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A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal

Yun Fang1, Hulin Wu, Li-Xing Zhu

  • 1East China Normal University, University of Rochester and Hong Kong Baptist University.

Statistica Sinica
|December 16, 2011
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Summary
This summary is machine-generated.

We introduce a computationally efficient two-stage estimation method for random coefficient ordinary differential equation (ODE) models. This approach offers an alternative to complex likelihood methods and aids in estimating parameters for ODE models.

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Area of Science:

  • Statistics
  • Computational Biology
  • Biostatistics

Background:

  • Ordinary differential equation (ODE) models are crucial for dynamic systems.
  • Estimating parameters in random coefficient ODE models presents computational challenges.
  • Existing methods may struggle with model complexity and high-dimensional parameter spaces.

Purpose of the Study:

  • To propose a novel two-stage estimation method for random coefficient ODE models.
  • To establish the asymptotic properties of the proposed estimator for population parameters.
  • To provide a computationally efficient alternative to existing estimation techniques.

Main Methods:

  • A two-stage estimation approach is proposed.
  • A maximum pseudo-likelihood estimator (MPLE) is derived using a mixed-effects modeling framework.
  • The method avoids repeated ODE solving and does not require initial state variable values.

Main Results:

  • Asymptotic properties for population parameters are established.
  • The method is computationally efficient, offering an alternative when exact likelihood methods fail.
  • Monte Carlo simulations demonstrate favorable finite sample properties.

Conclusions:

  • The proposed MPLE offers an efficient and practical approach for random coefficient ODE models.
  • This method is particularly useful for complex models and can provide starting estimates for other methods.
  • The approach retains the benefits of mixed-effects modeling and was validated with AIDS clinical data.