Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats
Artikel i vetenskaplig tidskrift, 2015

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

parameter estimation

nonlinear kinetics

model uncertainty

extended Kalman filter

state prediction


Jacob Leander

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Joachim Almquist

Chalmers, Biologi och bioteknik, Systembiologi

Christine Ahlström

AstraZeneca AB

Johan Gabrielsson

Sveriges lantbruksuniversitet (SLU)

Mats Jirstrand

Chalmers, Biologi och bioteknik, Systembiologi

AAPS Journal

1550-7416 (eISSN)

Vol. 17 3 586-596


Informations- och kommunikationsteknik

Livsvetenskaper och teknik (2010-2018)



Farmakologi och toxikologi


Grundläggande vetenskaper



Mer information

Senast uppdaterat