Do we need full compliance data for population pharmacokinetic analysis?

For population pharmacokinetic analysis of multiple oral doses one of the key issues is knowing as precisely as possible the dose inputs in order to fit a model to the input-output (dose-concentration) relationship. Recently developed electronic monitoring devices, placed on pill containers, permit precise records to be obtained over months, of the time/date opening of the container. Such records are reported to be the most reliable measurement of drug taking behavior for ambulatory patients. To investigate strategies for using and summarizing this new abundant information, a Markov chain process model was developed, that simulates compliance data from real data from electronically monitored patients, and data simulations and analyses were conducted. Results indicate that traditional population pharmacokinetic analysis methods that ignore actual dosing information tend to estimate biased clearance and volume and markedly overestimate random interindividual variability. The best dosing information summarization strategies consist of initially estimating population pharmacokinetic parameters, using no covariates and only a limited number of dose records, the latter chosen based on an a priori estimate of the half-life of the drug in the compartment of interest; then resummarizing the dose records using either population or individual posterior Bayes parameter estimates from the first population fit; and finally reestimating the population parameters using the newly summarized dose records. Such summarization strategies yield the same parameter estimates as using full dosing information records while reducing by at least 75% the CPU time needed for a population pharmacokinetic analysis. Work supported in part by Cooperative agreements AI 27663 and AI 27666 from the National Institute of Allergy and Infectious Diseases, U.S. Department of Health and Human Services. Dr. Girard's salary supported in part by Grant No. 1 F05 TW05185-01 from the Fogarty International Center, National Institutes of Health, U.S. Department of Health and Human Services.     

迭代二步法估算阿米卡星的群体药动学参数

目的：用迭代二步法估算阿米卡星的群体药动学参数。方法：收集58例呼吸系统感染病人静脉滴注阿米卡星的临床血药浓度监测数据,用荧光偏振免疫法测定阿米卡星血药浓度。用迭代二步法估算阿米卡星的群体及个体药动学参数。比较性别、年龄、体重、肌酐清除率等因素对药动学参数的影响。结果：性别对药动学参数无影响,CL与CLcr呈正相关,Vd与体重呈正相关。结论：迭代二步法能较好地估算出阿米卡星的群体及个体药动学参数,用于优化给药方案及预测血药浓度可满足临床需要。     

基于D最优设计的最大后验贝叶斯法估算个体药动学参数

本研究以基于D最优设计的最大后验贝叶斯法(MAPB)估算个体药动学参数,并与多元线性回归(MLR)法比较。以吡格列酮为模型药物,非线性混合效应模型(NONMEM)法考察药物的群体药动学特征。WinPOPT软件进行D最优采样设计,获得1～4点的采样方案。采用蒙特卡罗法产生模拟数据集,对估算方法进行评估。结果显示:随采样点数量的下降,MAPB估算CL和V的准确度和精密度均下降;随CL和V个体间变异增高,基于2点D最优设计的MAPB估算CL和V的精密度下降;随残差变异增高,MAPB估算的准确度和精密度均下降。与MLR比较结果显示:MAPB 2点D最优方案和MLR的2点估算AUC的准确度和精密度较接近,但在最佳采样点前后调整1 h采样,MAPB估算准确度和精密度优于MLR法。总体而言,MAPB法估算AUC的能力与MLR较为接近,但较MLR更具采样灵活性。     

Estimation of population characteristics of pharmacokinetic parameters from routine clinical data

A general data analysis technique estimates average population values of pharmacokinetic parameters and their interindividual variability from clinical pharmacokinetic data gathered during the routine care of patients. Several drug concentration values from each individual, along with dosage information and the values of other routinely assessed variables suffice for purposes of analysis. The Maximum Likelihood principle estimates underlying population values without the necessity for the intermediate estimation of individual parameter values. The approach is quite general, permitting the use of nonlinear statistical models with both fixed and random effects. Complex expressions involving physiological variables can be used to define the pharmacokinetic parameters. Thus, the relationship of physiological factors to parameter values can be assessed. The generality and appropriateness of the analysis technique are demonstrated by analysis of a set of data derived from 141 patients receiving the drug digoxin.This work was supported in part by NIH Grant GM 16496.     

Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there were no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 g/ml by the naive pooled data, two-stage, and NONMEM approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage appproach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEM produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.Work supported in part by NIH Grants GM 26676 and GM 26691.     

Predictive performance of the Bayesian analysis: Effects of blood sampling time,population parameters,and pharmacostatistical model

The present paper reports theoretical equations for the predictive performance of the Bayesian forecasting method. The precision of parameter estimates and predicted concentrations for an individual was described by general equations with the aid of a variance-covariance matrix of parameter estimates that involved the Bayes theorem. The equations were applied to assess the predictive performance of the one-point Bayesian method in association with blood sampling time, the population parameters, and the pharmacostatistical model. The simulation study showed that the prediction error in parameter estimates essentially depended upon the sampling time but the magnitude of dependency was affected by the size of inter-and intraindividual variances. With a smaller value of interindividual variance, the dependency on sampling time was less apparent. Effects of sampling time were further examined using clinical data obtained from 20 patients taking theophylline, and the results were in good agreement with the theoretical consideration. The present general equations are useful to investigate the sampling strategy as well as structural and variance modeling on the predictive performance of the Bayesian method.     

Recent advances in pharmacokinetic modeling

A major part of the science of pharmacokinetics is the modeling of the underlying processes that contribute to drug disposition. The purpose of pharmacokinetic models is to summarize the knowledge gained in preclinical and clinical studies at various stages in drug development and to rationally guide future studies with the use of adequately predictive models. This review highlights a variety of recent advances in mechanistic pharmacokinetic modeling. It is aimed at a broad audience, and hence, an attempt was made to maintain a balance between technical information and practical applications of pharmacokinetic modeling. It is hoped that drug researchers from all disciplines would be able to get a flavor of the function and capacity of pharmacokinetic modelers and their contribution to drug development. While this review is not intended to be a technical reference on modeling approaches, the roles of statistical applications and population methodologies are discussed where appropriate.     

A population pharmacokinetic model for paclitaxel in the presence of a novel P-gp modulator,Zosuquidar Trihydrochloride (LY335979)

AIMS: To develop a population pharmacokinetic model for paclitaxel in the presence of a MDR modulator, zosuquidar 3HCl. METHODS: The population approach was used (implemented with NONMEM) to analyse paclitaxel pharmacokinetic data from 43 patients who received a 3-h intravenous infusion of paclitaxel (175 mg x m(-2) or 225 mg x m(-2)) alone in cycle 2 or concomitantly with the oral administration of zosuquidar 3HCl in cycle 1. RESULTS: The structural pharmacokinetic model for paclitaxel, accounting for the Cremophor ELTM impact, was a three-compartment model with a nonlinear model for paclitaxel plasma clearance (CL), involving a linear decrease in this parameter during the infusion and a sigmoidal increase with time after the infusion. The final model described the effect of Zosuquidar 3HCl on paclitaxel CL by a categorical relationship. A 25% decrease in paclitaxel CL was observed, corresponding to an 1.3-fold increase in paclitaxel AUC (from 14829 microg x l(-1) x h to 19115 microg x l(-1) x h following paclitaxel 175 mg x m(-2)) when zosuquidar Cmax was greater than 350 microg x l(-1). This cut-off concentration closely corresponded to the IC50 of a sigmoidal Emax relationship (328 microg x l(-1)). A standard dose of 175 mg x m(-2) of paclitaxel could be safely combined with doses of zosuquidar 3HCl resulting in plasma concentrations known, from previous studies, to result in maximal P-gp inhibition. CONCLUSIONS: This analysis provides a model which accurately characterized the increase in paclitaxel exposure, which is most likely to be due to P-gp inhibition in the bile canaliculi, in the presence of zosuquidar 3HCl (Cmax > 350 microg x l(-1)) and is predictive of paclitaxel pharmacokinetics following a 3 h infusion. Hence the model could be useful in guiding therapy for paclitaxel alone and also for paclitaxel administered concomitantly with a P-gp inhibitor, and in designing further clinical trials.     

Estimation of population pharmacokinetics using the Gibbs sampler

Quantification of the average and interindividual variation in pharmacokinetic behavior within the patient population is an important aspect of drug development. Population pharmacokinetic models typically involve large numbers of parameters related nonlinearly to sparse, observational data, which creates difficulties for conventional methods of analysis. The nonlinear mixed-effects method implemented in the computer program NONMEM is a widely used approach to the estimation of population parameters. However, the method relies on somewhat restrictive modeling assumptions to enable efficient parameter estimation. In this paper we describe a Bayesian approach to population pharmacokinetic analysis which used a technique known as Gibbs sampling to simulate values for each model parameter. We provide details of how to implement the method in the context of population pharmacokinetic analysis, and illustrate this via an application to gentamicin population pharmacokinetics in neonates. A grant from the British Heart Foundation supported Nicola G. Best.     

Estimates of the population pharmacokinetic parameters and performance of Bayesian feedback: A sensitivity analysis

We investigated the influence of bias in the estimates of the population pharmacokinetic parameters on the performance of Bayesian feedback in achieving a desired drug serum concentration. Three specific cases were considered (i) steady-state case, (ii) lidocaine example, and (iii) mexiletine example. Whereas in the first case both the feedback and the desired concentration represented steady-state values, in the lidocaine and mexiletine examples the feedback concentration was assumed to be sampled shortly after starting therapy. RMSE was used as a measure of predictive performance. For the simple steady-state case the relationship between RMSE and bias in the parameter estimates describing the prior distribution could be derived analytically. Monte Carlo simulations were used to explore the two non-steady-state situations. In general, the performance of Bayesian feedback to predict serum concentrations was relatively insensitive to bad population parameter estimates. However, large changes in RMSE could be observed with small changes in the true variance component parameters in particular in the intraindividual residual variance, ² , indicating that the prediction interval, in contrast to point prediction, is sensitive to bias in the estimates of the population parameters.Supported by the Prof. Max Cloëtta Foundation. This work represents a part of an MD thesis of Christoph Steiner.     

Evaluation of Bayesian estimation in comparison to NONMEM for population pharmacokinetic data analysis: Application to pefloxacin in intensive care unit patients

The pharmacokinetics of pefloxacin (PF) were investigated in a population of 74 intensive care unit patients receiving 400 mg bid as 1-hr infusion using (i) Bayesian estimation (BE) of individual patient parameters followed by multiple linear regression (MLR) analysis and (ii) NONMEM analysis. The data consisted of 3 to 9 PF plasma levels per patient measured over 1 to 3 dosage intervals (total 113) according to four different limited (suboptimal) sampling 3-point protocols. Twenty-nine covariates (including 15 comedications) were considered to explain the interpatient variability. Predicted PFCLfor a patient with median covariates values was similar in both BE/ MLR and NONMEM analysis (4.02 and 3.92 L/hr, respectively). Bilirubin level and age were identified as the major determinants of PFCLby both approaches with similar predicted magnitude of effects (about 40 and 30% decrease of median CL,respectively). Confounding effects were observed between creatinine clearance (26% decrease of PF CLin the BE/MLR model), simplified acute physiology score (a global score based on 14 biological and clinical variables) (18% decrease of median CLin the NONMEM model) and age (entered in both models) which were highly correlated in our data base. However, both models predicted similar PF CLfor actual subpopulations by using actual covariate values. Finally, the NONMEM analysis allowed identification of an effect of weight on CL(decrease of CL for weight <65 kg) whereas the BE/MLR analysis predicted an increase of CLin patients treated with phenobarbital. In conclusion, both approaches allowed identification of the major risk factors of PF pharmacokinetics in ICU patients. Their potential use at different stages of drug development is discussed.     

Bayesian法估算丙戊酸动力学参数

目的采用丙戊酸(VPA)群体药动学参数结合Bayesian法估算癫疒间患者VPA的个体药动学参数。方法60例癫疒间患者口服VPA达稳态,取其每天早晨服药前10 min血样,用荧光偏振免疫法(FPIA)测得血清中VPA血药浓度谷值。用Bayesian法估算其药动学参数,并用逐步回归法分析个体的性别、年龄等18种因素对其药动学参数的影响。结果按口服一级吸收和消除的一房室开放模型用Bayesian法计算得VPA药动学参数清除率CL为(8.98±2.50)mL.h-1.kg-1,逐步回归CL方程:CL=5.858+1.423X5+1.593X11,式中X5表示身高(cm)体重(kg)比,X11表示当合并用苯妥英钠时系数为1,否则为0。估算的个体稳态VPA血药浓度谷值平均为(54.19±20.50)mg.L-1,实测结果平均为(53.58±20.85)mg.L-1,估算结果与实测结果之间无显著性差异(P>0.05)。结论可采用Bayesian法估算癫疒间患者VPA动力学参数CL和预测癫疒间患者个体稳态VPA血药浓度谷值;当癫疒间患者身高体重比增加或合并使用苯妥英时VPA动力学参数CL增加。     

Population pharmacokinetic parameters in patients treated with oral mexiletine

Summary A new data analysis approach, NONMEM, proposed by Sheiner and Beal, has been employed to estimate the population pharmacokinetic parameters of oral mexiletine in patients treated for arrhythmias. 452 serum concentration measurements in 58 patients were available for analysis. 27 patients had congestive heart failure and 8 had abnormal liver function tests at the time of the study. The population averages of the pharmacokinetic parameters and their interindividual variability were: oral total body clearance (Cl) 0.38 l/h/kg±43% (C. V.), apparent volume of distribution (Vd) 5.3 l/kg±40%, absorption rate constant 3.1 h^–1±205%, absorption time-lag 0.3 h. Congestive heart failure and sex did not show a significant effect on Cl and Vd; the number of patients with severe liver function impairment was too small for a definite conclusion. Normalizing Cl and Vd for body weight significantly decreased their interindividual variability. Based on these results, a dosage regimen is recommended which is expected to produce a therapeutic serum concentration (0.8–2 mg/l) in over 60% of patients. Because of its unique features, which allow estimation of pharmacokinetic parameters and their variability from fragmentary patient data, the NONMEM system has great potential applicability to clinical pharmacokinetic studies.Presented in part at the First European Congress on Biopharmaceutics and Pharmacokinetics, Clermont-Ferrand, April 1981     

Prospective evaluation of a D-optimal designed population pharmacokinetic study

Recently, methods for computing D-optimal designs for population pharmacokinetic studies have become available. However there are few publications that have prospectively evaluated the benefits of D-optimality in population or single-subject settings. This study compared a population optimal design with an empirical design for estimating the base pharmacokinetic model for enoxaparin in a stratified randomized setting. The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88). The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design with three sampling windows (0–30 min, 1.5–5 hr and 11–12 hr post-dose) for all patients. The empirical design consisted of three sample time windows per patient from a total of nine windows that collectively represented the entire dose interval. Each patient was assigned to have one blood sample taken from three different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal or empirical sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded. Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, while the optimal design supported a two compartment linear model with additive residual error as did the model derived from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the optimal design derived model was superior to the empirical design model in terms of precision and was similar to the model developed from the full dataset. This study suggests optimal design techniques may be useful, even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models and when the implementation of the optimal designed study deviated from the nominal design.     

Designs for population pharmacodynamics: Value of pharmacokinetic data and population analysis

Analyses of simulated data from pharmacokinetic/pharmacodynamic (PK/PD) studies varying with respect to the amount and timing of observations were undertaken to assess the value of these design choices. The simulation models assume mono- or biexponential drug disposition, andE _max-type pharmacodynamics. Data analysis uses a combined PK/PD population analysis or a hybrid, individual-PK/population-PD analysis. Assuming that the goal of the PK/PD studies is to estimate population PD, performance of designs is judged by comparing the precision of estimates of population mean PD parameters and of their interindividual variability. The simulations reveal that (i) PK data, even in small number (2 points per person from as few as 25–50% of persons) are very valuable for estimating population PD; (ii) designs involving more individuals, even if many are sparsely sampled, dominate designs calling for more complete study of fewer persons; (iii) the population analysis is generally superior to the hybrid analysis, especially when the PK model is misspecified (biexponential assumed to be monoexponential for analysis); (iv) varying sampling times and doses among subjects protects against the ill effects of model misspecification. In general, the results are quite encouraging about the usefulness of sparse data designs to estimate population dose response. Work supported in part by U.S. Department of Health, Education and Welfare, Grants GM26676, GM26691.     

Estimation of pharmacokinetic parameters based on the patient-adjusted population data

Population pharmacokinetic data, adjusted for patient characteristics, are recommended for the design of initial dosage regimens of some therapeutically monitored drugs in patients for whom patient-specific data are not available. However, despite widespread use by clinicians such as pharmacists, a clear understanding of the principles of population pharmacokinetics, including data collection and analysis and its limitations, is often lacking. This article describes the 2 main methods of obtaining population kinetic data, namely the two-stage method and nonlinear mixed effect model, and their applications to the pharmacokinetic-based design of dosage regimens. Additionally, some numerical examples are provided to assist the reader in understanding the material. The author uses these tools in a pharmacokinetics course taught to PharmD students.     

A population pharmacokinetic study of alminoprofen penetration into synovial fluid

The pharmacokinetics of alminoprofen in plasma and synovial fluid (SF) at steady state (300 mg t.i.d.) was studied in 45 patients with knee effusion. Plasma and SF samples, one each per patient, were obtained. Six groups were made according to the time of sampling after ingestion of the 13th dose: 1h (n = 7), 2h (n = 7), 4h (n = 7), 6h (n = 10), 8h (n = 6), 12h (n = 8). A three-compartment model was used to describe alminoprofen kinetics in plasma and SF, with two parameterizations, a ‘classical’ and a ‘physiological’ one. The non-linear mixed effect model approach was used to estimate the mean and variance of the pharmacokinetic parameters. The mean ±SE of the estimates (coefficient of variation of interindividual variability as a percentage) were volume of distribution, 11.0 ± 1.711 (12%); elimination rate constant, 0.236 ± 0.025 h^?1 (18%); absorption rate constant 2.80 ± 0.31 h^?1 (464%), clearance of influx into SF, 0.29 ± 0.14 mL min^?1; clearance of efflux into plasma, 0.56 ± 0.25 mL min^?1. These two clearances were not significantly different, which indicates that passive diffusion occurs in both directions. The mean ±SD alminoprofen concentration versus time curve in plasma and SF at steady state was simulated and showed that the mean ±SD maximal concentration in SF was 8.1 ± 6.3 mg L^?1 and was obtained 4h after dose administration.     

Validation of a population pharmacokinetic model for adjunctive lamotrigine therapy in children

AIMS: This analysis was performed to validate a previously developed population pharmacokinetic model for lamotrigine in order to establish a basis for dosage recommendations for children. METHODS: (a) The importance of the covariates in the final model was confirmed using the model validation dataset. Population and individual (Bayesian estimate) pharmacokinetic parameters were estimated using both the initial model, which included none of the covariates, and the final model. Accuracy and precision of parameter estimation and of concentration prediction were compared between the two models. (b) The performance in predicting the validation concentrations by the final model parameters obtained previously from the model development dataset was assessed. (c) The parameters of the final model were refined using a dataset combining both the development and validation data. RESULTS: Prediction performance of the final pharmacostatistical model was superior to that of the initial model. The results of the validation confirmed that concomitant antiepileptic drugs that increased or reduced lamotrigine clearance in adults had similar effects in children. The validation also verified the linear relationship between weight and clearance. The previously seen small sex effect on clearance was found statistically insignificant. CONCLUSIONS: The current analysis confirmed the previous findings. To achieve the same concentrations, children receiving enzyme-inducing antiepileptic drugs without valproate require higher doses than those receiving valproate; and heavier children require higher doses.