Incorporating measures of variability and uncertainty into the prediction of in vivo hepatic clearance from in vitro data.

The existing procedures for quantitative in vitro-in vivo clearance prediction can be significantly biased either by totally neglecting the existing variability and uncertainty by using mean parameter values or by implementing Monte Carlo simulation with statistical distribution of the parameters reconstructed from very small sets of data. The aim of the present study is to develop a methodology for the prediction of in vivo hepatic clearance in the presence of semiquantitative or qualitative data and accounting for the existing uncertainty and variability. The method consists of two steps: 1) transformation of the information available into fuzzy sets (fuzzification); and 2) computation of the in vivo clearance using arithmetic operations with fuzzy sets. To illustrate the approach, rat hepatocyte and microsomal data for eight benzodiazepine compounds are used. A comparison with a standard Monte Carlo procedure is made. The methodology proposed can be used when Monte Carlo simulation may be biased or cannot be implemented. The obtained fuzzy in vivo clearance can be used subsequently in fuzzy simulations of pharmacokinetic models.     

Fuzzy Simulation of Pharmacokinetic Models: Case Study of Whole Body Physiologically Based Model of Diazepam

The aim of the present study is to develop and implement a methodology that accounts for parameter variability and uncertainty in the presence of qualitative and semi-quantitative information (fuzzy simulations) as well as when some parameters are better quantitatively defined than others (fuzzy-probabilistic approach). The fuzzy simulations method consists of (i) representing parameter uncertainty and variability by fuzzy numbers and (ii) simulating predictions by solving the pharmacokinetic model. The fuzzy-probabilistic approach includes an additional transformation between fuzzy numbers and probability density functions. To illustrate the proposed method a diazepam WBPBPK model was used where the information for hepatic intrinsic clearance determined by in vitro-in vivo scaling was semi-quantitative. The predicted concentration time profiles were compared with those resulting from a Monte Carlo simulation. Fuzzy simulations can be used as an alternative to Monte Carlo simulation.     

Uncertainty Analysis in Pharmacokinetics and Pharmacodynamics: Application to Naratriptan

Purpose The aim of the study was to predict pain relief of migraine in patients following naratriptan oral (tablet) administration by using uncertainty analysis. The analysis was based on phase I pharmacokinetic naratriptan data, sumatriptan pharmacodynamic data, and naratriptan preclinical (animal) potency information, together with general knowledge as to how migraine affects oral absorption. Methods A previously developed pharmacokinetic (PK)/pharmacodynamic (PD) model for naratriptan disposition and effect was used. The uncertain parameters in the model, which were associated with absorption and scaling between first-in-class compound sumatriptan and naratriptan, were modeled using fuzzy sets theory. Global sensitivity analysis was then used to investigate the impact of each PK/PD parameter on the responses. Results Acknowledging parametric uncertainty did not improve prediction of the probability of pain relief. Global sensitivity analysis demonstrated that predictions were heavily influenced by interindividual variability in pharmacodynamics, as the dose response relationship was relatively insensitive to the pharmacokinetics. Conclusions To predict the probability of pain relief following oral (tablet) administration of naratriptan, a simple dose response, instead of the PK/PD model, would have yielded very similar predictions. The naratriptan PK/PD model may be improved by either refining the PD model or better still by specifying the interindividual error by additional data collecting with an improved design.     

Modelling and simulation of variability and uncertainty in toxicokinetics and pharmacokinetics

Two important methodological issues within the framework of the variability and uncertainty analysis of toxicokinetic and pharmacokinetic systems are discussed: (i) modelling and simulation of the existing physiologic variability in a population; and (ii) modelling and simulation of variability and uncertainty when there is insufficient or not well defined (e.g. small sample, semiquantitative, qualitative and vague) information available. Physiologically based pharmacokinetic models are especially suited for separating and characterising the physiologic variability from the overall variability and uncertainty in the system. Monte Carlo sampling should draw from multivariate distributions, which reflect all levels of existing dependencies in the intact organism. The population characteristics should be taken into account. A fuzzy simulation approach is proposed to model variability and uncertainty when there is semiquantitative, qualitative and vague information about the model parameters and their statistical distributions cannot be defined reliably.     

Deterministic identifiability of population pharmacokinetic and pharmacokinetic–pharmacodynamic models

Identifiability is an important component of pharmacokinetic–pharmacodynamic (PKPD) model development. Structural identifiability is concerned with the uniqueness of the model parameters for a set of perfect input–output data and deterministic identifiability with the precision of parameter estimation given imperfect input–output data. We introduce two subcategories of deterministic identifiability, external and internal, and consider factors that distinguish between these forms. We define external deterministic identifiability as a function of externally controllable variables, i.e., the design, and internal deterministic identifiability as a function of the model and its parameter values. The concepts are explored using three common PK and PKPD models, and verified for their precision for the selected set of parameter values under optimal design.     

Dichloroacetate: population pharmacokinetics with a pharmacodynamic sequential link model

Dichloroacetate (DCA) is a small molecule that reduces ambient concentrations of lactate in man. It was the purpose of this study to develop pharmacokinetic and pharmacodynamic models for determination of a dose for a pivotal Phase III clinical trial of DCA in patients with traumatic brain injury (TBI). Population pharmacokinetic and pharmacodynamic models were developed for DCA using NONMEM software. The pharmacokinetic data were fit to a physiologic two-compartment model, and the pharmacodynamic data were fit to an indirect physiologic response model. Simulations were employed to evaluate various dosing strategies for consideration in a pivotal Phase III clinical trial of DCA. For the pharmacokinetic model, it was discovered that the clearance of DCA decreased on multiple dosing from 4.82 L/h to 1.07 L/h and that the pharmacokinetics and pharmacodynamics in TBI patients could not be predicted from normal volunteers. Population pharmacokinetic modeling and simulation of the expected effects of several dosing strategies were useful procedures for designing a Phase III trial.     

dOFV distributions: a new diagnostic for the adequacy of parameter uncertainty in nonlinear mixed-effects models applied to the bootstrap

Knowledge of the uncertainty in model parameters is essential for decision-making in drug development. Contrarily to other aspects of nonlinear mixed effects models (NLMEM), scrutiny towards assumptions around parameter uncertainty is low, and no diagnostic exists to judge whether the estimated uncertainty is appropriate. This work aims at introducing a diagnostic capable of assessing the appropriateness of a given parameter uncertainty distribution. The new diagnostic was applied to case bootstrap examples in order to investigate for which dataset sizes case bootstrap is appropriate for NLMEM. The proposed diagnostic is a plot comparing the distribution of differences in objective function values (dOFV) of the proposed uncertainty distribution to a theoretical Chi square distribution with degrees of freedom equal to the number of estimated model parameters. The uncertainty distribution was deemed appropriate if its dOFV distribution was overlaid with or below the theoretical distribution. The diagnostic was applied to the bootstrap of two real data and two simulated data examples, featuring pharmacokinetic and pharmacodynamic models and datasets of 20–200 individuals with between 2 and 5 observations on average per individual. In the real data examples, the diagnostic indicated that case bootstrap was unsuitable for NLMEM analyses with around 70 individuals. A measure of parameter-specific “effective” sample size was proposed as a potentially better indicator of bootstrap adequacy than overall sample size. In the simulation examples, bootstrap confidence intervals were shown to underestimate inter-individual variability at low sample sizes. The proposed diagnostic proved a relevant tool for assessing the appropriateness of a given parameter uncertainty distribution and as such it should be routinely used.     

Population pharmacokinetics and pharmacodynamics of oral levodopa in parkinsonian patients

Objective: The population pharmacokinetics and pharmacodynamics of a standardised oral test dose of levodopa have been determined in patients with mild to severe Parkinson’s disease using parametric, non-linear mixed effect modelling with the program NONMEM. Levodopa plasma concentration data and motor effect behaviour (tapping times) were obtained from 46 patients, for whom a total of 970 observations were available (approximately 21 pharmacokinetic and pharmacodynamic observations per patient). The pharmacokinetic-pharmacodynamic model used was a one-compartment first-order absorption model linked to the sigmoid E_Max representation of the Hill equation via an equilibration rate-constant, ke₀. The model was also tested via a reduction in the number of pharmacokinetic and pharmacodynamic data points to a total of four to eight per patient. Results: In the final regression models the Hoehn and Yahr (HY) status of the patient and duration of disease (DUR) were found to be important determinants of the pharmacodynamic parameters for levodopa. The pharmacokinetic parameters were not significantly affected by any covariates. A test group of 16 additional parkinsonian patients was used to evaluate the predictive performance of the population parameters. The predictive performance of the pharmacokinetic-pharmacodynamic modelling using the full and reduced data sets was evaluated in NONMEM using posthoc, Bayesian forecasting. Statistically insignificant bias existed among predicted and observed levodopa concentrations, whereas the pharmacodynamic model underpredicted the observed tapping times. There was little difference in the pharmacokinetic-pharmacodynamic predictive performance among results for the full and the reduced data sets. Conclusion: In a clinical setting knowledge of the population pharmacokinetic and pharmacodynamic parameters for oral levodopa may prove useful in estimating the duration of the drug’s beneficial motor activity in patients with mild to severe Parkinson’s disease (Hoehn and Yahr status I–IV). Received: 13 November 1995/Accepted in revised form: 13 February 1996     

曲马多对小鼠镇痛作用的药物代谢动力学研究

目的　探讨曲马多在小鼠体内的药物代谢动力学。方法　采用药效—药代统一模型 ,以小鼠腹腔注射醋酸后扭体反应次数为镇痛效应指标 ,测定时—效、量—效关系 ,进一步求时间—体存生物相当药量曲线及相应药代动力学参数。结果　曲马多在小鼠的镇痛作用呈显著的时—效、量—效关系 ,其镇痛作用效量半衰期(T1 /2 ,ED)为 4 68min ,消除速率常数K为 0 1 4 8。结论　曲马多母核药物与多种代谢产物均有镇痛作用 ,此法比单纯测定曲马多的血药浓度更能科学地反映药物在作用部位的药效变化规律     

以药效学参数为终点指标的生物等效性评价方法

生物等效性是仿制药一致性评价的重要阶段。以药效学参数为终点指标评价生物等效性方法逐渐引发关注。在药动学方法无法实施或药动学参数无法灵敏地体现两药差异的情况下,选择合理的药效学参数作为终点指标可有效地评价药品之间的差异。参考相关指南、法规及文献,系统地阐述药效学方法的适用条件,根据量效曲线选择终点指标,终点参数分析以及具体药物方法设计等,为相关研究提供参考和帮助。     

基于随机微分方程的群体药物代谢动力学参数的极大似然估计

目的:阐述基于随机微分方程的混合模型在群体药物代谢动力学中参数估计的应用。方法:在随机微分方程的框架下,写出精确的似然函数,通过极大似然估计求解参数值。结果:利用计算机随机模拟证明方法的可行性,并对模拟的结果进行统计分析,得到各参数的点估计值和置信域,符合模拟的预设值。结论:在群体药物代谢动力学研究中,对基于随机微分方程的混合效应模型采用极大似然估计可以得到较好的估计值。     

Comparison of stepwise and simultaneous estimations of population pharmacokinetics and pharmacodynamics of TS-943.

The prediction performances of population pharmacokinetic-pharmacodynamic analysis of the two methods (a stepwise and a simultaneous estimations) were evaluated with respect to their accuracies and precisions. A study was designed to investigate the safety and efficacy of TS-943 by a 4 hours constant infusion in 36 healthy male subjects. Population analysis was performed using pharmacokinetic and pharmacodynamic models with NONMEM. The mean of the prediction error (MPE) and the root mean squared error (RMSE) served as a measure of accuracy and precision. In addition, a bootstrap validation was also performed. The results indicate that those population pharmacokinetic-pharmacodynamic parameters for the two methods were comparable. The results of simultaneous estimations are similar to those obtained using a stepwise estimation. The mean parameter estimates obtained with the additional 200 bootstrap replicates of data were within 15% of those obtained with the final model in both methods. The present results demonstrated that the accuracy of pharmacodynamic evaluations using a stepwise end a simultaneous estimations was comparable.     

Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004

Model evaluation is an important issue in population analyses. We aimed to perform a systematic review of all population pharmacokinetic and/or pharmacodynamic analyses published between 2002 and 2004 to survey the current methods used to evaluate models and to assess whether those models were adequately evaluated. We selected 324 articles in MEDLINE using defined key words and built a data abstraction form composed of a checklist of items to extract the relevant information from these articles with respect to model evaluation. In the data abstraction form, evaluation methods were divided into three subsections: basic internal methods (goodness-of-fit [GOF] plots, uncertainty in parameter estimates and model sensitivity), advanced internal methods (data splitting, resampling techniques and Monte Carlo simulations) and external model evaluation. Basic internal evaluation was the most frequently described method in the reports: 65% of the models involved GOF evaluation. Standard errors or confidence intervals were reported for 50% of fixed effects but only for 22% of random effects. Advanced internal methods were used in approximately 25% of models: data splitting was more often used than bootstrap and cross-validation; simulations were used in 6% of models to evaluate models by a visual predictive check or by a posterior predictive check. External evaluation was performed in only 7% of models. Using the subjective synthesis of model evaluation for each article, we judged the models to be adequately evaluated in 28% of pharmacokinetic models and 26% of pharmacodynamic models. Basic internal evaluation was preferred to more advanced methods, probably because the former is performed easily with most software. We also noticed that when the aim of modelling was predictive, advanced internal methods or more stringent methods were more often used.     

Regression methods for developing QSAR and QSPR models to predict compounds of specific pharmacodynamic, pharmacokinetic and toxicological properties

Quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) models have been extensively used for predicting compounds of specific pharmacodynamic, pharmacokinetic, or toxicological property from structure-derived physicochemical and structural features. These models can be developed by using various regression methods including conventional approaches (multiple linear regression and partial least squares) and more recently explored genetic (genetic function approximation) and machine learning (k-nearest neighbour, neural networks, and support vector regression) approaches. This article describes the algorithms of these methods, evaluates their advantages and disadvantages, and discusses the application potential of the recently explored methods. Freely available online and commercial software for these regression methods and the areas of their applications are also presented.     

喹诺酮类抗菌药物的药动学和药效学研究进展

喹诺酮类是目前临床普遍使用的一类抗菌药物.现从体外实验、动物实验和人体试验等方面对其药动学/药效学(PK/PD)研究进行了综述,并对PK/PD与细菌耐药及其在临床上的应用进行了简介.     

Physiological-model-based derivation of the adult and child pharmacokinetic intraspecies uncertainty factors for volatile organic compounds

The intraspecies uncertainty factor (UF(HH)=10x) is used in the determination of the reference dose or reference concentration and accounts for the pharmacokinetic and pharmacodynamic heterogeneity within the human population. The Food Quality Protection Act of 1996 mandated the use of an additional uncertainty factor (UF(HC)=10x) to take into account potential pre- and postnatal toxicity and lack of completeness of the data with respect to exposure and toxicity to children. There is no conclusive experimental or theoretical justification to support or refute the magnitude of the UF(HH) and UF(HC) nor any conclusive evidence to suggest that a factor of 100 is needed to account for intrahuman variability. This study presents a new chemical-specific method for estimating the pharmacokinetic (PK) component of the interspecies uncertainty factor (UF(HH-PK) and UF(HC-PK)) for volatile organic compounds (VOCs). The approach utilizes validated physiological-based pharmacokinetic (PBPK) models and simplified physiological-model-based algebraic equations to translate ambient exposure concentration to tissue dose in adults and children the ratio of which is the UF(HH-PK) and UF(HC-PK). The results suggest that: (i) the UF(HH-PK) and UF(HC-PK) are chemical specific; (ii) for the chemicals used in this study there is no significant difference between UF(HH-PK) and UF(HC-PK); (iii) the magnitude of UF(HH-PK) and UF(HC-PK) varies between 0.033 and 2.85 with respect to tissue and blood concentrations; (iv) the body weight, the rate of ventilation, the fraction of cardiac output flowing to the liver, the blood : air partition coefficient, and the hepatic extraction ratio are the only parameters that play a critical role in the variability of tissue and blood doses within species; and (v) the magnitude of the UF(HH-PK) and UF(HC-PK) obtained with the simplified steady-state equations is essentially the same with that obtained with PBPK models. Overall, this study suggests that no adult-children differences in the parent chemical concentrations of the VOCs are likely to be observed during inhalation exposures. The physiological-model-based approaches used in the present study to estimate the UF(HH-PK) and UF(HC-PK) provide a scientific basis for their magnitude. They can replace the currently used empirical default approaches to provide chemical-specific UF(HH-PK) in future risk assessments.     

用模型和模拟方法设计氨氯地平的群体药动学研究方案

合理的采样设计是建立可靠群体药动学模型的重要基础。应用非线性混合效应模型的群体药动学研究,是一种有效利用稀疏血样数据估算群体药动学参数的方法。本研究根据D最优化设计和贝叶斯法设计采样方案。以已报道的氨氯地平群体药动学模型为基础,根据临床研究的目的、给药方案和随访时间等设计几套采样方案,采用WinPOPT软件计算优化采样方案,用蒙特卡罗法(Monte Carlo)对各优化的采样方案分别建立一套含400个患者的NONMEM数据文件,用NONMEM7.2软件模拟氨氯地平的浓度数据,然后估算其重要药动学参数(CL/F,V/F和Ka),并计算其平均预测误差(MPE)和平均绝对预测误差(MAPE)。在6个采样方案中,以方案6和3对CL/F估算的准确度和精密度较优,MPE分别为0.1%和0.6%,MAPE均为0.7%。对V的估算,各采样方案间无明显差异。因此,选用氨氯地平拟合药动学参数的准确度和精密度较优,且采样点个数较少的方案3为最佳临床研究方案。本研究旨在为开展氨氯地平在肾功能损害合并高血压患者的群体药动学研究提供科学、有效的采样方法,为群体PK/PD研究提供一种优化设计临床研究方案的科学方法。     

Electroencephalogram-based pharmacodynamic measures: a review

Pharmacokinetics and pharmacodynamics can provide a useful modeling framework for predicting drug activity and can serve as a basis for dose optimization. Determining a suitable biomarker or surrogate measure of drug effect for pharmacodynamic models can be challenging. The electroencephalograph is a widely-available and non-invasive tool for recording brainwave activity simultaneously from multiple brain regions. Certain drug classes (such as drugs that act on the central nervous system) also generate a reproducible electroencephalogram (EEG) effect. Characterization of such a drug-induced EEG effect can produce pharmacokinetic/pharmacodynamic models useful for titrating drug levels and expediting development of chemically-similar drug analogs. This paper reviews the relevant concepts involved in pharmacokinetic/pharmacodynamic modeling using EEG-based pharmacodynamic measures. In addition, examples of such models for various drugs are organized by drug activity as well as chemical structure and presented.