Johan Areberg Simultaneous Population Pharmacokinetic Modelling of Parent
Compound and Metabolite in Plasma and Urine for a New Drug Candidate
J. Areberg, L.E. Broksø Kyhl
Dep. Clinical Pharmacology & PK, H. Lundbeck A/S, Denmark
Objectives: To construct a model that could describe the population pharmacokinetics of a potential drug candidate. Since the major metabolite apparently peaked earlier than the parent compound for many of the subjects, special attention was on the absorption of the parent compound and the metabolite.
Methods: Rich plasma concentration profiles for parent compound and the major metabolite for a new drug candidate from 113 healthy subjects (77 men, 36 women, age range [18,77]) were available. In addition, the amount of the parent compound and the major metabolite had been measured in urine for 67 of the 113 subjects. Population pharmacokinetic modelling was performed by means of non-linear mixed effect methods using the software NONMEM, version VI
(Globomax). Plasma and urine data for both parent compound and metabolite were modelled simultaneously using own defined differential equations in NONMEM (ADVAN6 TRANS1).
Results: The final model consisted of 8 compartments: gastrointestinal for parent compound (1,dosing compartment), gastrointestinal for metabolite (2), central (3,5) and peripheral (4,6) for both parent compound and metabolite and urine for both parent compound (7) and metabolite (8).
All transfers were described with first-order processes. A transfer directly from the gastrointestinal compartment for the parent compound to the gastrointestinal compartment for the metabolite was essential to be included in order to describe earlier plasma peaks for the metabolite. Inter-subject variability was modelled with exponential terms while a proportional error model was used for plasma data and a combined additive and proportional error model was used for urine data.
Conclusion: A model was created that adequately describe the population pharmacokinetics of the parent compound and the major metabolite for a new drug candidate. The model indicates that the parent compound undergoes gastrointestinal metabolism, which can explain the observation that the major metabolite in many cases apparently peaks before the parent compound
Poster: Methodology- Other topics
Martin Bergstrand A comparison of methods for handling of data below the limit of
quantification in NONMEM VI
Martin Bergstrand, Elodie Plan, Maria Kjellsson, Mats O Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Introduction: Common approaches for handling of concentration measurements reported as below the limit of quantification (BLQ), such as discharging the information or substitution with the limit of quantification (LOQ) divided by two, have been shown to introduce bias to parameter estimates [1-3]. In 2001, Stuart Beal published an overview of ways to fit a PK model in the presence of BLQ data [3]. New functionalities in NONMEM VI allow for simplified implementation of some
methods presented in the publication. The method referred to as M2 applies conditional likelihood estimation to the observations above LOQ and the likelihood for the data being above LOQ are maximized with respect to the model parameters. This approach can be implemented in NONMEM VI by utilization of the YLO functionality [4]. By simultaneous modeling of continuous and
categorical data where the BLQ data are treated as categorical, the likelihood for BLQ data to be indeed BLQ can be maximized with respect to the model parameters. The indicator variable
F_FLAG can be used to facilitate this approach in NONMEM VI [4]. This suggested method differs from the one referred to as M3 in the sense that the likelihood is only estimated for BLQ data as opposed to all data.
Methods: One hundred simulated population PK data sets, originally provided for comparison of estimation methods in nonlinear mixed effects modeling (PAGE 2005) [5], were analysed with 5 different methods for handling of BLQ data. The simulated datasets was based on a
one-compartment model with first order absorption and first order elimination. A second set with 100 data sets was simulated according to a two-compartment intravenous bolus model. The five methods for handling of BLQ data was used; (A) BLQ data omitted (B) First BLQ observation substituted with LOQ/2 (C) YLO functionality (D) F_FLAG functionality (E) Maximum likelihood estimation for all data (M3) [3].
Results and Discussion: The over all best performance was seen with method (D). Also method (E) and to some extent (C) showed favorable accuracy for the estimated population parameters and IIV compared to method (A). Method (C) and (E) did however result in several (13-52%) non-successful minimizations, primarily due to rounding error termination. Though parameter estimates following non-successful terminations did not seem to be systematically different. Substitution with LOQ/2 (B) was in one case shown to introduce bias compared to omitting BLQ data.
References:
[1] Hing, J.P., et al., Analysis of toxicokinetic data using NONMEM: impact of quantification limit and replacement strategies for censored data. J Pharmacokinet Pharmacodyn, 2001. 28(5): p. 465-79.
[2] Duval, V. and M.O. Karlsson, Impact of omission or replacement of data below the limit of quantification on parameter estimates in a two-compartment model. Pharm Res, 2002. 19(12): p.
1835-40.
[3] Beal, S.L., Ways to fit a PK model with some data below the quantification limit. J Pharmacokinet Pharmacodyn, 2001. 28(5): p. 481-504.
[4] Boeckmann A. J., B.S.L.a.S.L.B., NONMEM Users Guide PartVIII. 1996-2006, NONMEM
Project Group,: San Francisco.
[5] Girard P., Mentré F. A comparison of estimation methods in nonlinear mixed effects models using a blind analysis. PAGE 14 (2005) Abstr 834 [www.page-meeting.org/?abstract=834].
Poster: Methodology- Other topics
Robert Bies An MCPEM approach to understanding animal and
inter-treatment changes with in vivo striatal dopamine clearance in rats.
Robert R. Bies1, Serge Guzy2, Joshua Sokoloski3, Laura Drewencki3, and Amy K. Wagner3.
1.Department of Pharmaceutical Sciences and Psychiatry, University of Pittsburgh, Pittsburgh, PA, USA
Objective: To capture the between animal, between occasion and between treatment differences in striatal dopamine clearance kinetics using a nonlinear mixed effects approach.
Methods: Striatal dopamine (DA) concentration versus time profiles were measured using fast scan cyclic voltammetry and a stimulated release paradigm in naïve rats and rats subjected to
experimental traumatic brain injury (TBI). Three stimulus responses (occasions), reported as DA concentration versus time, were collected both before and after treatment with either saline (vehicle) or 5mg/kg methylphenidate (MPH). Pdx-MCPEM was used to evaluate the DA clearance profiles for each stimulus response using a Vmax and Km (saturable) model parameterization with 200 EM evaluations and between 3,000 and 30,000 vectors in the likelihood space for each assessment.
Results: The system was best described using both between animal and inter-occasion variability to obtain the Vmax and the Km values reflective of DA clearance after evoked release (>300 objective function value point reduction).
Conclusions: A between animal and within animal (between occasion) structure best described differences across this experimental design using two induced conditions and three different treatments. Specific deviations from this structure will guide the implementation of the structure of covariate relationships with treatment and injury status.
Poster: Methodology- Other topics
sophie callies Modelling pharmacokinetic and pharmacodynamic properties of
second generation antisense-oligonucleotides (ASOs).
Callies Sophie, Andre Valerie, Vick Andrew-Mark, Graff Jeremy, Patel Bharvin, Brail Leslie, Lahn Michael
Eli Lilly and Company
Acknowledgement: Richard Geary, Rosie Yu (ISIS pharmaceuticals, Inc)
Introduction: One example of targeted therapy is the development of ASOs against a variety of mRNA coding for proteins involved in the pathogenesis of various diseases. By inhibiting the expression of the proteins, ASOs treatment may stop or slow down the disease process.
Objectives: A platform based plasma-tissue PK model was developed for three ASOs (A, B & C).
This model was used to select the dose regimen for ASOs B & C.
Material and modelling strategy: NONMEM version V was used to model the data. A six compartments PK model with elimination from the distribution compartments was fitted to ASO PK data. Four compartments corresponded to plasma, liver, kidney and lung and two empirical compartments were included for the remaining tissues. Finally the pharmacodynamic parameters derived from preclinical in vivo and in vitro target inhibition data were used in the PK/PD model which link ASO tissue exposure to mRNA and protein concentration using two consecutive indirect response models. ASOs A was in phase I clinical development, and ASO B and C were between candidate selection and clinical development.
Results: The PK model adequately fitted ASO C monkey and human PK data. This model built using ASO A was predictive of ASO B and C preclinical and clinical PK and confirmed that
allometric scaling per body weight is appropriate for ASOs (coefficient 0.922 and 1.19 for clearance and volume, respectively). ASOs are rapidly distributed into tissues following intravenous
administration with the distribution half-lives of approximately 30-60 minutes and 2-3 h accounting for approximately 45%, 46% of the plasma exposure, respectively. The plasma clearance varies from 2 to 5 L/h. Following tissue distribution ASOs are cleared (metabolism via
endo-exonucleases), with a long half- life in tissue matching the terminal elimination half-life in the plasma (about 20 days accounting for 9 % of plasma AUC). The total tissue clearance and tissue volume of distribution were high (approximately 150 L/h and 65000 L). From the preclinical target
Poster: Methodology- Other topics
Didier Concordet How to estimate population variance matrices with a Prescribed
Pattern of Zeros?
Didier Concordet, Djalil Chafaï
UMR181 Physiopathologie et Toxicologie Expérimentales, INRA, ENVT, Toulouse France Background: One of the main goal of population PK/PD studies is to describe the population distribution by observation of concentrations. In parametric models, this distribution is often assumed Gaussian up to a monotone transformation. In many real situations, kineticists knowledge of the drug mechanism imposes some independence pattern on the individual parameters. This simply means that the variance matrix contains a prescribed pattern of zeros (PPZ). Estimation of such matrices is problematic due to the positive definiteness constraint in the optimization. Pinheiro and Bates [1] studied different parameterizations that ensure the definite positiveness of the
estimate. In particular they suggested the usage of a Cholesky like parameterization. Unfortunately, except for the case where the variance matrix is block diagonal matrix (up to coordinates
permutation), Cholesky like parameterizations do not preserve the structure of the PPZ and are thus useless. Another common method is to estimate the variance matrix in two steps. First, estimation is performed without any constraint, then zeros are plugged according to the PPZ into the estimate provided by the first step. Unfortunately, by "forcing the zeros" by this way, nothing guarantees that the obtained estimate is still a positive matrix, and even when it is positive definite, it is not the maximum likelihood in general. Recently, the Iterative Conditional Fitting (ICF) method has been proposed to deal with the analysis of graphical models [2]. We propose a method that couples ICF and EM algorithm. It enables to reach the maximum likelihood estimator of the population variance matrix whatever the PPZ.
Method: The ICF method is mainly based on the specific properties of the Schur complement of a matrix. The Schur complement appears naturally in the distribution of the conditional distribution of a Gaussian vector with respect to another Gaussian vector. Writing the EM contrast using these properties leads to a standard least-squares problem that has to be solved at each EM iteration. For homoscedastic models, the least-squares problem is quadratic with respect to the components of variance to be estimated. This nice property is lost when considering heteroscedastic models.
Results: Simulations were performed with a four parameters sigmoid model that contains a PPZ to compare the statistical properties of the zeros forced and the proposed estimators. If both estimators are consistent, the EM+ICF estimator has smaller bias and variance that the zero forced estimator.
Surprisingly, the mean population estimate was better (smaller bias and variance) when the variance was estimated with EM+ICF suggesting that the mean and variance estimations are heavily
dependent. This sheds light on approaches, like the zero forced method, that relies on estimating the full variance matrix first and modify it by forcing the PPZ: since all the non zeros entries are estimated under the assumption that the variance matrix has no zeros, they could be poorly estimated. This is consistent with the results obtained by Ye and Pan [3] that conclude, in another context, that misspecification of the working variance structure may lead to a large loss of
efficiency of the estimators of the mean parameters.
Conclusion: In the framework of parametric nonlinear mixed-effects models, the method we propose enables estimation of population variance matrices with PPZ. Simulations suggest that the EM+ICF estimator reaches efficiency where traditional methods fail. However, this optimality
result is only valid when the pattern of zeros is a priori known. Finding a reasonable pattern of zeros is another problem that could be addressed using multiple likelihood ratio-tests that fully needs an EM+ICF method to be performed.
References:
[1] Pinheiro JC and Bates DM. Unconstrained Parametrizations for Variance-Covariance Matrices, Statistics and Computing, 6 (1996), 289-296.
[2] Chaudhuri S, Drton M and Richardson TS. Estimation of a covariance matrix with zeros.
Biometrika, 94(2007),199-216.
[3] Ye H and Pan J. Modelling of covariance structures in generalised estimating equations for longitudinal data. Biometrika, 93(2006),927--=941.
Poster: Methodology- Other topics
Carine CREPIN Elimination of anti-epileptic compounds in Marseille aquatic
environment from private hospital effluent - modelling versus measurements
C.Crepin(1), E.Fuseau(1), M.Portugal(2), D.Humilier(2)
(1) EMF consulting, Aix en Provence (2) Hôpital Henri Gastaut, Marseille,
Introduction: European directives require that residues of drug found in the aquatic environment should be taken account for a new drug application submission. [1].
A lot of anti-epileptic drugs (AED) are used to reduce the number of seizures in patients (children, adolescents and adults) with epilepsy. The metabolism of each AED is influenced by concurrent anti-epileptic medication. Carbamazepine, second generation of AED was recognised as a
compound that is not affected by conventional sewage treatment and that is also highly persistent in the aquatic environment. [2]
Objectives: The objectives are to predict the load of two AEDs (valproate (VAL) and
carbamazepine (CAR)), originating from hospital in Marseille in the sewer system and the receiving sewage treatment plants (STPs) using AED PK excretion model and to compare these results with actual measurements of AED concentrations collected from the hospital effluents and from general Marseille sewage.
Methods: The population used is a database including the number of patients treated in the Henri Gastaut hospital in Marseille during one year. Only patients (children, adolescents, adults) receiving carbamazepine and /or valproate are considered.
Using the relevant population PK models and the exposed population, Monte Carlo simulations of exposure and excretion are performed with NONMEM. Concentrations of AEDs in the hospital effluents will be extrapolated over one year and compared to actual measurements in Henri Gastaut hospital.
References:
[1] EMEA/CHMP/SWP/4447/00, Guideline on the environmental risk assessment of medicinal products for human use (2006)
[2] Thomas Heberer, Dirk Feldmann, Contribution of effluents from hospitals and private households to the total loads of diclofenac and carbamazepine in municipal sewage effluents-modelling versus measurements, Journal of hazardous Materials 122 (2005) 211-218
Poster: Methodology- Other topics
Mike Dunlavey Next-Generation Modeling Language Mike Dunlavey
Pharsight Corp.
Objectives: Develop new language-based tools for modeling and simulation.
Methods: A new modeling language has been developed by Pharsight and is currently being tested together with model function evaluation, NLME estimation, and trial simulation algorithms. It is designed to be a fairly easy transition from NONMEM®, but have a more modern structure and provide direct language support for expressing models with multiple responses, multiple
administration routes, non-Gaussian responses (categorical, time-to-event, and counting-process), gaussian responses with quantification limits, and differential equations. Arbitrary variable names for fixed and random effects and free-form syntax are used. A full set of simulation and table-generation capabilities is also supported. The language is designed to make it easy to incorporate fitted models into subsequent trial design simulations, as well as to facilitate covariate selection and optimization procedures.
Supported NLME algorithms include FO, FOCE, Laplacian, and a sophisticated nonparametric method based on modern primal-dual optimization methods. The model function evaluation algorithm for models expressed with differential equations can automatically recognize systems for which matrix exponentiation is appropriate. All NLME algorithms have been parallelized using MPI for multiprocessor execution of single jobs.
The syntax is designed so that it can be used stand-alone or in concert with scripts in the S-PLUS®
language.
Results: Example code will be displayed.
Poster: Methodology- Other topics
Iñaki F. Trocóniz Modelling Overdispersion and Markovian Features in Count
Data
Iñaki F. Trocóniz (1), Raymond Miller (2), Mats O. Karlsson (3)
1) Department of Pharmacy and Pharmaceutical Technology, School of Pharmacy; University of Navarra; Pamplona; Spain; (2) Pfizer Global Research and Development, Ann Arbor, MI 48108,
USA; (3) Division of Pharmacokinetics and Drug Therapy, Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Uppsala, Sweden
Background: The number of counts (events) per unit of time is a discrete response variable that is generally analyzed with the Poisson distribution (PS) model.[1] The PS model makes two
assumptions: the mean number of counts (lambda) is equal to the variance of the data, and the number of counts occurring in non-overlapping intervals of time are assumed independent.
However, many counting outcomes show greater variability than that predicted by the PS model, a phenomenon called overdispersion.[2] Moreover we are currently realizing that an increasing number of pharmacodynamic variables show a certain degree of interdependency between
neighbouring measurements, a feature that has been modelled incorporating Markovian elements.[3]
Objectives: To implement and explore, in the population context, different distribution models accounting for the overdispersion and Markovian patterns in the analysis of count data.
Methods: Daily seizure count data obtained from 551 subjects during the 12 weeks screening phase of a double-blind, placebo-controlled, parallel-group multicenter study performed in epileptic patients with medically refractory partial seizures, were used in the current investigation.
The following distribution models were fitted to the data to account for overdispersion:[2] (1) the Zero Inflated Poisson (ZIP), (2) the Inverse Binomial (INB), (3) the Zero Inflated Inverse Binomial, (ZINB), and (4) mixture models. The Markovian patterns were introduced estimating different lambdass and overdispersion parameters depending on whether the previous day was a seizure or non-seizure day. All analyses were performed with NONMEN VI.
Results: All were successfully implemented in NONMEM and all overdispersed models improved the fit in respect to the PS model. The INB model resulted in the best model fit to the data providing a minimum value of the objective function 7275 points lower than the PS model for six extra parameters. Including Markovian patterns in l and in the overdispersion parameter improved the fit significantly (P<0.0001). The typical population estimates of lambda if the previous day was a seizure or a non-seizure day were 0.53 and 0.32, respectively. For the case of the overdispersion parameter the values were 0.15, and 0.58, respectively.
Conclusions: The ZIP, INB, ZINB and mixture models were all capable of dealing with the overdispersion in count data and allowed the flexible incorporation of Markovian elements. They provide, in addition to the mean number of counts, additional possibilities to test
placebo/drug/disease progression effects such as the degree of overdispersion, and transition probabilities.
References:
response analysis of pregabalin add-on treatment of patients with refractory partial seizures.
Clinical Pharmacology & Therapeutics 73: 491-505 (2003)
[2] Slymen DJ, Ayala GX, Arredondo EM, Elder JP. A demostration of modeling count data with an application to physical activity. Epidemiologic Perspectives & Innovations 3: 1-9 (2006) [3] Karlsson MO, Schoemaker RC, Kemp B, Cohen AF, van Gerven JMA, Tuk B, Peck CC, Danhof M. A pharmacodynamic Markov mixed-effects model for the effect of temazepan on sleep.
Clinical Pharmacology & Therapeutics: 68
Poster: Methodology- Other topics
Clare Gaynor An assessment of prediction accuracy of two IVIVC modelling
methodologies.
Clare Gaynor (1), Adrian Dunne (1) and John Davis (2)
(1) UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (2) Clinical Pharmacology, Pfizer Global Research and Development, Sandwich, England Introduction: In Vitro - In Vivo Correlation (IVIVC) models are extensively used in the drug development process. The accuracy with which In Vitro observations can be used to predict an In
(1) UCD School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (2) Clinical Pharmacology, Pfizer Global Research and Development, Sandwich, England Introduction: In Vitro - In Vivo Correlation (IVIVC) models are extensively used in the drug development process. The accuracy with which In Vitro observations can be used to predict an In