Estimation and inference for a spline-enhanced population pharmacokinetic model

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

Research output: Contribution to journalArticle

29 Scopus citations


This article is motivated by an application where subjects were dosed three times with the same drug and the drug concentration profiles appeared to be the lowest after the third dose. One possible explanation is that the pharmacokinetic (PK) parameters vary over time. Therefore, we consider population PK models with time-varying PK parameters. These time-varying PK parameters are modeled by natural cubic spline functions in the ordinary differential equations. Mean parameters, variance components, and smoothing parameters are jointly estimated by maximizing the double penalized log likelihood. Mean functions and their derivatives are obtained by the numerical solution of ordinary differential equations. The interpretation of PK parameters in the model and its flexibility are discussed. The proposed methods are illustrated by application to the data that motivated this article. The model's performance is evaluated through simulation.

Original languageEnglish (US)
Pages (from-to)601-611
Number of pages11
Issue number3
StatePublished - Sep 2002


  • Double penalized log-likelihood function
  • Multicompartment models
  • Natural cubic spline
  • Runge-Kutta method

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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