Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

• Published in: Computational statistics Vol. 39; no. 6; pp. 2975 - 3005
• Main Authors: Clairon, Quentin, Pasin, Chloé, Balelli, Irene, Thiébaut, Rodolphe, Prague, Mélanie
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024; Springer Nature B.V
• Subjects: Accuracy; Approximation; Cost function; Differential equations; Economic Theory/Quantitative Economics/Mathematical Methods; Epidemiology; Initial conditions; Mathematics and Statistics; Maximum likelihood estimation; Maximum likelihood method; Nonlinear control; Optimal control; Ordinary differential equations; Original Paper; Parameter estimation; Parameter identification; Pharmacodynamics; Pharmacokinetics; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Virology; Mechanistic models; Clinical trial analysis; Ordinary differential equations; Optimal control theory; Nonlinear mixed effects models; Dynamic population models
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-023-01420-x

We present a method for parameter estimation for nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs). It aims to regularize the estimation problem in the presence of model misspecification and practical identifiability issues, while avoiding the need to know or estimate initial conditions as nuisance parameters. To this end, we define our estimator as a minimizer of a cost function that incorporates a possible gap between the assumed population-level model and the specific individual dynamics. The computation of the cost function leads to formulate and solve optimal control problems at the subject level. Compared to the maximum likelihood method, we show through simulation examples that our method improves the estimation accuracy in possibly partially observed systems with unknown initial conditions or poorly identifiable parameters with or without model error. We conclude this work with a real-world application in which we model the antibody concentration after Ebola virus vaccination.