Analysis of population pharmacokinetic data using NONMEM and WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.     

基于NONMEM法建立紫杉醇群体药动学模型

目的：建立国人紫杉醇（paclitaxel,PTX）群体药动学（population pharmacokinetic,PPK）模型,为制定个体化给药方案提供理论支持。方法：收集138例接受紫杉醇治疗的肿瘤患者（建模组105例,验证组33例）210个血样,HPLC法测定紫杉醇血药浓度,PCR-RFLP法检测MDR1 C3435T。应用非线性混合效应模型（NONMEM）法,考察MDR1 C3435T基因多态性、合并用药及病理生理因素对紫杉醇药动学参数的影响,建立紫杉醇PPK模型。对模型进行拟合优度诊断、自举法（Bootstrap）内部验证,正态预测分布误差法（NPDE）及外部验证考察模型预测能力。结果：紫杉醇清除率（CL）和表观分布容积（V_d）的群体典型值分别为64.7 L·h^-1和1 240 L,患者内生肌酐清除率（CLcr）和给药速率（RATE）显著影响紫杉醇清除率。最终模型Bootstrap法验证结果与模型计算值相符,拟合优度、准确度及精密度均优于最简模型。结论：紫杉醇PPK最终模型稳定、有效,可结合Bayesian反馈法为临床优化给药方案提供科学依据。     

Predictive performance of population pharmacokinetic parameters of tianeptine as applied to plasma concentrations from a post-marketing study

Summary The predictive ability of population pharmacokinetic parameters of tianeptine, obtained from a mixed effect analysis of pre-marketing pharmacokinetic studies, was evaluated using tianeptine plasma concentrations obtained during a large multi-center post-marketing surveillance study.The mean prediction error was 7.8 ng·ml^–1 and the root mean square prediction error was 52.1 ng/ml when initial estimates of population pharmacokinetic parameters were used to predict drug concentrations in one half of the post-marketing data. When the population parameters were revised to reflect the data collected in the first half of the post-marketing study, the mean prediction error was reduced to –3.2 ng·ml^–1 and the root mean square prediction error was reduced to 29.5 ng·ml^–1.These results suggest that population pharmacokinetic parameters obtained from pre-marketing data may not accurately predict drug concentrations in patients receiving the drug in the post-marketing setting. Once the population parameters are updated to reflect data from the post-marketing period, the predictive ability of the database increases, but substantial variability in the prediction error remains.     

Evaluation of the autoinduction of ifosfamide metabolism by a population pharmacokinetic approach using NONMEM

AIMS: This study investigated the population pharmacokinetics of ifosfamide in 15 patients treated for soft tissue sarcoma with 9 or 12 g m-2 ifosfamide by means of a 72 h continuous i.v. infusion. METHODS: A model was developed using nonlinear mixed effects modelling (NONMEM) to describe the nonlinear pharmacokinetics of ifosfamide by linking the ifosfamide plasma concentrations to the extent of the autoinduction. RESULTS: The proposed model revealed the effect of autoinduction on the disposition of ifosfamide. The initial clearance, volume of distribution, rate constant for enzyme degradation, induction half-life of the enzyme and the ifosfamide concentration at 50% of the maximum inhibition of enzyme degradation were estimated at 2.94 +/- 0.27 l h-1, 43.5 +/- 2.9 l, 0.0546 +/- 0. 0078 h-1, 12.7 h and 30.7 +/- 4.8 microM, respectively. Interindividual variabilities of initial clearance, volume of distribution, rate constant for enzyme degradation were 24.5, 23.4 and 22.7%, respectively. Proportional and additive variability not explained by the model were 13.6% and 0.0763 microM, respectively. CONCLUSIONS: The absence of a lag time for the autoinduction of ifosfamide metabolism could be the result of an immediate inhibition of the enzymatic degradation of CYP3A4 by ifosfamide. By application of the autoinduction model individual pharmacokinetic profiles of patients were described with adequate precision. This model may therefore be used in the future development of a model to individualize dose selection in patients.     

基于NONMEN法建立万古霉素新生儿群体药动学模型

目的:建立新生儿万古霉素群体药动学模型,为临床个体化给药方案提供参考。方法:回顾性收集80例静脉使用万古霉素新生儿的170个稳态血药浓度数据及临床资料,运用非线性混合效应模型(NONMEM),建立新生儿万古霉素群体药动学(PPK)模型;考察各项协变量对药动学参数的影响,对最终模型进行拟合优度、自举法(Bootstrap)及正态预测分布误差法(NPDE)验证。利用蒙特卡洛法评估患儿在不同给药方案下的血药浓度范围。结果:一室模型能较好地拟合万古霉素体内过程,清除率(CL)和表观分布容积(V)的群体典型值分别为0.297L·h-1和2.230L,表观分布容积对CL有显著影响。拟合优度、Bootstrap和NPDE表明最终模型稳定、预测结果可靠。建立不同体质量范围新生儿万古霉素初始剂量推荐表。结论:本研究建立的新生儿万古霉素PPK模型稳定可靠,可为优化新生儿给药方案提供依据。     

Predictive capacity of carbamazepine pharmacokinetic parameters in a Portuguese outpatient population

The individualization of anticonvulsant therapy regimens can contribute to the implementation of appropriate carbamazepine (CBZ) maintenance doses in epileptic patients. An accurate method for the prediction of concentrations based on a determination of parameters and serum concentrations could be of clinical relevance in the management of epilepsy. In this study, we retrospectively evaluated the predictive performance in an adult outpatient population of six different methods, representing six sets of CBZ pharmacokinetic parameters selected according to the literature using a Bayesian computer program (PKS System; Abbott Laboratories, Abbott Park, IL, USA). The study involved 50 patients with two or more available concentrations selected under several inclusion criteria. The patients were taking CBZ (between 200 and 1600 mg/d) in monotherapy or polytherapy regimens and had no hepatic or renal disease. Steady state concentrations were predicted according to the use of prior information and using one and two feedback patient concentrations. Accuracy and precision were assessed by mean prediction error (ME), mean squared prediction error (MSE) and root mean squared prediction error (RMSE). The analysis showed CL = 0.067 L/hour/kg and Vd = 1.19 L/kg as the most accurate and precise set of pharmacokinetic parameters, presenting the highest percentage of clinically acceptable estimates (error < 2 microg/mL). Additionally, predictions based on one measured feedback concentration were found to be more accurate and precise than prior population-based predictions; the use of two previous patient concentrations further improved predictive capacity but failed to show a significant difference when compared with predictions based on one measured feedback concentration. In conclusion, the adoption of the previously mentioned set of parameters as population estimates and the use of at least one feedback concentration through the Bayesian approach seems to be essential for a better CBZ use in clinical practice. Finally, despite the obtained results, we believe that the Portuguese pharmacokinetic parameter determination of antiepileptics should be carried out to improve the rationale and cost-effectiveness of anticonvulsant therapy.     

NONMEM法在估算依托度酸胶囊人体相对生物利用度和药代动力学参数的应用

目的 用NONMEM法估算依托度酸胶囊的药动学参数并进行相对生物利用度研究。方法 用HPLC方法测定健康受试者交叉服用400mg依托度酸胶囊参比制剂和试验制剂的血药浓度，使用NONMEM法估算药动学参数和相对生物利用度。并与3P97分析结果进行t检验统计分析。结果 用NONMEM法估算依托度酸胶囊的相对生物利用度为94．8％，对照制剂与试验制剂k10分别为0．204，0．231，k12分别为0．309，0．302，k21分别为0．124，0．117，Vc分别为1．01，1．07。与3P97分析结果比较，进行t检验统计分析对照制剂与试验制剂Vc值存在显著差异，其他参数均无显著性差异。结论 NONMEM法估算药动学参数与经典药动学分析方法比较基本无显著性差异。用其进行生物利用度研究简便快捷，准确度较高，是药动学研究的一种新的数据分析方法。     

Evaluation of population (NONMEM) pharmacokinetic parameter estimates

The application of population pharmacokinetic analysis has received increasing attention in the last few years. The main goal of this report is to make investigators aware of the necessity of independent evaluation of the results obtained from a population analysis based on observational studies. We also describe with the help of a specific example (a new synthetic opiate Alfentanil) how such evaluation can be performed for parameter estimates obtained with the software system NONMEM. The method differs depending on the type of serum concentration data that are used for the evaluation. A general method is described, based on the regression model used in NONMEM, that can test for bias in the estimates af fixed and random effects independent of the number of observations per patient and dosing. Since the procedure for testing for statistically significant bias in the prediction of the average concentration and its variability can be relatively complex, we propose that generally available program packages performing estimation of the pharmacokinetic parameters from observational data should contain the necessary software to evaluate the reliability of the parameter estimates on a second data set.Supported by the Professor Max Cloëtta Foundation, Switzerland and the National Institute on Aging Grant ROI-04594.     

Evaluation of population (NONMEM) pharmacokinetic parameter estimates

The application of population pharmacokinetic analysis has received increasing attention in the last few years. The main goal of this report is to make investigators aware of the necessity of independent evaluation of the results obtained from a population analysis based on observational studies. We also describe with the help of a specific example (a new synthetic opiate Alfentanil) how such evaluation can be performed for parameter estimates obtained with the software system NONMEM. The method differs depending on the type of serum concentration data that are used for the evaluation. A general method is described, based on the regression model used in NONMEM, that can test for bias in the estimates of fixed and random effects independent of the number of observations per patient and dosing. Since the procedure for testing for statistically significant bias in the prediction of the average concentration and its variability can be relatively complex, we propose that generally available program packages performing estimation of the pharmacokinetic parameters from observational data should contain the necessary software to evaluate the reliability of the parameter estimates on a second data set.     

Prediction of the tacrolimus population pharmacokinetic parameters according to CYP3A5 genotype and clinical factors using NONMEM in adult kidney transplant recipients

Purpose

Tacrolimus is a commonly used immunosuppressant in solid organ transplantation recipients, but it is characterized by a narrow therapeutic range and large inter-individual variability. The purpose of this study was to establish a population pharmacokinetic (PK) model of tacrolimus and evaluate the influence of clinical covariates, including the genetic polymorphisms of the cytochrome P450 3A5 gene (CYP3A5) and gene encoding P-glycoprotein (ABCB1), on the PK parameters in adult Korean kidney transplant recipients.

Methods

Clinical data were collected retrospectively for 400 days after the initiation of a tacrolimus-based immunosuppression therapy. Data from 2,788 trough blood samples obtained from 80 subjects were used to perform a population PK analysis with a nonlinear mixed-effect model (NONMEM).

Results

The estimated population mean values of clearance (CL/F) and volume of distribution (V/F) were 22.9 L/h and 716 L, respectively, and the k _a was fixed to 4.5 h^-1. The CYP3A5 genotype, hematocrit level, and post-operative days were identified as the main covariates that influence CL/F, and body weight was found to have a significant effect on V/F. Other covariates, including ABCB1 genotype, corticosteroid dosage, sex, and other clinical data, did not contribute to the pharmacokinetics of tacrolimus.

Conclusions

This tacrolimus population PK model will be a valuable tool in developing rational guidelines and provides a basis for individualized therapy after kidney transplantation in clinical settings of Korea.     

NONMEM法建立大鼠外周和中枢左旋多巴群体药动学模型

目的:建立大鼠左旋多巴(levodopa, LD)群体药动学模型,考察LD药动学参数的影响因素。方法:14只大鼠随机分为高、低两个剂量组,单次灌胃给予多巴丝肼片。采用脑微透析技术收集大鼠纹状体细胞外液透析液,同时采集外周血;高效液相色谱-电化学法测定透析液及血浆LD浓度,并利用非线性混合效应模型(Nonlinear mixed effect model, NONMEM)进行群体药动学数据分析。结果:建立了包含大鼠个体间变异、个体自身变异及体质量、给药剂量等固定效应参数的统计学模型,原始数据估算的参数值均位于Bootstrap估算参数值的2.5%~97.5%范围内,视觉预测评估法显示建模大鼠外周血和中枢纹状体LD浓度基本位于90%百分位数范围之内,所建立的最终模型稳定、有效、且有较强的预测能力。体质量可影响LD药动参数K₃₂。结论:建立的群体药动学模型能较好地描述LD在大鼠中枢及外周血的药动学特点。大鼠给药剂量对LD药动参数无影响,体质量可影响LD药动参数。     

APriori lithium dosage regimen using population characteristics of pharmacokinetic parameters

The important problem of initiation of long-term lithium treatments tackled by means of the selection of an a prioridosage regimen based on the presumed efficacy of lithium and absence of toxicity. The pharmacokinetics of Li ⁺ ion is represented by a four-compartment open model including the supposed first-order processes for the release of the active compound from the dosage form and its absorption. Experimental protocols for measurements of serum concentrations and of urinary amounts after single and multiple dosing to healthy volunteers were derived with several oral dosage forms. Estimation of the pharmacokinetic parameters for each subject made it possible to validate the model for the various dosage forms. The interindividual variability of these parameters is taken into account by estimating the characteristics of the statistical distribution for the whole population. A dosage regimen is considered optimum when serum concentration profiles at steady state range from the threshold of efficacy (0.8 mmol/liter) to the threshold of toxicity (2.0 mmol/liter). When the number of daily intakes is fixed, the search for the optimum dose for the whole population is effected by minimizing the expected value of the random variable which characterizes the risks of excursion out of the therapeutic range. By this means universal dosages are shown to be unsatisfactory. However, certain dosage regimens individualized with respect to the renal clearance value of lithium and based on two or three daily intakes can give excellent results even when conventional dosage forms are used.This work was partly supported by grants D.G.R.S.T. No. 75.7.1267 (Adersa-Gerbios) and No. 75.7.1268 (Theraplix Laboratory).     

Comparison of two population pharmacokinetic programs,NONMEM and P-PHARM,for tacrolimus

OBJECTIVES: To compare the population modelling programs NONMEM and P-PHARM during investigation of the pharmacokinetics of tacrolimus in paediatric liver-transplant recipients. METHODS: Population pharmacokinetic analysis was performed using NONMEM and P-PHARM on retrospective data from 35 paediatric liver-transplant patients receiving tacrolimus therapy. The same data were presented to both programs. Maximum likelihood estimates were sought for apparent clearance (CL/F) and apparent volume of distribution (V/F). Covariates screened for influence on these parameters were weight, age, gender, post-operative day, days of tacrolimus therapy, transplant type, biliary reconstructive procedure, liver function tests, creatinine clearance, haematocrit, corticosteroid dose, and potential interacting drugs. RESULTS: A satisfactory model was developed in both programs with a single categorical covariate--transplant type--providing stable parameter estimates and small, normally distributed (weighted) residuals. In NONMEM, the continuous covariates--age and liver function tests--improved modelling further. Mean parameter estimates were CL/F (whole liver) = 16.3 l/h, CL/F (cut-down liver) = 8.5 l/h and V/F = 565 l in NONMEM, and CL/F = 8.3 l/h and V/F = 155 l in P-PHARM. Individual Bayesian parameter estimates were CL/F (whole liver) = 17.9 +/- 8.8 l/h, CL/F (cut-down liver) = 11.6 +/- 8.8 l/h and V/F = 712 +/- 792 l in NONMEM, and CL/F (whole liver) = 12.8 +/- 3.5 l/h, CL/F (cut-down liver) = 8.2 +/- 3.4 l/h and V/F = 221 +/- 164 l in P-PHARM. Marked interindividual kinetic variability (38-108%) and residual random error (approximately 3 ng/ml) were observed. P-PHARM was more user friendly and readily provided informative graphical presentation of results. NONMEM allowed a wider choice of errors for statistical modelling and coped better with complex covariate data sets. CONCLUSION: Results from parametric modelling programs can vary due to different algorithms employed to estimate parameters, alternative methods of covariate analysis and variations and limitations in the software itself.     

Population pharmacokinetic modeling of oral cyclosporin using NONMEM: comparison of absorption pharmacokinetic models and design of a Bayesian estimator

There have been very few population pharmacokinetic (PopPK) studies and Bayesian forecasting methods dealing with cyclosporin (CsA) so far, probably because of the difficulty of modeling the particular absorption profiles of CsA. The present study was conducted in stable renal transplant patients treated with Neoral and employed the NONMEM program. Its goals were (1) to develop a population pharmacokinetic model for CsA based on an Erlang frequency distribution (which describes asymmetric S-shaped absorption profiles) combined with a 2-compartment model; (2) to compare this model with models combining a time-lag parameter and either a zero-order or first-order rate constant and with a model based on a Weibull distribution; and (3) to develop a PK Bayesian estimator for full AUC estimation based on that "Erlang model." The PopPK model was developed in an index set of 70 patients, and then individual PK parameters and AUC were estimated in 10 other patients using Bayesian estimation. The "Erlang" model best described the data, with mean absorption time (MAT), apparent clearance (CL/F), and apparent volume of the central compartment (Vc/F) of 0.78 hours, 26.3 L/h, and 76 L, respectively (interindividual variability CV = 33, 30, and 48%). Bayesian estimation allowed accurate prediction of systemic exposure using only 3 samples collected at 0, 1, and 3 hours. Regression analysis found no significant difference between the predicted and observed concentrations (10 per patient), and AUC(0-12) were estimated with a nonsignificant bias (0.6 to 8.7%) and good precision (RMSE = 5.3%). In conclusion, the Erlang distribution best described CsA absorption profiles, and a Bayesian estimator developed using this model and a mixed-effect PK modeling program provided accurate estimates of CsA systemic exposure using only 3 blood samples.     

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, sigma 2 epsilon, indicating that the prediction interval, in contrast to point prediction, is sensitive to bias in the estimates of the population parameters.     

Experiences in the application of NONMEM to pharmacokinetic data analysis

Ethical issues arising from the use of patients in medical research have stimulated pharmacokinetic research in population kinetics, which requires only a few concentration samples of each individual. Using historical maprotiline data, the new approach of population kinetics was investigated and compared to individually estimated kinetics. Two different population kinetic methods were applied. The naive approach, a quick and dirty method, was compared to the nonlinear mixed-effects method, which was applied by the NONMEM package. Based on the results we obtained from actual maprotiline data as well as from simulated data, NONMEM is a reasonable tool for the estimation of population pharmacokinetic parameters. The main advantage of NONMEM over the naive approach lies in the possibility of obtaining standard deviations of random effects related to the variability between subjects.     

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。     

Determination of the population pharmacokinetic parameters of sustained-release and enteric-coated oral formulations,and the suppository formulation of diclofenac sodium by simultaneous data fitting using NONMEM

Data from sustained-release and enteric-coated oral formulations, and the suppository formulation of diclofenac sodium are fitted simultaneously using NONMEM® and the general linear model, ADVAN 5. Absorption and disposition parameters, serum levels, and absorption profiles were determined. The in vivo absorption profiles were determined using the program TOPFIT®. The in vivo absorption for the sustained-release formulation is slow first order and follows a flip-flop model since disposition rate constants are greater than absorption rate constants. Absorption from the enteric-coated form is essentially complete (≥95%) at about 7.5 h, while it is 95% complete at 24 h from the sustained-release formulation. This suggests likely absorption from the colon in the case of the sustained-release formulation since absorption is only 75% complete during the first 10 h. The sustained-release relative bioavailability is 90–99%. Absorption from the suppository is essentially complete at about 4.5 h. However, the relative bioavailability of the suppository formulation is low (55%), since defecation may remove the drug from the absorption site before complete absorption. © 1998 John Wiley & Sons, Ltd.     

A priori lithium dosage regimen using population characteristics of pharmacokinetic parameters

The important problem of initiation of long-term lithium treatment is tackled by means of the selection of an a priori dosage regimen based on the presumed efficacy of lithium and absence of toxicity. The pharmacokinetics of Li+ ion is represented by a four-compartment open model including the supposed first-order processes for the release of the active compound from the dosage form and its absorption. Experimental protocols for measurements of serum concentrations and of urinary amounts after single and multiple dosing to healthy volunteers were derived with several oral dosage forms. Estimation of the pharmacokinetic parameters for each subject made it possible to validate the model for the various dosage forms. The interindividual variability of these parameters is taken into account by estimating the characteristics of the statistical distribution for the whole population. A dosage regimen is considered optimum when serum concentration profiles at steady state range from the threshold of efficacy (0.8 mmol/liter) to the threshold of toxicity (2.0 mmol/liter). When the number of daily intakes is fixed, the search for the optimum dose for the whole population is effected by minimizing the expected value of the random variable which characterizes the risks of excursion out of the therapeutic range. By this means universal dosages are shown to be unsatisfactory. However, certain dosage regimens individualized with respect to the renal clearance value of lithium and based on two or three daily intakes can give excellent results even when conventional dosage forms are used.     

Predictive Performance of a Semiparametric Method to Estimate Population Pharmacokinetic Parameters Using NONMEM

Routine clinical pharmacokinetic (PK) data collected from patients receiving inulin were analyzed to estimate population PK parameters; 560 plasma concentration determinations for inulin were obtained from 90 patients. The data were analyzed using NONMEM. The population PK parameters were estimated using a Constrained Longitudinal Splines (CLS) semiparametric approach and a first-order conditional method (FOCE). The mean posterior individual clearance values were 7.73 L/hr using both parametric and semiparametric methods. This estimation was compared with clearances estimated using standard nonlinear weighted least squares approach (reference value, 7.64 L/hr). The bias was not statistically different from zero and the precision of the estimates was 0.415 L/hr using parametric method and 0.984 L/hr using semiparametric method. To evaluate the predictive performances of the population parameters, 17 new subjects were used. First, the individual inulin clearance values were estimated from drug concentration–time curve using a nonlinear weighted least-squares method then they were estimated using the NONMEM POSTHOC method obtained using parametric and CLS methods as well as an alternative method based on a Monte Carlo simulation approach. The population parameters combined with two individual inulin plasma concentrations (0.25 and 2 hr) led to an estimation of individual clearances without bias and with a good precision. This paper not only evaluates the relative performance of the parametric and the CLS methods for sparse data but also introduces a new method for individual estimation.