Using spline-enhanced ordinary differential equations for PK/PD model development

J Pharmacokinet Pharmacodyn. 2008 Oct;35(5):553-71. doi: 10.1007/s10928-008-9101-9. Epub 2008 Nov 7.

Abstract

A spline-enhanced ordinary differential equation (ODE) method is proposed for developing a proper parametric kinetic ODE model and is shown to be a useful approach to PK/PD model development. The new method differs substantially from a previously proposed model development approach using a stochastic differential equation (SDE)-based method. In the SDE-based method, a Gaussian diffusion term is introduced into an ODE to quantify the system noise. In our proposed method, we assume an ODE system with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function vector that is estimated using penalized splines. B(t) is used to construct a quantitative measure of model uncertainty useful for finding the proper model structure for a given data set. By means of two examples with simulated data, we demonstrate that the spline-enhanced ODE method can provide model diagnostics and serve as a basis for systematic model development similar to the SDE-based method. We compare and highlight the differences between the SDE-based and the spline-enhanced ODE methods of model development. We conclude that the spline-enhanced ODE method can be useful for PK/PD modeling since it is based on a relatively uncomplicated estimation algorithm which can be implemented with readily available software, provides numerically stable, robust estimation for many models, is distribution-free and allows for identification and accommodation of model deficiencies due to model misspecification.

MeSH terms

  • Algorithms
  • Animals
  • Computer Simulation
  • Humans
  • Models, Biological*
  • Pharmaceutical Preparations / administration & dosage
  • Pharmaceutical Preparations / blood
  • Pharmaceutical Preparations / metabolism
  • Pharmacokinetics*
  • Pharmacology / statistics & numerical data*
  • Statistics, Nonparametric
  • Stochastic Processes

Substances

  • Pharmaceutical Preparations