2019 - Stockholm - Sweden

PAGE 2019: Drug/Disease modelling
Coralie Tardivon

Association between tumor size kinetics and survival in advanced urothelial carcinoma patients treated with atezolizumab: implication for patient’s follow-up

Coralie Tardivon (1), Solène Desmée (2), Marion Kerioui (1,2), René Bruno (4), Benjamin Wu (5), France Mentré (1), François Mercier (3), Jérémie Guedj(1)

(1) IAME, UMR 1137, INSERM, Université Paris Diderot, Sorbonne Paris Cité Paris, France; (2) Université de Tours, Université de Nantes, Inserm SPHERE, UMR 1246, Tours, France; (3) Clinical Pharmacology, Roche Innovation Center Basel, Switzerland; (4) Clinical Pharmacology, Roche/Genetech, Marseille France; (5) Clinical Pharmacology, Genentech Inc., South San Francisco, CA, USA


Immune-oncology is revolutionizing cancer treatment, but the association between treatment response and survival remains poorly understood. The response kinetics, as guided by the longitudinal evolution of a biomarker (e.g. the tumor size), can help detect treatment relapse and identify patients most-at-risk of death or progression. In order to model these two responses, specific approaches, called “joint modelling”, are needed that acknowledge the correlation between response to treatment and survival [1]. In these joint models, the hazard rate is modeled by a parametric survival model that directly depends on the biomarker kinetics. Further, the biomarker kinetics, which may be a nonlinear process, is modeled using a nonlinear mixed-effects model [2]. Parameters estimation in nonlinear joint models are complex, as the likelihood does not have an analytical form. It requires specific algorithms such as the Stochastic Approximation Expectation Maximization algorithm [3,4]. Joint modeling of tumor size dynamics and overall survival has so far not been used to improve early detection of patients most-at-risk of death or progression that could benefit from alternative therapies.


To quantitatively evaluate the association between tumor size kinetics, baseline covariates and overall survival in metastatic urothelial carcinoma patients following atezolizumab immunotherapy treatment, using a nonlinear joint model.

To use this model to characterize “in real time” new patient’s profile of response, thus assessing its predictive ability for the early detection of patients at risk of death.


A phase 2 clinical trial of 309 advanced urothelial carcinoma patients treated with atezolizumab (IMvigor 210) [5] was used to build a joint model for tumor size kinetics and survival. Then the model was validated externally using a phase 3 clinical trial data from 457 patients in the same indication (IMvigor 211) [6]. Model predictions were assessed using time-dependent Area Under the ROC Curve (AUC) and Brier score to evaluate discrimination and calibration, using different follow-up times (called ”landmark”) and time of prediction (called ”horizon”) [7].


The best description of tumor size kinetics was obtained using a biphasic exponential model accounting for differential kinetics in tumor-sensitive and tumor-resistant cells, while overall survival was described using a parametric Weibull model. Using these models, we identified time-to-tumor growth and instantaneous changes in tumor size as the best on-treatment predictors of survival, showing that tumor size kinetics is an independent predictor of survival. As expected, model parameters were highly dependent on patient’s disease severity, in particular presence of liver metastasis, hemoglobin and alkaline phosphatase levels, ECOG performance status, or neutrophil-to-lymphocyte ratio.

Using the joint model for prediction on an external validation dataset, we found that the model reproduced the overall survival (OS) observed. Further, using various landmarks and horizons, we found AUC values comprised between 0.73 and 0.84, i.e. significantly higher than the ones obtained with an approach where OS is modeled ignoring tumor dynamic (“No link”: between 0.55 and 0.76). The Brier scores, summarizing the predictive performance of the joint model, showed more than 15% improvement with the best joint model compared to the model with no link between tumor kinetics and OS, for horizon times greater than 6 months.


We showed that including on-treatment tumor dynamic data in a relevant statistical framework improves the prediction of survival probability during immunotherapy treatment. In addition, the proposed model could be used to identify patients most-at-risk of death, in real time, hence giving the opportunity to optimize patients’ medical treatment.

[1] D. Rizopoulos, Joint models for longitudinal and time-to-event data: With applications in R, 2012.
[2] M. Lavielle, Mixed effects models for the population approach: models, tasks, methods and tools, 2014.
[3] E. Kuhn and M. Lavielle, Maximum likelihood estimation in nonlinear mixed effects models, 2005.
[4] C. Mbogning et al., Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm, J Stat Comput Simul., 2015.
[5] E. Rosenberg et al., Atezolizumab in patients with locally advanced and metastatic urothelial carcinoma who have progressed following treatment with platinum-based chemotherapy: a single-arm, multicentre, phase 2 trial, The Lancet, 2016.
[6] T. Powles et al., Atezolizumab versus chemotherapy in patients with platinum-treated locally advanced or metastatic urothelial carcinoma (IMvigor211): a multicentre, open-label, phase 3 randomised controlled trial, The Lancet, 2018.
[7] P. Blanche et al., Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks, Biometrics, 2015.

Reference: PAGE 28 (2019) Abstr 8824 [www.page-meeting.org/?abstract=8824]
Oral: Drug/Disease modelling
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