Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics
Journal article, 2018

Nonlinear mixed effects (NLME) modeling based on stochastic differential equations (SDEs) have evolved into a promising approach for analysis of PK/PD data. SDE-NLME models go beyond the realm of standard population modeling as they consider stochastic dynamics, thereby introducing a probabilistic perspective on the state variables. This article presents a summary of the main contributions to SDE-NLME models found in the literature. The aims of this work were to develop an exact gradient version of the first-order conditional estimation (FOCE) method for SDE-NLME models and to investigate whether it enabled faster estimation and better gradient precision/accuracy compared to the use of gradients approximated by finite differences. A simulation-estimation study was set up whereby finite difference approximations of the gradients of each level were interchanged with the exact gradients. Following previous work, the uncertainty of the state variables was accounted for using the extended Kalman filter (EKF). The exact gradient FOCE method was implemented in Mathematica 11 and evaluated on SDE versions of three common PK/PD models. When finite difference gradients were replaced by exact gradients at both FOCE levels, relative runtimes improved between 6- and 32-fold, depending on model complexity. Additionally, gradient precision/accuracy was significantly better in the exact gradient case. We conclude that parameter estimation using FOCE with exact gradients can successfully be applied to SDE-NLME models.

extended Kalman filter

sensitivity equations

first-order conditional estimation (FOCE)

stochastic differential equations

nonlinear mixed effects modeling

Author

Helga Kristín Ólafsdóttir

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fraunhofer-Chalmers Centre

Jacob Leander

Chalmers, Mathematical Sciences, Analysis and Probability Theory

AstraZeneca AB

Fraunhofer-Chalmers Centre

Joachim Almquist

AstraZeneca AB

System Biology

Fraunhofer-Chalmers Centre

Mats Jirstrand

Fraunhofer-Chalmers Centre

AAPS Journal

1550-7416 (eISSN)

Vol. 20 5 88

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering

DOI

10.1208/s12248-018-0232-7

More information

Latest update

9/18/2018