Joint modelling of individual target lesions and survival to characterize the variability in the response to immunotherapy versus chemotherapy in advanced bladder cancer
Marion Kerioui (1,2,3,4), Julie Bertrand (1), François Mercier (5), Solène Desmée (2), René Bruno (6), Jérémie Guedj (1)
(1) Université de Paris INSERM IAME, F-75018 Paris France (2) Université de Tours, Université de Nantes, INSERM SPHERE, UMR 1246, Tours, France (3) Institut Roche, Boulogne-Billancourt, France (4) Clinical Pharmacolgy, Genentech/Roche, Paris, France (5) F. Hoffmann-La Roche AG, Biostatistics, Basel, Switzerland (6) Clinical Pharmacology, Genentech Inc., Marseille, France
Context: In oncology, a common marker of tumor burden is the Sum of Longest Diameters (SLD) of target lesions, and is part of the RECIST criteria, which evaluate the response and the progression in clinical trials . However, using a composite marker such as the SLD has several limitations, as it neglects the heterogeneity in lesion dynamics, which might be partly explained by their location. This might be even more damaging under immunotherapy treatments, as they might increase the proportion of dissociated responses across lesions , which could directly impact the survival . However, there is a lack of modelling tool to properly characterize the variability in the response to immunotherapy treatments in comparison with chemotherapy. To precisely characterize the association between the tumor size dynamics and the survival, one can simultaneously fit both longitudinal and time-to-event data using a nonlinear joint model . This approach might help to better understand the underlying mechanism of treatment , and to avoid the bias of early end of follow-up in the most severe patients . However, these models are generally limited to the description of the SLD dynamics , and incorporating all the source of variability into one model requires specific developments .
Objectives: We aim to develop a nonlinear joint model of individual target lesion dynamics and survival to compare the variability in the response to immunotherapy versus chemotherapy.
Methods: To address this problematic, we relied on a rich dataset from a phase 3 clinical trial IMvigor211  of 900 advanced bladder cancer patients, randomized between an atezolizumab (457 patients) and a chemotherapy control arm (443 patients). Each patient had up to 5 target lesions followed over time, resulting in a total of 2133 target lesions and 6697 measurements.
To account for the hierarchical structure of the data, we added an extra lesion random-effect level and a location fixed-effect on each biological parameter of the structural sTGI model  for the four main locations, namely the lymph, the lung, the liver and the bladder. We assumed a Weibull baseline hazard function and baseline covariates were included on the instantaneous risk of death based on results from a previous work . The link function between the longitudinal and the survival processes assumed an interaction between the lesion dynamics and its location. Inference was lead in a Bayesian framework, using the Hamiltonian Monte-Carlo (HMC) algorithm implemented in Stan software. The parameters of the joint model were estimated in both treatment arm separately. Based on the model predictions, we investigated the proportion of dissociated responses within patients, defined as at least one lesion with a progression, defined as a 20% increase from the minimum size of the lesion over time, and at least one lesion without any progression.
Results: The parameters capturing the natural tumor growth behavior, namely the baseline tumor size and the tumor growth rate, were similar between the two treatment arms. Conversely, the shrinkage rate of the tumor induced by the treatment was faster during chemotherapy, although the rate of the treatment resistance appearance was faster in this treatment arm as compared to atezolizumab and regardless of tumor location. Interestingly, both inter-patient and inter-lesion variability were larger during atezolizumab as compared to chemotherapy on those two parameters, suggesting a larger variability in the effect of this treatment. In both treatment arms, lesions located in the liver or the bladder had twice as much impact on the instantaneous risk of death as compared to those located in the lymph or the lung. Based on the model, we predicted that the proportion of dissociated responses was about 15% in the overall population at 3 months after treatment initiation, and up to 25% at 9 months.
Conclusions: We showed the interest of a multilevel joint model to quantify the variability in the response to cancer treatments. In the future, this approach could be used to follow individual lesion kinetics and better predict their impact on survival at both individual and population levels.
 E.A. Eisenhauer et al, New response evaluation criteria in solid tu-
mours: Revised RECIST guideline (version 1.1). European Journal of Cancer, 45 (2):228–247, January 2009. ISSN 09598049. doi:10.1016/j.ejca.2008.10.026.
 E. Borcoman et al, Novel patterns of response under immunotherapy, Annals of Oncology: Official Journal of the European Society for Medical Oncology, 30(3):385–396, 2019. ISSN 1569-8041. doi: 10.1093/annonc/mdz003.
 T. Tozuka et al, Dissociated responses at initial computed tomography evaluation is a good prognostic factor in non-small cell lung cancer patients treated with anti-programmed cell death-1/ligand 1 inhibitors. BMC Cancer, 20(1):207, December 2020. ISSN 1471-2407. doi: 10.1186/s12885-020-6704-z.
 D. Rizopoulos, Joint models for longitudinal and time-to-event data: with applications in R. Number 6 in Chapman & Hall/CRC biostatistics series. CRC Press, Boca Raton, 2012. ISBN 978-1-4398-7286-4.
 S. Desmée et al, Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients: Joint Model for Nonlinear Kinetics and Survival Data. Biometrics, 73(1):305–312, March 2017. ISSN 0006341X. doi:10.1111/biom.12537
 S. Desmée et al, 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, May 2015. ISSN 1550-7416. doi: 10.1208/s12248-015-9745-5.
 C. Tardivon et al, Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow-Up. Clinical Pharmacology and Therapeutics, 106(4):810–820, 2019. ISSN 1532-6535. doi: 10.1002/cpt.1450
 M Kerioui et al, Bayesian modelling of individual lesions dynamics and survival to characterize response to immunotherapy cancer treatments. In PAGE 29 (2021) Abstr 9628, 2021. URL www.page-meeting.org/?abstract=9628
 T. Powles et al, Atezolizumab versus chemother-
apy in patients with platinum-treated locally advanced or metastatic urothelial carcinoma (IMvigor211): a multicentre, open-label, phase 3 randomised controlled trial. The Lancet, 391 (10122):748–757, February 2018. ISSN 01406736. doi: 10.1016/S0140-6736(17)33297-X.
 L. Claret et al, Evaluation of Tumor-Size Response Metrics to Predict Overall Survival in Western and Chinese Patients With First-Line Metastatic Colorectal Cancer. Journal of Clinical Oncology, 31(17):2110–2114, June 2013. ISSN 0732-183X, 1527-7755. doi:10.1200/JCO.2012.45.0973.
 M Kerioui et al, Assessing the impact of organ-specific lesion dynamics on survival in patients with recurrent urothelial carcinoma treated with atezolizumab or chemotherapy. ESMO Open, 7(1):100346, February 2022. ISSN 20597029. doi:10.1016/j.esmoop.2021.100346.