Using spline-enhanced ordinary differential equations for PK/PD model development.
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.
Wang
Yi
Y
Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE, 68583-0963, USA.
Eskridge
Kent
K
Zhang
Shunpu
S
Wang
Dong
D
D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D004364:Pharmaceutical Preparations / Q000008:administration & dosage / Q000097:blood / Q000378:metabolism; D010599:Pharmacokinetics; D010600:Pharmacology / Q000706:statistics & numerical data*; D018709:Statistics, Nonparametric; D013269:Stochastic Processes
D004364:Pharmaceutical Preparations