Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients

The pharmacokinetics of methadone in adolescents undergoing posterior spinal fusion

BACKGROUND

The optimal methadone dosing regimen for children undergoing spinal surgery is uncertain because of sparse pediatric pharmacokinetic data and a paucity of analgesic effect data. The minimum effective analgesic concentration of methadone in opioid naïve adults is 58 mcg · L(-1).

METHODS

Adolescents aged 12-19 years undergoing idiopathic scoliosis correction were administered 0.25 mg · kg(-1) racemic methadone IV prior to surgical incision. Arterial blood samples for methadone assay were obtained at 0 min, 5 min, 10 min, 15 min, 20 min, 40 min, 1 h, 2 h, 4 h, 5 h, 6 h, 8 h, 10 h, 12 h, 24 h, and 48 h. Compartment analysis was undertaken using nonlinear mixed effects models. Parameter estimates were standardized to a 70-kg person using allometric models.

RESULTS

A three-compartment linear disposition model best described observed time-concentration profiles. Population parameter estimates (between-subjects variability) were central volume (V1) 19.1 (126%) L 70 kg(-1), peripheral volumes of distribution V2 65.5 (60%) L 70 kg(-1), V3 485 (23%) L 70 kg(-1), clearance (CL) 9.3 (11%) L · h(-1) · 70 kg(-1), and inter-compartment clearances Q2 282 (95%) L · h(-1) 70 kg(-1), Q3 139 (42%) L · h(-1) 70 kg(-1). The terminal elimination half-life was 44.4 h. The mean observed methadone concentration was <58 mcg · L(-1) by the first hour after administration.

CONCLUSIONS

Current pharmacokinetic parameter estimates in adolescents are similar to those reported in adults. Methadone undergoes rapid redistribution after bolus administration. This may result in plasma concentrations that provide inadequate analgesia postoperatively. We would suggest following the bolus (0.25 mg.kg(-1)) with an infusion (0.1-0.15 mg · kg(-1) · h(-1) for 4 h) during spinal surgery to ensure adequate plasma concentrations for 24 h.

Study reanalysis using a mechanism-based pharmacokinetic/pharmacodynamic model of pramlintide in subjects with type 1 diabetes

This report describes a pharmacokinetic/pharmacodynamic model for pramlintide, an amylinomimetic, in type 1 diabetes mellitus (T1DM). Plasma glucose and drug concentrations were obtained following bolus and 2-h intravenous infusions of pramlintide at three dose levels or placebo in 25 T1DM subjects during the postprandial period in a crossover study. The original clinical data were reanalyzed by mechanism-based population modeling. Pramlintide pharmacokinetics followed a two-compartment model with zero-order infusion and first-order elimination. Pramlintide lowered overall postprandial plasma glucose AUC (AUC(net)) and delayed the time to peak plasma glucose after a meal (T (max)). The delay in glucose T (max) and reduction of AUC(net) indicate that overall plasma glucose concentrations might be affected by differing mechanisms of action of pramlintide. The observed increase in glucose T (max) following pramlintide treatment was independent of dose within the studied dose range and was adequately described by a dose-independent, maximum pramlintide effect on gastric emptying of glucose in the model. The inhibition of endogenous glucose production by pramlintide was described using a sigmoidal function with capacity and sensitivity parameter estimates of 0.995 for I (max) and 23.8 pmol/L for IC(50). The parameter estimates are in good agreement with literature values and the IC(50) is well within the range of postprandial plasma amylin concentrations in healthy humans, indicating physiological relevance of the pramlintide effect on glucagon secretion in the postprandial state. This model may prove to be useful in future clinical studies of other amylinomimetics or antidiabetic drugs with similar mechanisms of action.

Application of a systems approach to the bottom-up assessment of pharmacokinetics in obese patients: expected variations in clearance

BACKGROUND AND OBJECTIVES

The maintenance dose of a drug is dependent on drug clearance, and thus any biochemical and physiological changes in obesity that affect parameters such as cardiac output, renal function, expression of drug-metabolizing enzymes and protein binding may result in altered clearance compared with that observed in normal-weight subjects (corrected or uncorrected for body weight). Because of the increasing worldwide incidence of obesity, there is a need for more information regarding the optimal dosing of drug therapy to be made available to prescribers. This is usually provided via clinical studies in obese people; however, such studies are not available for all drugs that might be used in obese subjects. Incorporation of the relevant physiological and biochemical changes into predictive bottom-up pharmacokinetic models in order to optimize dosage regimens may offer a logical way forward for the cases where no clinical data exist. The aims of the current report are to apply such a 'systems approach' to identify the likelihood of observing variations in the clearance of drugs in obesity and morbid obesity for a set of compounds for which clinical data, as well as the necessary in vitro information, are available, and to provide a framework for assessing other drugs in the future.

METHODS

The population-specific changes in demographic, physiological and biochemical parameters that are known to be relevant to obese and morbidly obese subjects were collated and incorporated into two separate population libraries. These libraries, together with mechanistic in vitro-in vivo extrapolations (IVIVE) within the Simcyp Population-based Simulator™, were used to predict the clearance of oral alprazolam, oral caffeine, oral chlorzoxazone, oral ciclosporin, intravenous and oral midazolam, intravenous phenytoin, oral theophylline and oral triazolam. The design of the simulated studies was matched as closely as possible with that of the clinical studies. Outcome was measured by the predicted ratio of the clearance of the drug in obese and lean subjects ± its 90% confidence interval, compared with observed values. The overall statistical measures of the performance of the model to detect differences in compound clearance between obese and lean populations were investigated by measuring sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV). A power calculation was carried out to investigate the impact of the sample size on the overall outcome of clinical studies.

RESULTS

The model was successful in predicting clearance in obese subjects, with the degree to which simulations could mimic the outcome of in vivo studies being greater than 60% for six of the eight drugs. A clear difference in the clearance of chlorzoxazone was correctly picked up via simulation. The overall statistical measures of the performance of the Simcyp Simulator were 100% sensitivity, 66% specificity, 60% PPV and 100% NPV. Studies designed on the basis of the ratio of the absolute values required substantial numbers of participants in order to detect a significant difference, except for phenytoin and chlorzoxazone, where the ratios of the weight-normalized clearances generally showed statistically significant differences with a smaller number of subjects.

CONCLUSION

Extension of a mechanistic predictive pharmacokinetic model to accommodate physiological and biochemical changes associated with obesity and morbid obesity allowed prediction of changes in drug clearance on the basis of in vitro data, with reasonable accuracy across a range of compounds that are metabolized by different enzymes. Prediction of the effects of obesity on drug clearance, normalized by various body size scalars, is of potential value in the design of clinical studies during drug development and in the introduction of dosage adjustments that are likely to be needed in clinical practice.

PKgraph: an R package for graphically diagnosing population pharmacokinetic models

Population pharmacokinetic (PopPK) modeling has become increasing important in drug development because it handles unbalanced design, sparse data and the study of individual variation. However, the increased complexity of the model makes it more of a challenge to diagnose the fit. Graphics can play an important and unique role in PopPK model diagnostics. The software described in this paper, PKgraph, provides a graphical user interface for PopPK model diagnosis. It also provides an integrated and comprehensive platform for the analysis of pharmacokinetic data including exploratory data analysis, goodness of model fit, model validation and model comparison. Results from a variety of modeling fitting software, including NONMEM, Monolix, SAS and R, can be used. PKgraph is programmed in R, and uses the R packages lattice, ggplot2 for static graphics, and rggobi for interactive graphics.

A fast method for testing covariates in population PK/PD Models

The development of covariate models within the population modeling program like NONMEM is generally a time-consuming and non-trivial task. In this study, a fast procedure to approximate the change in objective function values of covariate-parameter models is presented and evaluated. The proposed method is a first-order conditional estimation (FOCE)-based linear approximation of the influence of covariates on the model predictions. Simulated and real datasets were used to compare this method with the conventional nonlinear mixed effect model using both first-order (FO) and FOCE approximations. The methods were mainly assessed in terms of difference in objective function values (ΔOFV) between base and covariate models. The FOCE linearization was superior to the FO linearization and showed a high degree of concordance with corresponding nonlinear models in ΔOFV. The linear and nonlinear FOCE models provided similar coefficient estimates and identified the same covariate-parameter relations as statistically significant or non-significant for the real and simulated datasets. The time required to fit tesaglitazar and docetaxel datasets with 4 and 15 parameter-covariate relations using the linearization method was 5.1 and 0.5 min compared with 152 and 34 h, respectively, with the nonlinear models. The FOCE linearization method allows for a fast estimation of covariate-parameter relations models with good concordance with the nonlinear models. This allows a more efficient model building and may allow the utilization of model building techniques that would otherwise be too time-consuming.

Exploring the pharmacokinetics of oral ketamine in children undergoing burns procedures

AIMS

The aim of this study was to describe ketamine pharmacokinetics when administered orally to children suffering from burn injury in >10% body surface area.

METHODS

Children (n = 20) were given ketamine 5 or 10 mg·kg(-1) orally 20 min prior to presentation for surgical procedures. Anesthesia during procedures was maintained with a volatile anesthetic agent. Additional intravenous ketamine was given as a bolus (0.5-1 mg·kg(-1)) to nine children during the procedure while a further nine children were given an infusion (0.1 mg·kg(-1)·h(-1)) continued for 4-19 h after the procedure. Blood was assayed for ketamine and norketamine on six occasions over the study duration of 8-24 h. Data were pooled with those from an earlier analysis (621 observations from 70 subjects). An additional time-concentration profile from an adult given oral ketamine was gleaned from the literature (17 observations). A population analysis was undertaken using nonlinear mixed-effects models.

RESULTS

The pooled analysis comprised 852 observations from 91 subjects. There were 20 children who presented for procedures related to burns management (age 3.5 sd 2.1 years, range 1-8 years; weight 14.7 sd 4.9 kg, range 7.9-25 kg), and these children contributed 214 ketamine and norketamine observations. A two-compartment (central, peripheral) linear disposition model fitted data better than a one-compartment model. Bioavailability of the oral formulation was 0.45 (90% CI 0.33, 0.58). Absorption half-time was 59 (90% CI 29.4, 109.2) min and had high between-subject variability (BSV 148%). Population parameter estimates, standardized to a 70-kg person, were central volume 21.1 (BSV 47.1%) l·70 kg(-1), peripheral volume of distribution 109 (27.5%) l·70 kg(-1), clearance 81.3 (46.1%) l·h(-1)·70 kg(-1), and inter-compartment clearance 259 (50.1%) l·h(-1)·70 kg(-1). Under the assumption that all ketamine was converted to norketamine, the volume of the metabolite was 151.9 (BSV 39.1%) l·70 kg(-1) with an elimination clearance of 64.4 (BSV 63.4%) l·h(-1) ·70 kg(-1) and a rate constant for intermediate compartments of 26.2 (BSV 52.1%) h(-1)·70 kg(-1).

CONCLUSIONS

The ketamine pharmacokinetics in children with minor burns are similar to those without burns. The peak ratio of norketamine/ketamine at 1 h is 2.8 after oral administration allowing an analgesic contribution from the metabolite at this time. There is low relative bioavailability (<0.5) and slow variable absorption. Dose simulation in a child (3.5 years, 15 kg) suggests a dose regimen of oral ketamine 10 mg·kg(-1) followed by intravenous ketamine 1 mg·kg(-1) i.v. with the advent of short-duration surgical dressing change at 45 min.

PKreport: report generation for checking population pharmacokinetic model assumptions

BACKGROUND

Graphics play an important and unique role in population pharmacokinetic (PopPK) model building by exploring hidden structure among data before modeling, evaluating model fit, and validating results after modeling.

RESULTS

The work described in this paper is about a new R package called PKreport, which is able to generate a collection of plots and statistics for testing model assumptions, visualizing data and diagnosing models. The metric system is utilized as the currency for communicating between data sets and the package to generate special-purpose plots. It provides ways to match output from diverse software such as NONMEM, Monolix, R nlme package, etc. The package is implemented with S4 class hierarchy, and offers an efficient way to access the output from NONMEM 7. The final reports take advantage of the web browser as user interface to manage and visualize plots.

CONCLUSIONS

PKreport provides 1) a flexible and efficient R class to store and retrieve NONMEM 7 output, 2) automate plots for users to visualize data and models, 3) automatically generated R scripts that are used to create the plots; 4) an archive-oriented management tool for users to store, retrieve and modify figures, 5) high-quality graphs based on the R packages, lattice and ggplot2. The general architecture, running environment and statistical methods can be readily extended with R class hierarchy. PKreport is free to download at http://cran.r-project.org/web/packages/PKreport/index.html.

Population pharmacokinetics of ganciclovir after intravenous ganciclovir and oral valganciclovir administration in solid organ transplant patients infected with cytomegalovirus

A population pharmacokinetics analysis was performed after intravenous ganciclovir and oral valganciclovir in solid organ transplant patients with cytomegalovirus. Patients received ganciclovir at 5 mg/kg of body weight (5 days) and then 900 mg of valganciclovir (16 days), both twice daily with dose adjustment for renal function. A total of 382 serum concentrations from days 5 and 15 were analyzed with NONMEM VI. Renal function given by creatinine clearance (CL(CR)) was the most influential covariate in CL. The final pharmacokinetic parameters were as follows: ganciclovir clearance (CL) was 7.49.(CL(CR)/57) liter/h (57 was the mean population value of CL(CR)); the central and peripheral distribution volumes were 31.9 liters and 32.0 liters, respectively; intercompartmental clearance was 10.2 liter/h; the first-order absorption rate constant was 0.895 h(-1); bioavailability was 0.825; and lag time was 0.382 h. The CL(CR) was the best predictor of CL, making dose adjustment by this covariate important to achieve the most efficacious ganciclovir exposure.

Importance of shrinkage in empirical bayes estimates for diagnostics: problems and solutions

Empirical Bayes ("post hoc") estimates (EBEs) of etas provide modelers with diagnostics: the EBEs themselves, individual prediction (IPRED), and residual errors (individual weighted residual (IWRES)). When data are uninformative at the individual level, the EBE distribution will shrink towards zero (eta-shrinkage, quantified as 1-SD(eta (EBE))/omega), IPREDs towards the corresponding observations, and IWRES towards zero (epsilon-shrinkage, quantified as 1-SD(IWRES)). These diagnostics are widely used in pharmacokinetic (PK) pharmacodynamic (PD) modeling; we investigate here their usefulness in the presence of shrinkage. Datasets were simulated from a range of PK PD models, EBEs estimated in non-linear mixed effects modeling based on the true or a misspecified model, and desired diagnostics evaluated both qualitatively and quantitatively. Identified consequences of eta-shrinkage on EBE-based model diagnostics include non-normal and/or asymmetric distribution of EBEs with their mean values ("ETABAR") significantly different from zero, even for a correctly specified model; EBE-EBE correlations and covariate relationships may be masked, falsely induced, or the shape of the true relationship distorted. Consequences of epsilon-shrinkage included low power of IPRED and IWRES to diagnose structural and residual error model misspecification, respectively. EBE-based diagnostics should be interpreted with caution whenever substantial eta- or epsilon-shrinkage exists (usually greater than 20% to 30%). Reporting the magnitude of eta- and epsilon-shrinkage will facilitate the informed use and interpretation of EBE-based diagnostics.

Evaluation of the nonparametric estimation method in NONMEM VI: application to real data

The aim of the study was to evaluate the nonparametric estimation methods available in NONMEM VI in comparison with the parametric first-order method (FO) and the first-order conditional estimation method (FOCE) when applied to real datasets. Four methods for estimating model parameters and parameter distributions (FO, FOCE, nonparametric preceded by FO (FO-NONP) and nonparametric preceded by FOCE (FOCE-NONP)) were compared for 25 models previously developed using real data and a parametric method. Numerical predictive checks were used to test the appropriateness of each model. Up to 1000 new datasets were simulated from each model and with each method to construct 90% and 50% prediction intervals. The mean absolute error and the mean error of the different outcomes investigated were computed as indicators of imprecision and bias respectively and formal statistical tests were performed. Overall, less imprecision and less bias were observed with nonparametric methods than with parametric methods. Across the 25 models, t-tests revealed that imprecision and bias were significantly lower (P < 0.05) with FOCE-NONP than with FOCE for half of the NPC outcomes investigated. Improvements were even more pronounced with FO-NONP in comparison with FO. In conclusion, when applied to real datasets and evaluated by numerical predictive checks, the nonparametric estimation methods in NONMEM VI performed better than the corresponding parametric methods (FO or FOCE).

Population pharmacokinetics of high-dose methotrexate after intravenous administration in pediatric patients with osteosarcoma

The goal of this study was to establish the population pharmacokinetics (PK) of high-dose methotrexate (HD-MTX) treatment in children with osteosarcoma and to explore the influence of patient covariates and between-occasion variability on drug disposition. Patient covariates and concentration-time data were collected. PK data analysis from 209 HD-MTX cycles from 14 patients was performed using the population approach (NONMEM V). Internal and external validations were performed to confirm the model. PK of methotrexate was best described by a 2-compartment open PK model with first-order elimination from the central compartment. Between-subject variability (BSV) was included in total plasma clearance (CL) and in central compartment distribution volume (V1) [coefficient of variation (CV) 11.9% and 8.9%, respectively]. The CV of BSV in the residual error was 25.5%. Between-occasion variability was only retained for CL (CV 8.2%). RE consisted of a proportional error of 41.6%. Age and body weight in CL and body weight in V1 were identified as the appropriate covariates. The final estimates of total CL and V1 were given by the equations CL = 88.5.(AGE/15) + 27.4 x (WGT/50) L/d and V1 = 11.0 + 5.6 x (WGT/50) L, respectively. Internal validation results showed that the 95% confidence interval covered all the observed MTX concentrations. Mean bias and precision of the individual predicted concentrations, calculated in a validation dataset, resulted in -1.36% and 19.71%, respectively. A population PK model was developed for HD-MTX in children with osteosarcoma. Validation studies confirmed the suitability of the model for further dose individualization by means of a Bayesian approach.

Population pharmacokinetics of atazanavir in human immunodeficiency virus-infected patients

The aim of this study was to determine the population pharmacokinetic (PK) parameters of atazanavir in adult human immunodeficiency virus-infected patients to build up a Bayesian strategy for dosage regimen individualization. This was an observational study of patients treated with the once-daily regimen atazanavir associated with 100 mg of ritonavir. Blood samples were drawn at steady state at various times ranging from 1 to 26 hours postdose. Atazanavir plasma concentrations were determined by a validated reverse-phase high-performance liquid chromatography method. PK analysis of the atazanavir population was performed using a nonlinear mixed-effects model (NONMEM version 6). One hundred eighty-seven patients were included in the study. The atazanavir doses prescribed were 300 mg (n = 169), 400 mg (n = 12), 200 mg (n = 1), and 150 mg (n = 5). The atazanavir population PK was described using a 1-compartment model with first-order absorption. Mean PK parameter estimations (95% confidence interval, coefficients of variation %) were as follows: oral clearance (CL) = 7.6 L/h (6.9-8.3; 34%), volume of distribution (V) = 80.8 L (67.4-94; 37%), and absorption constant rate (Ka) = 1.05 hours (0.01-2.09; 156%). The mean estimated half-life (T-half) was 7.5 hours (95% confidence interval: 7.2 -7.8 hours). The estimated T-half of atazanavir was in agreement with that previously reported of 8.6 and 8.8 hours. We observed a wide interpatient variability for the PK parameters, especially for Ka. This population approach allowed us to determine atazanavir PK parameters in human immunodeficiency virus-infected patients in a real-life context and to perform Bayesian analysis to predict Ctrough from samples collected at any moment during the dosing interval. This could therefore improve therapeutic drug monitoring interpretations and provide an interesting tool for correlation with virologic data.

Population pharmacokinetic analysis of voriconazole plasma concentration data from pediatric studies

Voriconazole is a potent triazole with broad-spectrum antifungal activity against clinically significant and emerging pathogens. The present population pharmacokinetic analysis evaluated voriconazole plasma concentration-time data from three studies of pediatric patients of 2 to <12 years of age, incorporating a range of single or multiple intravenous (i.v.) and/or oral (p.o.) doses. An appropriate pharmacokinetic model for this patient population was created using the nonlinear mixed-effect modeling approach. The final model described voriconazole elimination by a Michaelis-Menten process and distribution by a two-compartment model. It also incorporated a statistically significant (P < 0.001) influence of the CYP2C19 genotype and of the alanine aminotransferase level on clearance. The model was used in a number of deterministic simulations (based on various fixed, mg/kg of body weight, and individually adjusted doses) aimed at finding suitable i.v. and p.o. voriconazole dosing regimens for pediatric patients. As a result, 7 mg/kg twice a day (BID) i.v. or 200 mg BID p.o., irrespective of body weight, was recommended for this patient population. At these doses, the pediatric area-under-the-curve (AUC) distribution exhibited the least overall difference from the adult AUC distribution (at dose levels used in clinical practice). Loading doses or individual dosage adjustments according to baseline covariates are not considered necessary in administering voriconazole to children.

Population pharmacokinetic and pharmacodynamic modelling of the effects of nicorandil in the treatment of acute heart failure

AIMS

The aims of the study were 1) to evaluate the pharmacokinetics of nicorandil in healthy subjects and acute heart failure (AHF) patients and 2) to evaluate the exposure-response relationship with pulmonary arterial wedge pressure (PAWP) in AHF patients and to predict an appropriate dosing regimen for nicorandil.

METHODS

Based on the data from two healthy volunteer and three AHF patient studies, models were developed to characterize the pharmacokinetics and pharmacodynamics of nicorandil. PAWP was used as the pharmacodynamic variable. An asymptotic exponential disease progression model was used to account for time dependent changes in PAWP that were not explained by nicorandil exposure. The modelling was performed using NONMEM version V.

RESULTS

The pharmacokinetics of nicorandil were characterized by a two-compartment model with linear elimination. CL, V1 and V2 in AHF patients were 1.96, 1.39 and 4.06 times greater than in healthy subjects. Predicted plasma concentrations were assumed to have an immediate concentration effect relationship on PAWP. An inhibitory E(max) model with E(max) of -11.7 mmHg and EC(50) of 423 microg l(-1) was considered the best relationship between nicorandil concentrations and PAWP. PAWP decreased independently of nicorandil exposure. This drug independent decline was described by an asymptotic decrease of 6.1 mmHg with a half-life of 5.3 h.

CONCLUSIONS

AHF patients have higher clearance and initial distribution volume of nicorandil compared with healthy subjects. The median target nicorandil concentration to decrease PAWP by 30% is predicted to be 748 microg l(-1), indicating that a loading dose of 200 microg kg(-1) and a maintenance dose of 400 microg kg(-1) h(-1) would be appropriate for the initial treatment of AHF.

Does saturable formation of gemcitabine triphosphate occur in patients?

AIM

This study aims to determine if intracellular formation of gemcitabine triphosphate (dFdCTP), an active metabolite of gemcitabine, is saturable at doses used for treatment of Asian patients with lung cancer.

METHODS

From a phase II trial, plasma concentrations of gemcitabine, its inactive metabolite 2'-2'-difluorodeoxyuridine (dFdU), and mononuclear cell concentrations of gemcitabine-triphosphate were measured in 56 and 33 patients, respectively. The pharmacokinetics of gemcitabine and metabolites were modeled using nonlinear mixed effects modeling (NONMEM). A reduced dataset of ten randomly selected patients was employed to compare first-order and saturable formation of dFdCTP from gemcitabine.

RESULTS

The median population clearance estimate for dFdCTP formation with the full dataset was 70.2 L/h/70 kg/1.7 m. Modeling Michaelis-Menten formation of dFdCTP on a reduced dataset estimated K(m) to be 3.6 times higher than the maximum gemcitabine concentration (72.2 microM) measured in this study.

CONCLUSIONS

The results showed that first-order and nonsaturable clearance described intracellular dFdCTP formation at clinically applied doses of gemcitabine.

Diagnosing model diagnostics

Conclusions from clinical trial results that are derived from model-based analyses rely on the model adequately describing the underlying system. The traditionally used diagnostics intended to provide information about model adequacy have seldom discussed shortcomings. Without an understanding of the properties of these diagnostics, development and use of new diagnostics, and additional information pertaining to the diagnostics, there is risk that adequate models will be rejected and inadequate models accepted. Thus, a diagnosis of available diagnostics is desirable.

Overview of model-building strategies in population PK/PD analyses: 2002-2004 literature survey

AIMS

A descriptive survey of published population pharmacokinetic and/or pharmacodynamic (PK/PD) analyses from 2002 to 2004 was conducted and an evaluation made of how model building was performed and reported.

METHODS

We selected 324 articles in Pubmed using defined keywords. A data abstraction form (DAF) was then built comprising two parts: general characteristics including article identification, context of the analysis, description of clinical studies from which the data arose, and model building, including description of the processes of modelling. The papers were examined by two readers, who extracted the relevant information and transmitted it directly to a MySQL database, from which descriptive statistical analysis was performed.

RESULTS

Most published papers concerned patients with severe pathology and therapeutic classes suffering from narrow therapeutic index and/or high PK/PD variability. Most of the time, modelling was performed for descriptive purposes, with rich rather than sparse data and using NONMEM software. PK and PD models were rarely complex (one or two compartments for PK; E(max) for PD models). Covariate testing was frequently performed and essentially based on the likelihood ratio test. Based on a minimal list of items that should systematically be found in a population PK-PD analysis, it was found that only 39% and 8.5% of the PK and PD analyses, respectively, published from 2002 to 2004 provided sufficient detail to support the model-building methodology.

CONCLUSIONS

This survey allowed an efficient description of recent published population analyses, but also revealed deficiencies in reporting information on model building.

Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies

PURPOSE

To compare the performance of the standard lag time model (LAG model) with the performance of an analytical solution of the transit compartment model (TRANSIT model) in the evaluation of four pharmacokinetic studies with four different compounds.

METHODS

The population pharmacokinetic analyses were performed using NONMEM on concentration-time data of glibenclamide, furosemide, amiloride, and moxonidine. In the TRANSIT model, the optimal number of transit compartments was estimated from the data. This was based on an analytical solution for the change in drug concentration arising from a series of transit compartments with the same first-order transfer rate between each compartment. Goodness-of-fit was assessed by the decrease in objective function value (OFV) and by inspection of diagnostic graphs.

RESULTS

With the TRANSIT model, the OFV was significantly lower and the goodness-of-fit was markedly improved in the absorption phase compared with the LAG model for all drugs. The parameter estimates related to the absorption differed between the two models while the estimates of the pharmacokinetic disposition parameters were similar.

CONCLUSION

Based on these results, the TRANSIT model is an attractive alternative for modeling drug absorption delay, especially when a LAG model poorly describes the drug absorption phase or is numerically unstable.

Conditional Weighted Residuals (CWRES): A Model Diagnostic for the FOCE Method

PURPOSE

Population model analyses have shifted from using the first order (FO) to the first-order with conditional estimation (FOCE) approximation to the true model. However, the weighted residuals (WRES), a common diagnostic tool used to test for model misspecification, are calculated using the FO approximation. Utilizing WRES with the FOCE method may lead to misguided model development/evaluation. We present a new diagnostic tool, the conditional weighted residuals (CWRES), which are calculated based on the FOCE approximation.

MATERIALS AND METHODS

CWRES are calculated as the FOCE approximated difference between an individual's data and the model prediction of that data divided by the root of the covariance of the data given the model.

RESULTS

Using real and simulated data the CWRES distributions behave as theoretically expected under the correct model. In contrast, in certain circumstances, the WRES have distributions that greatly deviate from the expected, falsely indicating model misspecification. CWRES/WRES comparisons can also indicate if the FOCE estimation method will improve the results of an FO model fit to data.

CONCLUSIONS

Utilization of CWRES could improve model development and evaluation and give a more accurate picture of if and when a model is misspecified when using the FO or FOCE methods.

Population pharmacokinetics of S(-)-carvedilol in healthy volunteers after administration of the immediate-release (IR) and the new controlled-release (CR) dosage forms of the racemate

Carvedilol is a beta(1)-, beta(2)-, and alpha(1)-adrenoreceptor blocker indicated for treatment of hypertension and mild-to-severe congestive heart failure. The objective of this study was to develop and evaluate a single population model that describes S(-)-carvedilol pharmacokinetics from both the immediate-release (IR) and the new controlled-release dosage forms of the racemate. Carvedilol IR data (1270 measurements) were obtained from 2 open-label studies (50 mg/25 mg Q12 hours for 2 doses). Carvedilol CR data (2058 measurements) were obtained from an open-label, nonrandomized, dose-rising (10, 20, 40, and 80 mg), 4-period balanced crossover study. All data were simultaneously analyzed using NONMEM V. Leverage analysis and internal evaluations were conducted for the final model. A 2-compartment model with first-order absorption and elimination provided the best fit. The model included different absorption rates (KAs) for the CR and IR morning (IR(AM)) and evening (IR(PM)) doses; incorporating change-points at certain times. Estimates of KAs indicated that the absorption was slower at equivalent times and extended for CR relative to IR carvedilol. Oral clearance of S(-)-carvedilol was 149 L/h. The IR(PM) and the CR doses had bioavailability (F(rel)) of 0.80 and 0.76, respectively, relative to the IR(AM) dose. The inter-subject variability in KAs was lower for the CR dosage form than the original IR dosage form. Estimation of interoccasion variability on KAs and F(rel) for the CR dosage form improved the fit. The model performed well in simulation and leverage analysis indicated its robustness. The model will be a useful tool for future simulation studies.

A matlab framework for estimation of NLME models using stochastic differential equations

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Minimal effect of MDR1 and CYP3A5 genetic polymorphisms on the pharmacokinetics of indinavir in HIV-infected patients

AIMS

The protease inhibitor indinavir is characterized by an important interindividual pharmacokinetic variability, which results from the actions of the metabolizing enzymes cytochrome P450 (CYP) 3A and the multidrug efflux pump P-glycoprotein (P-gp), encoded by MDR1. Using a population pharmacokinetic approach, we investigated the effect of several MDR1 and CYP3A5 polymorphisms on the pharmacokinetic parameters of indinavir in HIV-infected patients.

METHODS

Twenty-eight patients receiving indinavir alone or together with ritonavir were included. Indinavir pharmacokinetics were studied over a 12 h interval. Genetic polymorphisms were assessed by real-time PCR assays and direct sequencing for MDR1 and by PCR-SSCP analysis for CYP3A5.

RESULTS

The pharmacokinetics of indinavir were best described by a one-compartment model with first-order absorption. In the final model, the MDR1 C3435T genotype and ritonavir were identified as statistically significant covariates (P </= 0.001) for the absorption rate constant (95% confidence interval on the difference between CC and CT genotype 0.37, 5.53) and for clearance (95% confidence interval on the difference 5.8, 26.2), respectively. Patients with the CYP3A5*3/*3 genotype receiving indinavir alone had a 31% decrease in the indinavir clearance rate compared with patients carrying the CYP3A5*1/*3 genotype.

CONCLUSIONS

The MDR1 C3435T genotype affects the absorption constant of indinavir suggesting that P-gp may be implicated in its pharmacokinetic variability. Through its inhibition of CYP3A and P-gp, ritonavir could attenuate the pharmacokinetic variability linked to genetic differences, reducing significantly the interindividual variability of indinavir. However, genotyping MDR1 and/or CYP3A5 to optimize protease inhibitor boosted regimens does not seem clinically relevant.

Randomized exposure-controlled trials; impact of randomization and analysis strategies

AIMS

In the literature, five potential benefits of randomizing clinical trials on concentration levels, rather than dose, have been proposed: (i) statistical study power will increase; (ii) study power will be less sensitive to high variability in the pharmacokinetics (PK); (iii) the power of establishing an exposure-response relationship will be robust to correlations between PK and pharmacodynamics (PD); (iv) estimates of the exposure-response relationship are likely to be less biased; and (v) studies will provide a better control of exposure in situations with toxicity issues. The main aim of this study was to investigate if these five statements are valid when the trial results are evaluated using a model-based analysis.

METHODS

Quantitative relationships between drug dose, concentration, biomarker and clinical end-point were defined using pharmacometric models. Three randomization schemes for exposure-controlled trials, dose-controlled (RDCT), concentration-controlled (RCCT) and biomarker-controlled (RBCT), were simulated and analysed according to the models.

RESULTS

(i) The RCCT and RBCT had lower statistical power than RDCT in a model-based analysis; (ii) with a model-based analysis the power for an RDCT increased with increasing PK variability; (iii) the statistical power in a model-based analysis was robust to correlations between CL and EC(50) or E(max); (iv) under all conditions the bias was negligible (<3%); and (v) for studies with equal power RCCT could produce either more or fewer adverse events compared with an RDCT.

CONCLUSION

Alternative randomization schemes may not have the proposed advantages if a model-based analysis is employed.

Assessment of the validity of a population pharmacokinetic model for epirubicin

AIMS

The aim of this study was to evaluate a population model for epirubicin clearance using internal and external validation techniques.

METHODS

Jackknife samples were used to identify outliers in the population dataset and individuals influencing covariate selection. Sensitivity analyses were performed in which serum aspartate transaminase (AST) values (a covariate in the population model) or epirubicin concentrations were randomly changed by +/-10%. Cross-validation was performed five times, on each occasion using 80% of the data for model development and 20% to assess the performance of the model. External validation was conducted by assessing the ability of the population model to predict concentrations and clearances in a separate group of 79 patients.

RESULTS

Structural parameter estimates from all jackknife samples were within 7.5% of the final population estimates and examination of log likelihood values indicated that the selection of AST in the final model was not due to the presence of outliers. Alteration of AST or epirubicin concentrations by +/-10% had a negligible effect on population parameter estimates and their precision. In the cross-validation analysis, the precision of clearance estimates was better in patients with AST concentrations>150 U l-1. In the external validation, epirubicin concentrations were over-predicted by 81.4% using the population model and clearance values were also poorly predicted (imprecision 43%).

CONCLUSIONS

The results of internal validation of population pharmacokinetic models should be interpreted with caution, especially when the dataset is relatively small.

A Bayesian Design and Analysis for Dose-Response Using Informative Prior Information

We wish to use prior information on an existing drug in the design and analysis of a dose-response study for a new drug candidate within the same pharmacological class. Using the Bayesian methodology, this prior information can be used quantitatively and the randomization can be weighted in favor of the new compound, where there is less information. An Emax model is used to describe the dose-response of the existing drug. The estimates from this model are used to provide informative prior information used for the design and analysis of the new study to establish the relative potency between the new compound and the existing drug therapy. The assumption is made that the data from previous trials and the new study are exchangeable. The impact of departures from this assumption can be quantified through simulations and by assessing the operating characteristics of various scenarios. Simulations show that relatively modest sample sizes can yield informative results about the magnitude of the relative potency using this approach. The operating characteristics are good when assessing model estimates against clinically important changes in relative potency.

Population pharmacokinetics of ceftriaxone and pharmacodynamic considerations in haemodialysed patients

OBJECTIVES

To determine the pharmacokinetic parameters of ceftriaxone following an infusion in haemodialysed outpatients and to use these parameters for an optimisation of dosing based on pharmacodynamic indices.

METHODS

Fifty haemodialysed patients were enrolled in a single-centre, prospective, open-label study. They received short intravenous infusions of ceftriaxone 1 or 2 g every 48 hours for bronchopneumonia immediately after the dialysis session. Total plasma concentrations of ceftriaxone were analysed with a population pharmacokinetic approach using nonlinear mixed-effects modelling. Free drug concentrations were derived from published binding parameters in order to estimate the time when they exceed the minimum inhibitory concentration (MIC).

RESULTS

The pharmacokinetics were best described by a two-compartment model. None of the covariates tested (age, bodyweight, height, sex, body mass index, albumin) influenced the pharmacokinetic parameters. The estimated population pharmacokinetic parameters (interindividual variability [percentage of coefficient of variation]) were clearance 0.36 L/h (48%), volume of distribution of the central compartment 4.53 L (47%), intercompartmental clearance 10.8 L/h and volume of distribution of the peripheral compartment 9.54 L (63%). The terminal elimination half-life (t(1/2)beta) from plasma was 27.5 hours. The mean (range) times when the free drug concentration exceeded the MIC (T>MIC) following ceftriaxone 1 g infusion were 60.3 (53.0-67.7) hours and 2.5 (1.0-3.9) hours for the breakpoints 1 and 8 mg/L (based on free drug concentration), respectively. After administration of ceftriaxone 2 g, the T>MIC was 88.5 (78.8-98.3) hours and 17.7 (13.3-22.0) hours for the breakpoints 1 and 8 mg/L, respectively. The simulated free drug concentrations (median, first and third quartile) for 48 and 72 hours following the first dose of ceftriaxone 1g were 1.11, 0.63 and 1.89 mg/L, and 0.63, 0.28 and 1.18 mg/L, respectively. For ceftriaxone 2g infusion, the simulated free concentrations (median, first and third quartile) at 48 and 72 hours were 2.50, 1.40 and 4.52 mg/L, and 1.37, 0.60 and 2.70 mg/L, respectively.

CONCLUSIONS

On the basis of decreased clearance in haemodialysed patients, it can be argued that the dose of ceftriaxone should be decreased or the delay between doses should be increased. However, taking into account pharmacodynamic considerations, this study showed that following intravenous administration of ceftriaxone 1 g after each dialysis session, some patients were at risk of achieving a concentration below the MIC (1 mg/L), particularly if the second administration occurred 72 hours after the first dosing. Thus, a dose of ceftriaxone 2 g intravenously is recommended immediately following dialysis, particularly in patients with severe infections or when the dosing interval will be higher than 48 hours.

Apparent Clearance of Sirolimus in Heart Transplant Recipients: Impact of Primary Diagnosis and Serum Lipids

The study was aimed to identify factors affecting sirolimus apparent clearance (CL/F) in de novo heart transplant recipients using a population pharmacokinetic approach. A total of 31 patients (7 female and 24 male) originally included in a formal clinical trial, contributed 524 sirolimus blood concentrations with the time after dose ranging from 11.08 to 31.83 hours. Sirolimus concentrations were measured using liquid chromatography-tandem mass spectrometry and data analysis was carried out using NONMEM (Globomax LLC, Hanover, MD) software. Factors screened included age, weight, gender, primary diagnosis, biochemical and hematological indices, cyclosporine dose, days post-transplant and potential interacting medications. The predictive performance of the final model was evaluated using a data-splitting method. Sirolimus apparent clearance (CL/F) was decreased by 20.8% for every 100-mg increase in cyclosporine daily dose and was 62.1% lower in patients with primary diagnosis of ischemic heart disease (IHD). Sirolimus apparent clearance was 37.8% lower when triglyceride was greater than 2 mmol/L. Based on the final model, the average values for sirolimus CL/F and apparent volume of distribution were 7.09 and 1,350 L/h, respectively. Inter-subject variability in CL/F was 27.5% and residual random error was 24.1%. This study identified cyclosporine dose, hypertriglyceridemia and primary diagnosis of IHD as the most important factors affecting sirolimus CL/F. This information may assist in dose individualization of sirolimus in transplant recipients.

The population pharmacokinetics of citalopram after deliberate self-poisoning: a Bayesian approach

Defining the pharmacokinetics of drugs in overdose is complicated. Deliberate self-poisoning is generally impulsive and associated with poor accuracy in dose history. In addition, early blood samples are rarely collected to characterize the whole plasma-concentration time profile and the effect of decontamination on the pharmacokinetics is uncertain. The aim of this study was to explore a fully Bayesian methodology for population pharmacokinetic analysis of data that arose from deliberate self-poisoning with citalopram. Prior information on the pharmacokinetic parameters was elicited from 14 published studies on citalopram when taken in therapeutic doses. The data set included concentration-time data from 53 patients studied after 63 citalopram overdose events (dose range: 20-1700 mg). Activated charcoal was administered between 0.5 and 4 h after 17 overdose events. The clinical investigator graded the veracity of the patients' dosing history on a 5-point ordinal scale. Inclusion of informative priors stabilised the pharmacokinetic model and the population mean values could be estimated well. There were no indications of non-linear clearance after excessive doses. The final model included an estimated uncertainty of the dose amount which in a simulation study was shown to not affect the model's ability to characterise the effects of activated charcoal. The effect of activated charcoal on clearance and bioavailability was pronounced and resulted in a 72% increase and 22% decrease, respectively. These findings suggest charcoal administration is potentially beneficial after citalopram overdose. The methodology explored seems promising for exploring the dose-exposure relationship in the toxicological settings.

Population Pharmacokinetics of Allopurinol in Full-Term Neonates With Perinatal Asphyxia

In newborn infants, allopurinol is being tested as a free radical scavenger to prevent brain damage caused by reperfusion and oxygenation after perinatal hypoxia and ischemia (birth asphyxia). To develop rational dosing schemes for future studies, knowledge of the pharmacokinetics in this patient group is essential. In the present study, a population pharmacokinetic model was designed and validated for allopurinol in this specific patient group. One-compartment and 2-compartment models were fitted to plasma concentration time data of 24 newborns entered in 2 clinical trials using nonlinear mixed effects modeling. A bootstrap procedure was performed to check the robustness of the model. The data were best described using a 1-compartment model with linear elimination. Estimated pharmacokinetic parameters were volume of the central compartment (V, 0.79 L/kg) and total body clearance (CL, 0.078 L/h/kg), with 42% and 60% interindividual variability, respectively. The median values for these parameters of 1000 bootstrap replicates were very similar (95% confidence intervals were 0.67 to 0.96 and 0.054 to 0.10 for V and CL, respectively), indicating the robustness of the model. A population pharmacokinetic model has been designed and validated which adequately describes the data of 2 clinical studies in critically ill newborn infants. The model will be used to design dosing strategies for future evaluation of the benefits of allopurinol in these patients.

Population pharmacokinetic estimation of tacrolimus apparent clearance in adult liver transplant recipients

The goal was to study the factors affecting tacrolimus apparent clearance (CL/F) in adult liver transplant recipients. Tacrolimus dose and concentration data (n = 694) were obtained from 67 liver transplant recipients (22 female and 45 male), and the data were analyzed using a nonlinear mixed-effect modeling (NONMEM) method. A 1-compartment pharmacokinetic model with first-order elimination, an absorption rate constant fixed at 4.5 hours, and first-order conditional estimation was used to describe tacrolimus disposition. The predictive performance of the final model was evaluated using data splitting and assessing bias and precision of the estimates. The population estimate of tacrolimus CL/F and apparent volume of distribution (V/F) were found to be 21.3 L/h (95% confidence interval, CI, 18.0-24.6 L/h) and 316.1 L (95% CI 133-495 L), respectively. Neither patient's age, weight, gender, nor markers of liver function influenced tacrolimus CL/F. The final model was TVCL = 21.3 + 9.8 x (1 - HEM) + 3.4 x (1 - ALB) - 2.1 x (1 - DIL) - 7.4 x (1 - FLU), where TVCL, typical estimate of apparent clearance, HEM = 0 if hematocrit <35%, otherwise 1; ALB = 0 if albumin <3.5 g/dL, otherwise 1; DIL = 0 if diltiazem is coadministered, otherwise 1; FLU = 0 if fluconazole is coadministered, otherwise 1. This study identified the factors that significantly affect tacrolimus disposition in adult liver transplant recipients during the early posttransplantation period. This information will be helpful to clinicians for dose individualization of tacrolimus in liver transplant recipients with different clinical conditions including anemia or hypoalbuminemia or in those patients receiving diltiazem or fluconazole.

Population pharmacokinetics of indinavir alone and in combination with ritonavir in HIV-1-infected patients

AIMS

The aim of the study was to characterize the population pharmacokinetics of indinavir, define the relationship between the pharmacokinetics of indinavir and ritonavir, and to identify the factors influencing the pharmacokinetics of indinavir alone or when given with ritonavir.

METHODS

HIV-1-infected patients being treated with an indinavir-containing regimen were included. During regular visits, 102 blood samples were collected for the determination of plasma indinavir and ritonavir concentrations. Full pharmacokinetic curves were available from 45 patients. Concentrations of indinavir and ritonavir were determined by liquid chromatography coupled with electrospray tandem mass spectrometry. Pharmacokinetic analysis was performed using nonlinear mixed effect modelling (NONMEM).

RESULTS

The disposition of indinavir was best described by a single compartment model with first order absorption and elimination. Values for the clearance, volume of distribution and the absorption rate constant were 46.8 l h(-1) (24.2% IIV), 82.3 l (24.6% IIV) and 02.62 h(-1), respectively. An absorption lag-time of 0.485 h was detected in patients also taking ritonavir. Furthermore this drug, independent of dose (100-400 mg) or plasma concentration, decreased the clearance of indinavir by 64.6%. In contrast, co-administration of efavirenz or nevirapine increased the clearance of indinavir by 41%, irrespective of the presence or absence of ritonavir. Female patients had a 48% higher apparent bioavailability of indinavir than males.

CONCLUSIONS

The pharmacokinetic parameters of indinavir were adequately described by our population model. Female gender and concomitant use of ritonavir and non-nucleoside reverse transcriptase inhibitors strongly influenced the pharmacokinetics of this drug. The results support the concept of ritonavir boosting, maximum inhibition of indinavir metabolized being observed at 100 mg.

Conditioning on Certain Random Events Associated with Statistical Variability in PK/PD

In PK/PD data analysis, statistical models involving random variables are developed. At times an analysis can be carried out by conditioning on certain random events involving these variables. This paper attempts to clarify issues regarding conditioning. In particular, conditioning is examined as it relates to a number of disparate practical matters: missing covariate values, dose titration, BQL data, "no change from baseline" data, and the use of a truncated intraindividual probability distribution for PK observations.

Recommended reading in population pharmacokinetic pharmacodynamics

Developing the skills or expertise to create useful population pharmacokinetic-pharmacodynamic models can be a daunting task-the level of mathematical and statistical complexity is such that newcomers to the field are frequently overwhelmed. A good place to start in learning the field is to read articles in the literature. However, the number of articles dealing with population pharmacokinetic pharmacodynamics is exponentially increasing on a yearly basis, so choosing which articles to read can be difficult. The purpose of this review is to provide a recommended reading list for newcomers to the field. The list was chosen based on perceived impact of the article in the field, the quality of the article, or to highlight some important detail contained within the article. After reading the articles in the list, it is believed that the reader will have a broad overview of the field and have a sound foundation for more-detailed reading of the literature.

Population pharmacokinetics of cyclosporine in cardiopulmonary transplant recipients

A population pharmacokinetic analysis of cyclosporine (CsA) was performed, and the influence of covariates on CsA oral clearance and relative bioavailability was investigated. Data from 48 recipients of heart-lung (n = 21) or single (n = 18) or double (n = 9) lung transplant were included in the study. Patients received oral CsA as either a conventional formulation (Sandimmune) or a microemulsion (Neoral). Steady-state CsA concentrations were measured before and at approximately 2 and 6 hours after the morning dose of CsA at the end of weeks 1, 2, 3, 4, 13, 26, 39, and 52 posttransplantation. A total of 1004 CsA concentration observations were analyzed using mixed effects-modeling (NONMEM). A 1-compartment pharmacokinetic model and first-order oral absorption were used to fit the data. The absorption rate constants were fixed at 0.25 L/h for Sandimmune and 1.35 L/h for Neoral formulations. Oral clearance (CL/F) was estimated to be 22.1 L/h (95% confidence intervals [CI] 19.5-24.7 L/h). Itraconazole (ITRA), cystic fibrosis (CF), and weight (WT) were identified as significant covariates for CL/F according to the final model: CL/F = 22.1 - 11.3 x ITRA + 23.5 x CF + 0.129 x (WT - 58.7) L/h; where ITRA = 1 if the patient was taking concomitant itraconazole, otherwise 0; CF = 1 if the patient had cystic fibrosis, otherwise CF = 0; and WT is patient weight in kilograms. The relative oral bioavailability of Sandimmune to Neoral was 0.82. The bioavailability of both preparations increased during the first month posttransplantation. Age, gender, and type of transplant (single, double, or heart-lung) were not identified as significant covariates for CsA clearance. The population pharmacokinetic model developed identified some sources of variability in CsA pharmacokinetics; however, an appreciable degree of variability is still present in this patient population.

Development and validation of a population pharmacokinetic model for ritonavir used as a booster or as an antiviral agent in HIV-1-infected patients

AIMS

The aim of this study was to develop and validate a population pharmacokinetic model of ritonavir, used as an antiviral agent or as a booster, in a large patient population and to identify factors influencing its pharmacokinetics.

METHODS

Ambulatory HIV-1-infected patients from the outpatient clinic of the Slotervaart Hospital, Amsterdam, the Netherlands, who were being treated with a ritonavir-containing regimen were included. During regular visits, blood samples were collected for the determination of ritonavir plasma concentrations and several clinical chemistry parameters. Furthermore, complete pharmacokinetic curves were available in some patients. Single and multiple compartment models with zero-order and first-order absorption, with and without absorption lag-time, with linear and nonlinear elimination were tested, using nonlinear mixed effect modelling (NONMEM). Pharmacokinetic parameters and interindividual, interoccasion and residual variability were estimated. In addition, the influence of several factors (e.g. patient characteristics, comedication) on the pharmacokinetics of ritonavir was explored.

RESULTS

From 186 patients 505 ritonavir plasma concentrations at a single time-point and 55 full pharmacokinetic profiles were available, resulting in a database of 1228 plasma ritonavir concentrations. In total 62% of the patients used ritonavir as a booster of their protease inhibitor containing antiretroviral regimen. First order absorption in combination with one-compartment disposition best described the pharmacokinetics of ritonavir. Clearance, volume of distribution and absorption rate constant were 10.5 l h(-1) (95% prediction interval (95% PI) 9.38-11.7), 96.6 l (95% PI 67.2-121) and 0.871 h(-1) (95% PI 0.429-1.47), respectively, with 38.3%, 80.0% and 169% interindividual variability, respectively. The interoccasion variability in the apparent bioavailability was 59.1%. The concomitant use of lopinavir resulted in a 2.7-fold increase in the clearance of ritonavir (P value < 0.001). No patients characteristics influenced the pharmacokinetics of ritonavir.

CONCLUSIONS

The pharmacokinetic parameters of ritonavir were adequately described by our population pharmacokinetic model. Concomitant use of the protease inhibitor lopinavir strongly influenced the pharmacokinetics of ritonavir. The model has been validated and can be used for further investigation of the interaction between ritonavir and other protease inhibitors.

Bayesian estimation of cyclosporin exposure for routine therapeutic drug monitoring in kidney transplant patients

AIMS

AUC-based monitoring of cyclosporin A (CsA) is useful to optimize dose adaptation in difficult cases. We developed a population pharmacokinetic model to describe dose-exposure relationships for CsA in renal transplant patients and applied it to the Bayesian estimation of AUCs using three blood concentrations.

METHODS

A total of 84 renal graft recipients treated with CsA microemulsion were included in this study. Population pharmacokinetic analysis was conducted using NONMEM. A two-compartment model with zero-order absorption and a lag time best described the data. Bayesian estimation was based on CsA blood concentrations measured before dosing and 1 h and 2 h post dose. Predictive performance was evaluated using a cross-validation approach. Estimated AUCs were compared with AUCs calculated by the trapezoidal method. The Bayesian approach was also applied to an independent group of eight patients exhibiting unusual pharmacokinetic profiles.

RESULTS

Mean population pharmacokinetic parameters were apparent clearance 30 l h(-1), apparent volume of distribution 79.8 l, duration of absorption 52 min, absorption lag time 7 min. No significant relationships were found between any of the pharmacokinetic parameters and individual characteristics. A good correlation was obtained between Bayesian-estimated and experimental AUCs, with a mean prediction error of 2.8% (95% CI [-0.6, 6.2]) and an accuracy of 13.1% (95% CI [7.5, 17.2]). A good correlation was also obtained in the eight patients with unusual pharmacokinetic profiles (r(2) = 0.96, P < 0.01).

CONCLUSIONS

Our Bayesian approach enabled a good estimation of CsA exposure in a population of patients with variable pharmacokinetic profiles, showing its usefulness for routine AUC-based therapeutic drug monitoring.

Application of population pharmacokinetics to cladribine

Background

The nucleoside analog cladribine is used for the treatment of a variety of indolent B- and T-cell lymphoid malignancies. The primary aim of the study was to evaluate the population distribution of pharmacokinetic parameters in patients undergoing treatment with cladribine and to detect the influence of different covariates on the pharmacokinetic parameters.

Methods

This pharmacokinetic study presents the results of a retrospective population pharmacokinetic analysis based on pooled data from 161 patients, who were given cladribine in different administration routes in various dosing regimens. The plasma concentrations of cladribine were determined by reversed-phase high-performance liquid chromatography using a solid phase extraction with a limit of quantitation of 1 nM using 1 mL of plasma.

Results

A three compartment structural model best described the disposition of cladribine. Clearance was found to be 39.3 L/hour, with a large interindividual variability. The half-life for the terminal phase was 16 hours. Bioavailability was 100% and 35% for subcutaneous and oral administration, respectively, with low interindividual variability. None of the investigated covariates were found to be correlated with the pharmacokinetic parameters.

Conclusion

As interindividual variability in apparent clearance after oral administration was not significantly higher compared to that following infusion, cladribine could be administered orally instead of intravenously if compensated for its lower bioavailability. Individualized dosing on basis of body surface area or weight does not represent an improvement in this study as compared to administering a fixed dose to all patients.

Pharmacokinetics and renal excretion of desmopressin after intravenous administration to healthy subjects and renally impaired patients

OBJECTIVE

To evaluate the influence of renal impairment on the pharmacokinetics of desmopressin.

METHODS

Twenty-four subjects were enrolled in the study, 18 with varying degrees of renal impairment and six healthy volunteers. Each subject received a single intravenous dose of 2 microg desmopressin. Blood and urine samples were collected for 24 h and assayed for desmopressin by radioimmunoassay. Plasma concentrations and the amounts of desmopressin excreted in the urine were analysed simultaneously by use of mixed effects modelling.

RESULTS

Only mild adverse events were observed. Both the renal and the nonrenal clearance of desmopressin were found to vary with the creatinine clearance (CrCL). A decrease of 1.67% in the CrCL (corresponding to 1 ml min(-1) from 60 ml min(-1)) was found to cause a 1.74% decrease in the renal clearance and a 0.93% decrease in the nonrenal clearance. The fall in renal clearance caused the amount of desmopressin excreted in urine to decrease from 47% in healthy subjects to 21% in the patients with severe renal impairment. The mean systemic clearance of desmopressin was 10 litres h(-1) in healthy subjects and 2.9 litres h(-1) in patients with severe renal impairment (difference -7.5 litres h(-1), 95% CI [-11; -4.3] litres h(-1)). Correspondingly, the mean terminal half-life, was 3.7 h in healthy subjects and 10 h in patients with severe renal impairment (difference 6.7 h, 95% CI [4.0; 9.4] h).

CONCLUSION

Although desmopressin appears to be safe and well-tolerated by patients with impaired renal function, great caution should be exercised when titrating towards an efficient dosage regimen if patients with moderately or severely impaired renal function are to be treated with desmopressin at all.

Models for time-varying covariates in population pharmacokinetic-pharmacodynamic analysis

AIM

If appropriately accounted for in a pharmacokinetic (PK)-pharmacodynamic (PD) model, time-varying covariates can provide additional information to that obtained from time-constant covariates. The aim was to present and apply two models applicable to time-varying covariates that capture such additional information.

METHODS

The first model estimates different covariate-parameter relationships for within- and between-individual variation in covariate values, by splitting the standard covariate model into a baseline covariate (BCOV) effect and a difference from baseline covariate (DCOV) effect. The second model allows the magnitude of the covariate effect to vary between individuals, by inclusion of interindividual variability in the covariate effect. The models were applied to four previously analysed data sets.

RESULTS

The models were applied to 10 covariate-parameter relationships and for three of these the first extended model resulted in a significant improvement of the fit. Even when this model did not improve the fit significantly, it provided useful information because the standard covariate model, which assumes within- and between-patient covariate relationships of the same magnitude, was only supported by the data in four cases. The inclusion of BCOV was not supported in two cases and DCOV was unnecessary in three cases. In one case, significantly different, nonzero, relationships were found for DCOV and BCOV. The second extended model was found to be significant for four of the 10 covariate-parameter relationships.

CONCLUSIONS

On the basis of the examples presented, traditionally made simplifications of covariate-parameter relationships are often inadequate. Extensions to the covariate-parameter relationships that include time-varying covariates have been developed, and their appropriateness and benefits have been described.

Estimating bias in population parameters for some models for repeated measures ordinal data using NONMEM and NLMIXED

The application of proportional odds models to ordered categorical data using the mixed-effects modeling approach has become more frequently reported within the pharmacokinetic/pharmacodynamic area during the last decade. The aim of this paper was to investigate the bias in parameter estimates, when models for ordered categorical data were estimated using methods employing different approximations of the likelihood integral; the Laplacian approximation in NONMEM (without and with the centering option) and NLMIXED, and the Gaussian quadrature approximations in NLMIXED. In particular, we have focused on situations with non-even distributions of the response categories and the impact of interpatient variability. This is a Monte Carlo simulation study where original data sets were derived from a known model and fixed study design. The simulated response was a four-category variable on the ordinal scale with categories 0, 1, 2 and 3. The model used for simulation was fitted to each data set for assessment of bias. Also, simulations of new data based on estimated population parameters were performed to evaluate the usefulness of the estimated model. For the conditions tested, Gaussian quadrature performed without appreciable bias in parameter estimates. However, markedly biased parameter estimates were obtained using the Laplacian estimation method without the centering option, in particular when distributions of observations between response categories were skewed and when the interpatient variability was moderate to large. Simulations under the model could not mimic the original data when bias was present, but resulted in overestimation of rare events. The bias was considerably reduced when the centering option in NONMEM was used. The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.

Pharmacokinetic Profile of Ganciclovir After its Oral Administration and From its Prodrug, Valganciclovir, in Solid Organ Transplant Recipients

BACKGROUND

Valganciclovir (Valcyte) has recently been approved for the prevention of cytomegalovirus (CMV) disease in high-risk (CMV donor positive [D+]/recipient negative [R-]) solid organ transplant (SOT) recipients. Large-scale studies describing the pharmacokinetics of valganciclovir in SOT recipients are lacking. A recent randomised, double-blind study of valganciclovir in 364 D+/R- (intent-to-treat population) SOT recipients provided valuable data on which a population pharmacokinetic analysis was performed.

METHODS

The pharmacokinetics of ganciclovir from oral ganciclovir (Cymevene, 1000 mg three times daily) and from valganciclovir (900 mg once daily) were described with plasma levels from 240 patients (1181 datapoints describing 449 pharmacokinetic profiles) using nonlinear mixed-effects modelling (NONMEM) software. A two-compartment pharmacokinetic model with separate absorption/metabolism and absorption parameters for valganciclovir and ganciclovir, respectively, was developed.

RESULTS

Exposure to ganciclovir from valganciclovir averaged 1.65-fold greater than that from oral ganciclovir (95% CI 1.58, 1.81); respective daily area under the plasma concentration-time curve values were 46.3 +/- 15.2 microg . h/mL and 28.0 +/- 10.9 microg . h/mL. The relative systemic exposure of ganciclovir was approximately 8-fold higher from valganciclovir than oral ganciclovir. Exposure to ganciclovir from valganciclovir was similar among liver, heart and kidney transplant recipients (46.0 +/- 16.1, 40.2 +/- 11.8 and 48.2 +/- 14.6 microg . h/ mL, respectively). Adherence to the prescribed dosing regimens, which were reduced for renal impairment, gave consistent exposure to ganciclovir.

CONCLUSION

Oral valganciclovir produces exposures of ganciclovir exceeding those attained with oral ganciclovir, but in line with those reported after standard intravenous administration of ganciclovir. This indicates that oral valganciclovir is suitable in circumstances requiring prophylactic use of ganciclovir and allows for more convenient management of patients at risk of CMV disease.