A two-stage estimation method for random coefficient differential equation models with application to longitudinal hiv dynamic data

Yun Fang*, Hulin Wu, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

Original languageEnglish
Pages (from-to)1145-1170
Number of pages26
JournalStatistica Sinica
Volume21
Issue number3
DOIs
Publication statusPublished - Jul 2011

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • AIDS/HIV data
  • Local polynomial kernel smoothing
  • Longitudinal data
  • Mixed-effects models
  • Ordinary differential equation
  • Pseudo likelihood
  • Viral dynamics

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