A population pharmacokinetic model with time-dependent covariates measured with errors

Lang Li, Xihong Lin, Morton B. Brown, Suneel Gupta, Kyung Hoon Lee

Research output: Contribution to journalArticle

8 Scopus citations


We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second-order two-step method with numerical solutions of differential equations (2orderND), and the second-order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear mixed model at the second step. We apply the proposed methods to the analysis of the Ditropan data, and evaluate their performance using a simulation study. Our results show that the 2orderND method performs well, while the 2orderAD method can yield PK parameter estimators that are subject to considerable biases.

Original languageEnglish (US)
Pages (from-to)451-460
Number of pages10
Issue number2
StatePublished - Jun 1 2004



  • Differential equations
  • Laplace approximation
  • Measurement error
  • Nonlinear mixed models
  • Pharmacokinetics
  • Two-compartment model

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

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