Bayesian individual dynamic predictions via a convenient R function using MonolixSuite
Pauline Traynard , Géraldine Cellière, Jonathan Chauvin
Simulations Plus, Lixoft division, Antony, France
Objectives: Given an NLME population model, Bayesian individual dynamic prediction can be performed for new patients to predict the future evolution of PK concentrations, biomarkers or outcomes. This is for instance useful to predict the tumor burden evolution and risk of death to support clinical decisions in the framework of personalized medicine [1]. Another example is in therapeutic drug monitoring (TDM) to predict the trough concentration and make individual dose adjustment decisions when the concentration was not measured at trough [2]. While these approaches have already been applied in the past, they require quite extensive coding which prevents their use by a larger community. Here, we present an R function to easily perform Bayesian individual dynamic predictions, using MonolixSuite.
Methods: The key idea of Bayesian individual dynamic prediction is to use the distribution of parameters of the NLME model as priors and obtain a posterior distribution for the new patient of interest given its individual data. Depending on the situation, the individual data can be one TDM concentration measurement or a few biomarkers measurements for instance. The posterior distribution, also called conditional distribution, represents the uncertainty of the parameter of this individual. The posterior distribution has no closed form solution but it is possible to sample from it using Markov-Chain Monte-Carlo procedures. Once many samples from the posterior distribution have been obtained, they can be used to predict the evolution of the model variable after the time of the last observation.
These different steps can be done within the MonolixSuite. First, in Monolix, a population model can be defined and a dataset containing the data for the new individual loaded. To obtain samples from the posterior distribution, the “conditional distribution” task is run with modified settings to request many samples. Next, the run is exported to Simulx to perform the predictions. The design for the individual is read automatically from the Monolix run, the samples from the conditional distribution are imported manually and the output time grid is defined by the user. The MonolixSuite easily handles joint models, for both continuous and non-continuous (e.g survival) data. Monolix has already been shown to provide reliable parameter estimates for Bbayesian individual dynamic prediction, in particular for joint tumor-size and survival models [3].
To automate these steps, we have created an R function which applies these steps sequentially. The input arguments are a Monolix project describing the population model, the data of the new individuals and the desired prediction time grid.
Results: The R function is applied to two examples:
Case 1: A nonlinear joint mode of prostate-specific antigen (PSA) kinetics and survival in metastatic prostate cancer.
The model and individual data are obtained from [4] and truncated at various landmark times. The evolution of PSA and the survival probability after the landmark time are predicted. As expected, the prediction intervals become more narrow when more individual data is available (i.e for late landmark times).
Case 2: A population PK model for sunitinib
The model is obtained from [5] and single steady-state concentration is simulated per individual, at various times in between two doses (non-trough). The R function is used to obtain trough concentrations, which can be used forto dose-adjustement decisions.
Conclusion: The implemented R function allows users to perform bayesian individual dynamic predictions with minimal coding expertise.
References:
[1] 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. 17, 105 (2017).
[2] Gotta, V. et al. Therapeutic drug monitoring of imatinib: Bayesian and alternative methods to predict trough levels. Clin. Pharmacokinet. 51, 187–201 (2012).
[3] Riglet, F., Mentre, F., Veyrat-follet, C. & Bertrand, J. Bayesian Individual Dynamic Predictions with Uncertainty of Longitudinal Biomarkers and Risks of Survival Events in a Joint Modelling Framework : a Comparison Between Stan , Monolix , and NONMEM. (2020)
[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 73, 305–312 (2017).
[5] Houk, B. E., Bello, C. L., Kang, D. & Amantea, M. A population pharmacokinetic meta-analysis of sunitinib malate (SU11248) and its primary metabolite (SU12662) in healthy volunteers and oncology patients. Clin. Cancer Res. 15, 2497–2506 (2009).