title: Stochastic nonlinear mixed effects: a metformin case study.
abstract: In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi for their stochastic deconvolution.
authors.affiliation: Department of Mathematics, North Carolina State University, Raleigh, NC, USA. bjmatzuk@ncsu.edu.|Department of Pharmacology and Therapeutic innovation, Children's Mercy Hospital, Kansas City, MO, USA. bjmatzuk@ncsu.edu.
authors.forename: Brett
authors.initials: B
authors.lastname: Matzuka
authors.affiliation: qPharmetra, LLC, Raleigh, NC, USA.
authors.forename: Jason
authors.initials: J
authors.lastname: Chittenden
authors.affiliation: Alexion Pharmaceuticals Inc., New Haven, CT, USA.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Monteleone
authors.affiliation: Department of Mathematics, North Carolina State University, Raleigh, NC, USA.
authors.forename: Hien
authors.initials: H
authors.lastname: Tran
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D018592:Cross-Over Studies; D003692:Delayed-Action Preparations; D006801:Humans; D007004:Hypoglycemic Agents / Q000008:administration & dosage / Q000493:pharmacokinetics*; D008687:Metformin / Q000008:administration & dosage / Q000493:pharmacokinetics*; D017711:Nonlinear Dynamics; D016032:Randomized Controlled Trials as Topic; D013269:Stochastic Processes
chemical_list: D003692:Delayed-Action Preparations; D007004:Hypoglycemic Agents; D008687:Metformin
keywords: Kalman filter; Model development; Nonlinear mixed effects; Parameter estimation; Population pharmacokinetics; Stochastic differential equations