Henrik Agersø

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

PurposeThe objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling.MethodsThe 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.ResultsVarious 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.ConclusionsThe 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.

Pharmacokinetics of Desmopressin Administrated as an Oral Lyophilisate Dosage Form in Children With Primary Nocturnal Enuresis and Healthy Adults

The population pharmacokinetics of desmopressin in children with nocturnal enuresis and in healthy adults were compared using a 1‐compartment model with first‐order absorption and first‐order elimination. In addition, the model consisted of a number of transit compartments before absorption to describe a lag‐time. The model gave an adequate description of adult as well as children data and provided a statistically significant better fit to data than a standard lag‐time model. The main difference in the pharmacokinetics between children and adults was the absorption delay. The pharmacokinetic difference was minor and presumably of no clinical relevance.

Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

The standard software for non-linear mixed-effect analysis of pharmacokinetic/pharmacodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as long as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential equation (ODE) solver package odesolve and the non-linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlmeODE package for population PK/PD analysis using the available data analysis tools in R for model inspection and validation. The nlmeODE package is numerically stable and provides accurate parameter estimates which are consistent with NONMEM estimates.

Pharmacokinetics and pharmacodynamics of a new formulation of recombinant human growth hormone administered by ZomaJet 2 Vision, a new needle-free device, compared to subcutaneous administration using a conventional syringe.

The objective of the present study was to investigate the applicability of a new human growth hormone (Zomacton®) formulation, administered both by a conventional syringe and by a new needle‐free device (ZomaJet 2 Vision). The study was performed according to a randomized, controlled, three‐period crossover design. On 3 separate days, all subjects received in a random order a single subcutaneous injection of 1.67 mg hGH as follows: Zomacton® 4 mg/ml conventional syringe administration (Treatment A), Zomacton® 10 mg/ml conventional syringe administration (Treatment B), or Zomacton® 10 mg/ml ZomaJet 2 Vision administration (Treatment C). The pharmacokinetic parameters were assessed for the individual subjects in each group by noncompartmental methods. Bioequivalence was assessed based on log‐transformed AUC and Cmax values. To investigate the effectiveness of two formulations and the different administration methods, the pharmacodynamic parameters (insulin‐like growth factor‐1 [IGF‐1] and free fatty acids [FFA]) were also evaluated. No subjects were withdrawn due to adverse events. The local tolerance assessment (assessed by inspection) revealed no differences between ZomaJet 2 Vision application and conventional injections by syringe. Administration of the new hGH formulation by syringe was found to be bioequivalent with the reference treatment, both based on AUC and Cmax values; the new formulation administered by use of ZomaJet 2 Vision was found to be bioequivalent based on AUC values only. When using the ZomaJet 2 Vision, the absorption of hGH was faster, resulting in higher Cmax values. The maximum hGH serum concentration of around 20 ng/ml was observed 3.5 to 4 hours after drug administration. The terminal half‐life was found to be around 2.5 hours. Comparison of the pharmacodynamic profiles (both IGF‐1 and FFA) demonstrated bioequieffectiveness. These results support the use of jet injectors as a viable alternative to the traditional injection pens.

Pharmacokinetic/Pharmacodynamic Modelling of GnRH Antagonist Degarelix: A Comparison of the Non-linear Mixed-Effects Programs NONMEM and NLME

In this paper, the two non-linear mixed-effects programs NONMEM and NLME were compared for their use in population pharmacokinetic/pharmacodynamic (PK/PD) modelling. We have described the first-order conditional estimation (FOCE) method as implemented in NONMEM and the alternating algorithm in NLME proposed by Lindstrom and Bates. The two programs were tested using clinical PK/PD data of a new gonadotropin-releasing hormone (GnRH) antagonist degarelix currently being developed for prostate cancer treatment. The pharmacokinetics of intravenous administered degarelix was analysed using a three compartment model while the pharmacodynamics was analysed using a turnover model with a pool compartment. The results indicated that the two algorithms produce consistent parameter estimates. The bias and precision of the two algorithms were further investigated using a parametric bootstrap procedure which showed that NONMEM produced more accurate results than NLME together with the nlmeODE package for this specific study.