Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models

  • Authors:

  • Guanghui Huang;Jianping Wan;Hui Chen

  • Affiliations:

  • Department of Pharmacology, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430030, China and College of Mathematics and Statistics, Chongqing University, Chongqing 40 ...;College of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;Department of Pharmacology, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430030, China

  • Venue:
  • Computers in Biology and Medicine
  • Year:
  • 2013

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Abstract

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error.