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

Nevirapine and Efavirenz Pharmacokinetics and Covariate Analysis in the 2Nn Study

Objective

The aim of this 2NN pharmacokinetic substudy was to investigate the population pharmacokinetics of nevirapine and efavirenz.

Methods

Treatment-naive, HIV-1-infected patients received nevirapine (once or twice daily), efavirenz or a combination with lamivudine and stavudine. Blood samples were collected on day 3 and weeks 1, 2, 4, 24 and 48. Using non-linear mixed effects modelling, pharmacokinetics of nevirapine and efavirenz and factors involved in the inter-individual variability were investigated.

Results

Clearance of nevirapine in the induction phase (<14 days) and at steady state (>28 days) were 2.02 l/h and 2.81 l/h, respectively. Volume of distribution and absorption rate constant were 77.0 l and 1.66 h-1, respectively. Clearance of nevirapine was lower in females (13.8%) and in patients with hepatitis B (19.5%). Patients from South America and Western countries had higher clearance of nevirapine compared with Thai and South African patients. The clearances of efavirenz in the induction phase and at steady state were 7.95 l/h and 8.82 l/h, respectively. The volume of distribution and absorption rate constant were 418 l and 0.287 h-1, respectively. Concomitant use of nevirapine increased clearance of efavirenz (43%). Patients from Thailand had lower clearance than the rest of the population.

Conclusions

The population pharmacokinetics of nevirapine and efavirenz were assessed in the 2NN trial. For both drugs, an induction phase was distinguished from the steady-state phase. Gender, hepatitis B and geographical region were involved in the variability of the pharmacokinetics of nevirapine. Region and concomitantly used nevirapine were determinants of the pharmacokinetics of efavirenz.

Population pharmacokinetic analysis of 17-(allylamino)-17-demethoxygeldanamycin (17AAG) in adult patients with advanced malignancies

PURPOSE

17-(Allylamino)-17-demethoxygeldanamycin (17AAG) is a novel anticancer agent in clinical development. The objectives of this study were to develop a population pharmacokinetic model for 17AAG and its major metabolite, 17AG, and to investigate influences of patient characteristics and biochemical markers on pharmacokinetic parameters estimated for 17AAG and 17AG.

EXPERIMENTAL DESIGN

In a phase I clinical study, 17AAG was administered by intravenous infusion to 43 patients with refractory, advanced malignancies. Plasma concentrations of 17AAG and 17AG were determined by high-performance liquid chromatography. Plasma concentration vs time data were modeled using NONMEM. Nine covariates (age, sex, performance status, weight, height, body surface area, AST, bilirubin and serum creatinine) were investigated for their influences on individual pharmacokinetic parameters.

RESULTS

Plasma concentration vs time data were best described by a two-compartment model for 17AAG and a one-compartment model for 17AG. Volumes of distribution were 24.2 and 89.6 l for 17AAG. Total elimination clearances were 26.7 and 21.3 l/h for 17AAG and 17AG, respectively. Both fixed and random effects pharmacokinetic parameters were well estimated. None of the covariates explained the interindividual variability in 17AAG and 17AG pharmacokinetic parameters or improved the fit of the model based on objective function changes.

CONCLUSIONS

A population pharmacokinetic model was developed to describe 17AAG and 17AG population pharmacokinetic parameters and interindividual variabilities. There were substantial interindividual variabilities in 17AAG and 17AG pharmacokinetic parameters despite BSA-normalized dosing.

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

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

The back-step method--method for obtaining unbiased population parameter estimates for ordered categorical data

A significant bias in parameters, estimated with the proportional odds model using the software NONMEM, has been reported. Typically, this bias occurs with ordered categorical data, when most of the observations are found at one extreme of the possible outcomes. The aim of this study was to assess, through simulations, the performance of the Back-Step Method (BSM), a novel approach for obtaining unbiased estimates when the standard approach provides biased estimates. BSM is an iterative method involving sequential simulation-estimation steps. BSM was compared with the standard approach in the analysis of a 4-category ordered variable using the Laplacian method in NONMEM. The bias in parameter estimates and the accuracy of model predictions were determined for the 2 methods on 3 conditions: (1) a nonskewed distribution of the response with low interindividual variability (IIV), (2) a skewed distribution with low IIV, and (3) a skewed distribution with high IIV. An increase in bias with increasing skewness and IIV was shown in parameters estimated using the standard approach in NONMEM. BSM performed without appreciable bias in the estimates under the 3 conditions, and the model predictions were in good agreement with the original data. Each BSM estimation represents a random sample of the population; hence, repeating the BSM estimation reduces the imprecision of the parameter estimates. The BSM is an accurate estimation method when the standard modeling approach in NONMEM gives biased estimates.

Assessment of the relative in vivo potency of the hydroxylated metabolite of darifenacin in its ability to decrease salivary flow using pooled population pharmacokinetic-pharmacodynamic data

AIMS

To describe the population pharmacokinetic-pharmacodynamic relationship between darifenacin (UK-88,525) and its hydroxylated metabolite (UK-148,993), and the reduction in salivary flow (SF, a M3-mediated response). This enabled an estimation of the in vivo potency of the metabolite to decrease SF relative to that of the parent drug.

METHODS

A total of 262 individuals were pooled from 11 Phase 1 studies and one Phase 2 study. A comparison was made between a series of pharmacodynamic models (direct-effect, indirect-effect, link and binding model) using NONMEM.

RESULTS

The binding model yielded the best description of the decrease in SF by fully accounting for the time course of the pharmacodynamic effect. An internal validation exercise demonstrated the robustness of this model. Covariate analysis identified a circadian rhythm in SF. This model, with confidence intervals (CI) determined by likelihood profiling, indicated that the relative potency of the metabolite to darifenacin to reduce SF was 11.1% (95% CI 3.8, 19.6). This implied that the metabolite was ninefold less potent than darifenacin in vivo. Accounting for the unbound fraction of darifenacin (2%) and its metabolite (13%), the in vivo protein binding-corrected relative potency was estimated to be 2.1%, indicating that the metabolite was 50-fold less potent than the parent drug. The model supported the assumption that no other metabolites contributing to the impairment of the SF were formed during first-pass, and that the development of sensitization or tolerance was not evident over time. The validation process indicated that the i.v.-oral crossover study was necessary for the estimation of the relative potency.

CONCLUSIONS

Population modelling of darifenacin and its hydroxylated metabolite yielded individual pharmacokinetic predictions that could be used to assess the in vivo potency of the metabolite to decrease SF relative to that of the parent drug. The metabolite had a negligible effect on SF.

Population pharmacokinetics of the novel anticancer agent E7070 during four phase I studies: model building and validation

PURPOSE

N-(3-Chloro-7-indolyl)-1,4-benzenedisulfonamide (E7070) is a novel sulfonamide anticancer agent currently in phase II clinical development for the treatment of solid tumors. Four phase I studies have been finalized, with E7070 administered at four different treatment schedules to identify the maximum-tolerated dose and the dose-limiting toxicities. Pharmacokinetic analyses of all studies revealed E7070 to have nonlinear pharmacokinetics. A population pharmacokinetic model was designed and validated to describe the pharmacokinetics of E7070 at all four treatment schedules and to identify the possible influences of patient characteristics on the pharmacokinetic parameters.

PATIENTS AND METHODS

Plasma concentration-time data of all patients (n = 143) were fitted to several pharmacokinetic models using NONMEM. Seventeen covariables were investigated for their relation with individual pharmacokinetic parameters. A bootstrap procedure was performed to check the validity of the model.

RESULTS

The data were best described using a three-compartment model with nonlinear distribution to a peripheral compartment and two parallel pathways of elimination from the central compartment: a linear and a saturable pathway. Body-surface area (BSA) was significantly correlated to both the volume of distribution of the central compartment and to the maximal elimination capacity. The fits of 500 bootstrap replicates of the data set demonstrated the robustness of the developed population pharmacokinetic model.

CONCLUSION

A population pharmacokinetic model has been designed and validated that accurately describes the data of four phase I studies with E7070. Furthermore, it has been demonstrated that BSA-guided dosing for E7070 is important.

Application of pharmacokinetic modelling to the routine therapeutic drug monitoring of anticancer drugs

Over the last 10 years, proofs of the clinical interest of therapeutic drug monitoring (TDM) of certain anticancer drugs have been established. Numerous studies have shown that TDM is an efficient tool for controlling the toxicity of therapeutic drugs, and a few trials have even demonstrated that it can improve their efficacy. This article critically reviews TDM tools based on pharmacokinetic modelling of anticancer drugs. The administered dose of anticancer drugs is sometimes adjusted individually using either a priori or a posteriori methods. The most frequent clinical application of a priori formulae concerns carboplatin and allows the computation of the first dose based on biometrical and biological data such as weight, age, gender, creatinine clearance and glomerular filtration rate. A posteriori methods use drug plasma concentrations to adjust the subsequent dose(s). Thus, nomograms allowing dose adjustment on the basis of blood concentration are routinely used for 5-fluorouracil given as long continuous infusions. Multilinear regression models have been developed, for example for etoposide, doxorubicin. carboplatin, cyclophosphamide and irinotecan, to predict a single exposure variable [such as area under concentration-time curve (AUC)] from a small number of plasma concentrations obtained at predetermined times after a standard dose. These models can only be applied by using the same dose and schedule as the original study. Bayesian estimation offers more flexibility in blood sampling times and, owing to its precision and to the amount of information provided, is the method of choice for ensuring that a given patient benefits from the desired systemic exposure. Unlike the other a posteriori methods, Bayesian estimation is based on population pharmacokinetic studies and can take into account the effects of different individual factors on the pharmacokinetics of the drug. Bayesian estimators have been used to determine maximum tolerated systemic exposure thresholds (e.g. for topotecan or teniposide) as well as for the routine monitoring of drugs characterized by a very high interindividual pharmacokinetic variability such as methotrexate or carboplatin. The development of these methods has contributed to improving cancer chemotherapy in terms of patient outcome and survival and should be pursued.

Errors-in-variables in joint population pharmacokinetic/pharmacodynamic modeling

Pharmacokinetic (PK) models describe the relationship between the administered dose and the concentration of drug (and/or metabolite) in the blood as a function of time. Pharmacodynamic (PD) models describe the relationship between the concentration in the blood (or the dose) and the biologic response. Population PK/PD studies aim to determine the sources of variability in the observed concentrations/responses across groups of individuals. In this article, we consider the joint modeling of PK/PD data. The natural approach is to specify a joint model in which the concentration and response data are simultaneously modeled. Unfortunately, this approach may not be optimal if, due to sparsity of concentration data, an overly simple PK model is specified. As an alternative, we propose an errors-in-variables approach in which the observed-concentration data are assumed to be measured with error without reference to a specific PK model. We give an example of an analysis of PK/PD data obtained following administration of an anticoagulant drug. The study was originally carried out in order to make dosage recommendations. The prior for the distribution of the true concentrations, which may incorporate an individual's covariate information, is derived as a predictive distribution from an earlier study. The errors-in-variables approach is compared with the joint modeling approach and more naive methods in which the observed concentrations, or the separately modeled concentrations, are substituted into the response model. Throughout, a Bayesian approach is taken with implementation via Markov chain Monte Carlo methods.

Pharmacodynamic models for the cardiovascular effects of moxonidine in patients with congestive heart failure

AIMS

To assess the pharmacodynamics of moxonidine in patients with functional NYHA Class II-III congestive heart failure (CHF).

METHODS

A parallel population pharmacokinetic/pharmacodynamic (PK/PD) analysis was performed to assess the effect of moxonidine (0.1, 0.2, 0.3 mg twice daily) and placebo treatment on plasma noradrenaline (NA) levels, standing systolic blood pressure (SBP), and heart rate (HR) over 12 weeks in 97 patients with CHF using a parallel group design with dose escalation. A sequential analysis was also developed, where the relative changes in NA concentration were related to both SBP and HR.

RESULTS

In the parallel PD analysis, an effect delay was shown for all three end points (NA, SBP, and HR). An inhibitory Emax model was used to characterize the concentration-effect relationships. For SBP and HR, the EC50 value increased over time. For NA, there was a positive baseline drift over the 12 weeks; this was interpreted as disease progression. Moxonidine delayed this increase by 9.8 weeks. For SBP, there was a circadian pattern at baseline. In the sequential PD analysis, the relationship between the drug response (NA) and SBP or HR was best described by an inhibitory Emax model. No effect delays between the response and effects were found.

CONCLUSIONS

Effects of moxonidine on NA, SBP, and HR could be quantified by an effect compartment model in the presence of disease progression and circadian variations. Disease progression, as judged by increasing NA levels with time, was delayed by moxonidine. A direct relationship was found between NA and SBP/HR.

Likelihood-based diagnostics for influential individuals in non-linear mixed effects model selection

PURPOSE

Data from single individuals, or a small group of subjects may influence non-linear mixed effects model selection. Diagnostics routinely applied in model building may identify such individuals, but these methods are not specifically designed for that purpose and are, therefore, not optimal. We describe two likelihood-based diagnostics for identifying individuals that can influence the choice between two competing models.

METHODS

One method is based on a jackknife of the raw data on the individual level and refitting the model to each new data set. The second method is a calculation which utilises the contribution each individual make to the objective function values under each of the two models. The two methods were applied to model selection during analysis of a real data set.

RESULTS

The agreement between the methods was high. Individuals for whom there was a discrepancy between the methods tended to be those for which neither of the contending models described the data appropriately. Both methods identified individuals that influenced the model selection.

CONCLUSIONS

Two objective, specific and quantitative methods for identifying influential individuals in nonlinear mixed effects model selection have been presented. One of the methods doesn't require additional model fitting and is therefore particularly attractive.

Population pharmacokinetics and pharmacodynamics of the anti-CD11a antibody hu1124 in human subjects with psoriasis

The pharmacokinetics of hu1124, a human anti-CD11a antibody, were investigated in human subjects with psoriasis. CD11a is a subunit of LFA-1, a cell surface molecule involved in T cell mediated immune responses. Subjects received a single dose of 0.03, 0.1, 0.3, 0.6, 1, 2, 3, or 10 mg/kg of hu1124 intravenously over 1-3 hr. Blood samples were collected at selected times from 60 min to 72 days after administration. Plasma samples were assayed for hu1124 by ELISA, and pharmacokinetic analyses were performed on the drug plasma concentrations. As the dose of hu1124 was increased, the clearance decreased from 322 ml/day per kg at 0.1 mg/kg to 6.6 ml/day per kg at 10 mg/kg of hu1124. The plasma hu1124 concentration-time profile suggested that the clearance of hu1124 was saturable above 10 micrograms/ml. In addition, treatment with hu1124 caused a rapid reduction in the level of CD11a expression on CD3-positive lymphocytes (T cells) to about 25% of pretreatment levels. Regardless of the hu1124 dose administered, cell surface CD11a remained at this reduced level as long as hu1124 was detectable (> 0.025 microgram/ml) in the plasma. When hu1124 levels fell below 3 micrograms/ml, the drug was rapidly cleared from the circulation and expression of CD11a returned to normal within 7-10 days thereafter. In vitro, half-maximal binding of hu1124 to lymphocytes was achieved at about 0.1 microgram/ml and saturation required more than 10 micrograms/ml. One of the receptor-mediated pharmacokinetic/pharmacodynamic models which was developed describes the dynamic interaction of hu1124 binding to CD11a, resulting in the removal of hu1124 from the circulation and reduction of cell surface CD11a. The model accounts for the continually changing number of CD11a molecules available for removing hu1124 from the circulation based on prior exposure of cells expressing CD11a to hu1124. In addition, the model also accounts for saturation of CD11a molecules by hu1124 at drug concentrations of approximately 10 micrograms/ml, thereby reducing the clearance rate of hu1124 with increasing dose.

Xpose--an S-PLUS based population pharmacokinetic/pharmacodynamic model building aid for NONMEM

The building of population pharmacokinetic/pharmacodynamic (PK/PD) models is a time consuming and complicated task. This is partly due the lack of specialized tools for the visualization and exploration requirements of this type of analysis. In this paper we present Xpose, a model building aid for population PK/PD analysis using NONMEM, which simplifies the task of producing documentation, data set checkout plots, goodness of fit plots and graphical model comparison. It also facilitates covariate model building by the use of stepwise generalized additive modeling (GAM), bootstrap of the GAM analyses and tree based modeling. The plots and analyses are presented in the form of a text based menu system and the only thing the user has to do is to make NONMEM produce one or more table files named in a specific way.