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.
Numerical Analysis and Computation | Statistical Models
Lil, Lang; Lin, Xihong; Brown, Mort B.; Gupta, Suneel; and Lee, Kyung-Hoon , "A POPULATION PHARMACOKINETIC MODEL WITH TIME-DEPENDENT COVARIATES MEASURED WITH ERRORS" (October 2003). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 15.