Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions

Area of Science:

• Statistics
• Computational Biology
• Mathematical Modeling

Background:

• Ordinary differential equation (ODE) models are widely used for dynamical systems.
• Gaussian distribution assumptions in ODE parameter estimation are not robust to abnormal data.
• Bayesian inference offers a flexible framework for complex statistical modeling.

Purpose of the Study:

• To develop a robust hierarchical semiparametric mixed-effects ODE model for longitudinal data.
• To address the limitations of Gaussian assumptions in the presence of noisy or abnormal data.
• To provide a reliable method for estimating ODE parameters in biological and other complex systems.

Main Methods:

• Developed a hierarchical semiparametric mixed-effects ODE model within a Bayesian framework.
• Utilized heavy-tailed distributions to model random effects and observation errors for robustness.
• Employed Markov Chain Monte Carlo (MCMC) methods for posterior distribution sampling of ODE parameters.

Main Results:

• The proposed model demonstrated satisfactory performance in simulation studies with finite samples.
• The method effectively handles noisy longitudinal data by employing robust distribution assumptions.
• Application to a gene regulation experiment showcased the model's practical utility.

Conclusions:

• The hierarchical semiparametric mixed-effects ODE model offers a robust alternative for parameter estimation.
• Heavy-tailed distributions enhance the reliability of ODE models with abnormal data.
• The Bayesian MCMC approach provides a computationally feasible method for robust ODE analysis.