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Statistica Sinica 22 (2012), 1199-1215





A SWITCHING MARKOV CHAIN MONTE CARLO

METHOD FOR STATISTICAL IDENTIFIABILITY

OF NONLINEAR PHARMACOKINETICS MODELS


Seongho Kim and Lang Li


University of Louisville and Indiana University School of Medicine


Abstract: We study the convergence rate of MCMC on the statistically unidentifiable nonlinear model involving the Michaelis-Menten kinetic equation. We have shown that, under certain conditions, the convergence diagnosis of Raftery and Lewis (1992) is consistent with the convergence rate argued by Brooks and Roberts (1999). Therefore, different MCMC schemes developed in linear models are further extended and compared in nonlinear models. We demonstrate that the single component MCMC (SCM) scheme is faster than the group component MCMC (GCM) scheme on unidentifiable models, while GCM is faster than SCM when the model is statistically identifiable. A novel MCMC method is then developed using both SCM and GCM schemes, termed the Switching MCMC (SWM) method. The proposed SWM possesses an advantage in that it is able to estimate parameters regardless of the statistically identifiable situations. In addition, simulations and data analysis suggest a better performance of the proposed SWM algorithm than SCM and GCM.



Key words and phrases: Convergence rate, Michaelis-Menten (MM) kinetics, Monte Carlo Markov chain (MCMC), statistical identifiability, pharmacokinetics (PK), switching algorithm.

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