Bayesian analysis of growth curves using mixed models defined by stochastic differential equations

Area of Science:

• Biostatistics
• Mathematical Biology
• Population Dynamics

Background:

• Growth curve data involve repeated measurements of continuous growth over time.
• Classical analysis uses nonlinear mixed models with standard growth functions.
• Existing models often assume monotone growth and struggle with rate variations.

Purpose of the Study:

• To propose stochastic differential equations (SDEs) for modeling variations in growth rates.
• To develop Bayesian inference methods for SDE mixed models.
• To enhance the analysis of growth curve data by incorporating random growth dynamics.

Main Methods:

• Deducing SDEs from deterministic growth functions by adding random variations.
• Implementing Bayesian inference using Gibbs algorithms for explicit SDE solutions.
• Approximating diffusion processes with the Euler-Maruyama scheme for non-explicit solutions.
• Validating the SDE approach using predictive posterior distribution criteria.

Main Results:

• The proposed SDE mixed models effectively capture unexpected changes in growth rates.
• Bayesian inference methods provide a robust framework for parameter estimation.
• The Euler-Maruyama scheme offers a practical approximation for complex SDEs.
• Validation criteria confirm the utility of the SDE approach.

Conclusions:

• Stochastic differential equations offer a powerful alternative for analyzing growth curve data with complex dynamics.
• The Bayesian inference framework and approximation schemes facilitate practical application.
• The SDE approach demonstrated improved modeling accuracy for chicken growth data using the Gompertz function.