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This article is part of the supplement: The ISIBM International Joint Conferences on Bioinformatics, Systems Biology and Intelligent Computing (IJCBS)

Open Access Research

Non-compartment model to compartment model pharmacokinetics transformation meta-analysis – a multivariate nonlinear mixed model

Zhiping Wang1, Seongho Kim1, Sara K Quinney1, Jihao Zhou2 and Lang Li1*

  • * Corresponding author: Lang Li

  • † Equal contributors

Author affiliations

1 Division of Biostatistics, Department of Medicine, School of Medicine, Indiana University, Indianapolis, IN, 46032, USA

2 Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI, 48109, USA

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Citation and License

BMC Systems Biology 2010, 4(Suppl 1):S8  doi:10.1186/1752-0509-4-S1-S8

Published: 28 May 2010



To fulfill the model based drug development, the very first step is usually a model establishment from published literatures. Pharmacokinetics model is the central piece of model based drug development. This paper proposed an important approach to transform published non-compartment model pharmacokinetics (PK) parameters into compartment model PK parameters. This meta-analysis was performed with a multivariate nonlinear mixed model. A conditional first-order linearization approach was developed for statistical estimation and inference.


Using MDZ as an example, we showed that this approach successfully transformed 6 non-compartment model PK parameters from 10 publications into 5 compartment model PK parameters. In simulation studies, we showed that this multivariate nonlinear mixed model had little relative bias (<1%) in estimating compartment model PK parameters if all non-compartment PK parameters were reported in every study. If there missing non-compartment PK parameters existed in some published literatures, the relative bias of compartment model PK parameter was still small (<3%). The 95% coverage probabilities of these PK parameter estimates were above 85%.


This non-compartment model PK parameter transformation into compartment model meta-analysis approach possesses valid statistical inference. It can be routinely used for model based drug development.