TY - JOUR
T1 - Using spline-enhanced ordinary differential equations for PK/PD model development
AU - Wang, Yi
AU - Eskridge, Kent
AU - Zhang, Shunpu
AU - Wang, Dong
PY - 2008/10
Y1 - 2008/10
N2 - 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.
AB - 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.
KW - Model uncertainty
KW - Nonparametric function
KW - Stochastic differential equation
UR - http://www.scopus.com/inward/record.url?scp=57749101107&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=57749101107&partnerID=8YFLogxK
U2 - 10.1007/s10928-008-9101-9
DO - 10.1007/s10928-008-9101-9
M3 - Article
C2 - 18989761
AN - SCOPUS:57749101107
VL - 35
SP - 553
EP - 571
JO - Journal of Pharmacokinetics and Pharmacodynamics
JF - Journal of Pharmacokinetics and Pharmacodynamics
SN - 1567-567X
IS - 5
ER -