| Parametric incomplete data models defined by ordinary differential equa- tions (ODEs) are widely used in biostatistics to describe biological processes accurately. Their parameters are estimated on approximate models, whose regression functions are evaluated by a numerical integration method. Ac- curate and efficient estimations of these parameters are critical issues. This paper proposes parameter estimation methods involving either a stochas- tic approximation EM algorithm (SAEM) in the maximum likelihood es- timation, or a Gibbs sampler in the Bayesian approach. Both algorithms involve the simulation of non-observed data with conditional distributions using Hastings-Metropolis (H-M) algorithms. A modified H-M algorithm, including an original Local Linearization scheme to solve the ODEs, is pro- posed to reduce the computational time significantly. The convergence on the approximate model of all these algorithms is proved. The errors induced by the numerical solving method on the conditional distribution, the likelihood and the posterior distribution are bounded. The Bayesian and maximum likelihood estimation methods are illustrated on a simulated pharmacoki- netic nonlinear mixed-effects model defined by an ODE. Simulation results illustrate the ability of these algorithms to provide accurate estimates. |
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