Mechanistic joint modelling for longitudinal PSA and survival data in advanced metastatic prostate cancer
Solène Desmée (1), Jérémie Guedj (2), Christine Veyrat-Follet (3) and Emmanuelle Comets (1,2)
(1) INSERM CIC 1414, Université Rennes 1, Rennes, France, (2) INSERM UMR1137 IAME, Paris, France; University Denis Diderot, Paris, France, (3) Translational Informatics, Translational Medicine, Sanofi, Bridgewater, USA
Objectives: In phase III clinical trials, treatments for metastatic Castration-Resistant Prostate Cancer (mCRPC) are evaluated on their impact on time-to-death. Prostate-specific antigen (PSA) is frequently monitored as it is assumed to be linked to survival. Using nonlinear joint modelling which consists in the simultaneous analysis of biomarker's evolution and survival [1,2], we aim here to characterize the relationship between PSA kinetics and risk-of-death and identify the impact of covariates on both processes, in mCRPC patients from the phase III study Proselica [3] who were previously non-responders to docetaxel and treated as second-line chemotherapy by Cabazitaxel.
Methods: 9443 PSA measurements from 1174 patients were used. 580 received Cabazitaxel at dose 20 mg/m² and 594 at dose 25 mg/m². The model developed in [4] relying on 3 mechanistic differential equations describing the PSA production by treatment-sensitive (S) and –resistant tumor cells was adapted to the main mechanism of action of Cabazitaxel, the stimulation of the S cells elimination. For joint modelling several links between PSA kinetics and risk-of-death were compared by BIC. After exploration of the impact of covariates on the individual Empirical Bayes Estimates (EBEs) and on Weibull survival model, stepwise elimination from the full joint model was carried out. Estimations were conducted using the SAEM algorithm [5] of Monolix2016R1. Model evaluation was based on individual weighted residuals (IWRES) and on Cox-Snell and Martingale residuals.
Results: The joint model involving current PSA provided the smallest BIC. The treatment increased the stimulation of the S cells elimination with a factor 1.6 and 1.9 for the doses 20 and 25 respectively, in absence of other covariates. Several covariates showed a significant effect on PSA and/or survival. In particular, the presence of liver metastases impacted both PSA kinetics and risk-of-death. Although the decrease of PSA was more pronounced in the 25mg/m² group compared to the 20mg/m² group, the difference appeared too small to significantly impact survival.
Conclusions: This mechanistic joint model developed in advanced prostate cancer allowed to study treatment response in subgroups of patients and identify covariates associated with survival. It could be used in personalized medicine to predict patient’s risk-of-death from baseline covariates and longitudinal measurements.
References:
[1] Tsiatis AA, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Stat Sin. 2004;14:809–834.
[2] Desmée S, Mentré F, Veyrat-Follet C, Guedj J. 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. AAPS J. 2015;17:691–9. doi:10.1208/s12248-015-9745-5.
[3] Proselica study funded by Sanofi (NCT01308580) https://clinicaltrials.gov/ct2/show/NCT01308580?term=proselica&rank=1
[4] Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J. Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients. Biometrics. 2016. doi:10.1111/biom.12537.
[5] Kuhn E, Lavielle M. Maximum likelihood estimation in nonlinear mixed effects models. Comput Stat Data Anal. 2005;49:1020–38. doi:10.1016/j.csda.2004.07.002.
