François Riglet (1), France Mentre (1), Julie Bertrand (1)
(1) INSERM, IAME, UMR 1137, and University Paris Diderot, F-75018, Paris, France
Objectives: Joint models of drug or biomarker kinetics and occurrence of event are increasingly used in drug development using nonlinear mixed effect model (NLMEM)[1]. Given a joint model, Bayesian individual prediction of biomarkers and probability of event can be performed for new patients at different landmark times i.e. different time of collection of the individual data[2,3]. Several software tools allow to perform these Bayesian individual dynamic predictions and to compute associated uncertainty. It has already been shown that Stan software is able to well predict the evolution of biomarkers and survival over time in a joint model[4]. This software uses MCMC-Hamiltonian Monte Carlo (HMC), a bayesian algorithm to obtain individual a posteriori distribution of parameters. Lately, this ability to generate individual predictions was incorporated in other software more often used in nonlinear mixed effect modelling such as Monolix2018R2 version, or NONMEM7.4 using MCMC-Metropolis Hasting (MH) algorithm[5]. MH allow to obtain individual dynamic predictions by drawing biomarker kinetic parameters from their conditional distribution of each subject, computed from the model population parameters and individual data available, and then extrapolated the individual survival probability.
The aim of the present study was to compare the abilities of three software used in nonlinear mixed effects modelling (Stan, Monolix, NONMEM) to perform Bayesian individual dynamic predictions, with uncertainty, of biomarker kinetics and risk of death using simulated data.
Methods: Simulations of biomarker and survival data were performed using a mechanistic joint model of prostate specific antigen (PSA) kinetics and risk of death in metastatic prostate cancer[3]. PSA was measured every 3 weeks for 2 years. The survival model was a Weibull proportional hazard model with association between the current PSA kinetics and survival. Two values for the strength of this association (β) were evaluated: low link (β=0.05) and high link (β=0.02). In addition, another simulation scenario of short survival, with a smaller Weibull scale parameter λ, was also evaluated. No other mechanism than death or the administrative end of the study (Tend = 2 years) were considered for dropout. For each scenario, one sample of N=200 ‘new’ patients using R software were simulated. Several landmark times s={0, 6, 12 and 18} months were studied. For each individual of each scenario, using individual data until each time s, a posteriori distribution of PSA kinetic individual parameters was estimated with each software. True population parameters were used as fixed effects in Monolix2018R2 and NONMEM7.4 and as prior in Stan. L=200 samples of individual parameters were drawn from the posterior distribution and, for each sample, biomarker and risk of death predictions were computed, given the survival model, for a horizon time th = Tend – (s+2) months. Median, 2.5% and 97.5% percentiles (to derive 95% prediction interval) were derived for each parameter, predicted biomarker and risk of death at each horizon time.
Relative estimation errors were used to assess bias and imprecision (RMSE) of individual parameter estimates. Similarly, bias and imprecision were also evaluated on individual PSA kinetic predictions at each horizon time. Moreover, coverages of 95% prediction interval of PSA and risk of death were also evaluated.
Results: We obtained similar results with each software tool. At each landmark, estimations of individual parameters had small biases regardless of the software. Imprecision on individual parameters was rather high but were similar with all software and showed marked improvements with increasing landmark time. In terms of coverage, results were roughly comparable with each software and these software were able to well predict individual PSA kinetics and survival during the follow-up. In term of computing time, Stan using HMC algorithm was faster than MH software in Monolix and NONMEM to obtain individual parameters, for every scenario and at every landmark time.
Conclusions: These findings suggest that Stan, Monolix2018R2, and NONMEM7.4 are able to characterize individual dynamic predictions of biomarkers and risk of event in joint modelling framework with correct uncertainty and hence could be useful in the context of individualized medicine.
*Francois Riglet is supported by a grant from Sanofi for his PhD.
References:
[1] Sudell M, Kolamunnage-Dona R, Tudur-Smith C. Joint models for longitudinal and time-to-event data: a review of reporting quality with a view to meta-analysis. BMC Med Res Methodol. 2016 ;16(1):168.
[2] Rizopoulos D. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics. 2011;67:819–29.
[3] 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.
[4] Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J. Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer. BMC Med Res Methodol. 2017;17:105.
[5] Lavielle M, Ribba B. Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions. Pharm Res. 2016;33:2979–88.
Reference: PAGE 28 (2019) Abstr 9111 [www.page-meeting.org/?abstract=9111]
Poster: Methodology - New Modelling Approaches