title: Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.
abstract: OBJECTIVE
  The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling.
  
  
  METHODS
  The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models.
  
  
  RESULTS
  Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix.
  
  
  CONCLUSIONS
  The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.
authors.affiliation: Experimental Medicine, Ferring Pharmaceuticals A/S, DK-2300, Copenhagen S, Denmark. christoffer.tornoe@ferring.com
authors.forename: Christoffer W
authors.initials: CW
authors.lastname: Tornøe
authors.forename: Rune V
authors.initials: RV
authors.lastname: Overgaard
authors.forename: Henrik
authors.initials: H
authors.lastname: Agersø
authors.forename: Henrik A
authors.initials: HA
authors.lastname: Nielsen
authors.forename: Henrik
authors.initials: H
authors.lastname: Madsen
authors.forename: E Niclas
authors.initials: EN
authors.lastname: Jonsson
mesh_terms: D000465:Algorithms; D000970:Antineoplastic Agents / Q000493:pharmacokinetics; D016208:Databases, Factual; D004305:Dose-Response Relationship, Drug; D006207:Half-Life; D006801:Humans; D007408:Intestinal Absorption; D016014:Linear Models; D008297:Male; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009842:Oligopeptides / Q000493:pharmacokinetics; D010599:Pharmacokinetics; D011471:Prostatic Neoplasms / Q000188:drug therapy; D011966:Receptors, LHRH / Q000037:antagonists & inhibitors; D012984:Software; D013269:Stochastic Processes
chemical_list: D000970:Antineoplastic Agents; D009842:Oligopeptides; D011966:Receptors, LHRH; C431566:acetyl-2-naphthylalanyl-3-chlorophenylalanyl-1-oxohexadecyl-seryl-4-aminophenylalanyl(hydroorotyl)-4-aminophenylalanyl(carbamoyl)-leucyl-ILys-prolyl-alaninamide