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

Yi Wang, Kent Eskridge, Shunpu Zhang, Dong Wang

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)553-571
Number of pages19
JournalJournal of Pharmacokinetics and Pharmacodynamics
Volume35
Issue number5
DOIs
StatePublished - Oct 1 2008

Fingerprint

Uncertainty
Software
Datasets

Keywords

  • Model uncertainty
  • Nonparametric function
  • Stochastic differential equation

ASJC Scopus subject areas

  • Pharmacology

Cite this

Using spline-enhanced ordinary differential equations for PK/PD model development. / Wang, Yi; Eskridge, Kent; Zhang, Shunpu; Wang, Dong.

In: Journal of Pharmacokinetics and Pharmacodynamics, Vol. 35, No. 5, 01.10.2008, p. 553-571.

Research output: Contribution to journalArticle

@article{0396b85058a5456d83200eac7d94f690,
title = "Using spline-enhanced ordinary differential equations for PK/PD model development",
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.",
keywords = "Model uncertainty, Nonparametric function, Stochastic differential equation",
author = "Yi Wang and Kent Eskridge and Shunpu Zhang and Dong Wang",
year = "2008",
month = "10",
day = "1",
doi = "10.1007/s10928-008-9101-9",
language = "English (US)",
volume = "35",
pages = "553--571",
journal = "Journal of Pharmacokinetics and Pharmacodynamics",
issn = "1567-567X",
publisher = "Springer New York",
number = "5",

}

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 - 2008/10/1

Y1 - 2008/10/1

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 -