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


Given a joint model and its parameters, Bayesian individual dynamic prediction (IDP) of biomarkers and risk of event can be performed for new patients at different landmark times using observed biomarker values. The aim of the present study was to compare IDP, with uncertainty, using Stan 2.18, Monolix 2018R2 and NONMEM 7.4. Simulations of biomarker and survival were performed using a nonlinear joint model of prostate-specific antigen (PSA) kinetics and survival in metastatic prostate cancer. Several scenarios were evaluated, according to the strength of the association between PSA and survival. For various landmark times, a posteriori distribution of PSA kinetic individual parameters was estimated, given individual observations, with each software. Samples of individual parameters were drawn from the posterior distribution. Bias and imprecision of individual parameters as well as coverage of 95% credibility interval for PSA and risk of death were evaluated. All software performed equally well with small biases on individual parameters. Imprecision on individual parameters was comparable across software and showed marked improvements with increasing landmark time. In terms of coverage, results were also comparable and all software were able to well predict PSA kinetics and survival. As for computing time, Stan was faster than Monolix and NONMEM to obtain individual parameters. Stan 2.18, Monolix 2018R2 and NONMEM 7.4 are able to characterize IDP of biomarkers and risk of event in a nonlinear joint modelling framework with correct uncertainty and hence could be used in the context of individualized medicine.

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The authors would like to acknowledge Dr. R. Bauer (ICON Development Solutions, Ellicott City, USA), for his valuable help in handling the NONMEM software. They also thank Hervé Le Nagard and Lionel de la Tribouille for the uses of CATIBioMed calculus facility.


François Riglet was supported by a grant from Sanofi, France.

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Riglet, F., Mentre, F., Veyrat-Follet, C. et al. 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. AAPS J 22, 50 (2020).

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  • Bayesian
  • individual predictions
  • joint model
  • nonlinear mixed effect model