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A Population Pharmacokinetic Model with Time-Dependent Covariates Measured with Errors

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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.
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Keywords: Differential equations; Laplace approximation; Measurement error; Nonlinear mixed models; Pharmacokinetics; Two-compartment model

Document Type: Research Article

Affiliations: 1: Department of Biostatistics, The University of Michigan, Ann Arbor, Michigan 48109, U.S.A. 2: ALZA Corporation, Clinical Pharmacology, Mountain View, California 94039, U.S.A. 3: Department of Pharmacology, Sungkyunkwan University, Suwon, Hyunggi do, 440-746, South Korea

Publication date: 01 June 2004

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