Estimation of mixed-effects ordinary differential equation models linear in the parameters

Area of Science:

• Statistics
• Dynamical Systems Modeling
• Computational Biology

Background:

• Ordinary Differential Equation (ODE) models are crucial for analyzing dynamical systems.
• Estimating fixed and random effects in ODE models with complex hierarchical structures remains challenging.
• Existing nonlinear mixed-effects models have limitations in handling diverse data structures.

Purpose of the Study:

• To propose a general framework for estimating fixed and random effects in ODE models.
• To extend mixed-effects ODE modeling to single-level, nested hierarchical, and crossed random-effect structures.
• To enhance the accessibility of statistical inference for a broad class of dynamical systems.

Main Methods:

• Developed Direct Integral Mixed-Effects (DIME), a novel framework for ODE models linear in parameters.
• Exploited parameter-state separability to reformulate the problem within a linear mixed-effects model framework.
• Provided theoretical guarantees of consistency and asymptotic normality.

Main Results:

• DIME demonstrated competitive bias and RMSE compared to nlme and nlmixr2.
• DIME showed superior coverage probabilities, especially for variance component estimation with limited data.
• The method proved applicable in scenarios where competing methods failed.
• Applied DIME to population growth and atmospheric dynamics data, yielding consistent and interpretable results.

Conclusions:

• DIME provides a flexible and accessible approach for mixed-effects ODE modeling.
• The framework effectively handles complex hierarchical data structures.
• DIME offers a powerful alternative for statistical inference in dynamical systems, outperforming existing methods in various scenarios.