survival data with a mechanistic basis, an approach fundamentally different to biologically-agnostic standard survival models. This allowed the discovery of causal relationships between imaging and exposure biomarkers and aggregated parameters of biological processes. This framework provides a quantitative basis for personalized post-surgical surveillance and therapeutic decision-making, by individualized simulations of therapeutic scenarii in clinical digital twins.
References:
1. Zer, A. et al. Early and locally advanced non-small-cell lung cancer: ESMO Clinical Practice Guideline for diagnosis, treatment and follow-up. Ann. Oncol. S0923753425009238 (2025) doi:10.1016/j.annonc.2025.08.003.
2. Thomas, P. & Rubinstein, L. Cancer recurrence after resection: T1 N0 non-small cell lung cancer. Ann. Thorac. Surg. 49, 242–247 (1990).
3. Iwata, K., Kawasaki, K. & Shigesada, N. A Dynamical Model for the Growth and Size Distribution of Multiple Metastatic Tumors. J. Theor. Biol. 203, 177–186 (2000).
4. Benzekry, S. et al. Modeling Spontaneous Metastasis following Surgery: An In Vivo-In Silico Approach. Cancer Res. 76, 535–547 (2016).
5. Nicolò, C. et al. Machine Learning and Mechanistic Modeling for Prediction of Metastatic Relapse in Early-Stage Breast Cancer. JCO Clin. Cancer Inform. 4, 259–274 (2020).
6. Bigarré, C. et al. Mechanistic modeling of metastatic relapse in early breast cancer to investigate the biological impact of prognostic biomarkers. Comput. Methods Programs Biomed. 231, 107401 (2023).
Reference: PAGE 34 (2026) Abstr 12056 [www.page-meeting.org/?abstract=12056]
Poster: Drug/Disease Modelling - Oncology