Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm

Area of Science:

• Pharmacometrics
• Mathematical Biology
• Computational Statistics

Background:

• Traditional pharmacokinetic/pharmacodynamic (PK/PD) modeling often relies on non-linear mixed-effects models (NLME) with ordinary differential equations (ODEs).
• These models typically assume uncorrelated intra-individual residuals, which may not fully capture complex biological system variations.
• Advanced residual error models, such as stochastic differential equations (SDEs) incorporating measurement noise, offer potential for improved model description.

Purpose of the Study:

• To implement SDEs within an NLME framework for PK/PD modeling.
• To develop a novel likelihood function approximation for parameter estimation in SDE-based NLME models.
• To investigate the capability of the proposed method in decomposing intra-individual residual variation into system and measurement noise.

Main Methods:

• Implementation of SDEs within a non-linear mixed-effects modeling framework.
• Development of a novel likelihood approximation combining the First-Order Conditional Estimation (FOCE) method and the Extended Kalman Filter (EKF).
• Simulation studies to evaluate the proposed model and estimation algorithm.

Main Results:

• The proposed method successfully decomposes intra-individual residual variation (epsilon) into system noise (w) and measurement noise (e).
• Simulation studies confirmed the effective separation of system noise from measurement noise.
• The approach also demonstrated successful differentiation between system noise and inter-individual variability.

Conclusions:

• Stochastic differential equations (SDEs) provide a more sophisticated approach to modeling residual variability in PK/PD.
• The novel FOCE-EKF approximation enables robust parameter estimation for SDE-based NLME models.
• This methodology enhances the ability to accurately characterize different sources of variability in PK/PD systems.