A Semiparametric Method for Describing Noisy Population Pharmacokinetic Data

We propose a semiparametric method to estimate model-independent pharmacokinetic (PK) measures such as area under concentration–time, peak concentration and time to peak concentration (T_peak ), for noisy population PK data from a sparsely sampled prospectively designed trial. The method is developed within the mixed-effect model framework, for the single-dose and steady-state case. We describe individual concentration vs. time using a longitudinal spline, consisting of a template spline, common to all individuals, and an individual-specific distortion spline accounting for individual differences. We impose a number of constraints on the longitudinal spline, including (i) it has a decreasing tail, (ii) its typical T_peak is near the modal T_peak observed in the population data, and (iii) its value is zero at time zero (single dose), or the same nonzero value at the beginning and end of a dosing interval (steady state). We test our method using simulated data and compare its performance to that of a parametric and a nonparametric method. An actual data example is also shown. The performance of the method is as good or better than that of a standard nonparametric method, and when the analysis model is misspecified, the method is superior to a standard parametric one. Since it is often not apparent that an analysis model is correct, we propose this approach as a general method for analysis.     

迭代二步法估算维拉帕米的群体药动学参数

目的 :为临床合理应用维拉帕米提供依据。方法 :53例高血压患者口服维拉帕米片 ,采用荧光分光光度法测定血浆中维拉帕米浓度 ,用迭代二步法估算维拉帕米的群体药动学参数 ,并与传统二步法的结果比较。结果 :迭代二步法估算维拉帕米的CL为(189 3±59 3)ml/(h·kg) ,Vd 为 (1 420±0 231)L/kg ,T1/2 为 (5 74±1 90)h ,与传统二步法拟合的结果基本一致。结论 :迭代二步法能较好地估算出维拉帕米的群体及个体药动学参数 ,可用于预测血药浓度及优化个体给药方案。     

Bayesian反馈法估算静脉输注伏立康唑的群体药动学参数

目的用Bayesian反馈法估算临床患者静脉输注伏立康唑的群体药动学(PPK)参数。方法收集静脉输注给药不同时间后的血样,采用HPLC法测定伏立康唑血药浓度,用Bayesian反馈法估算PPK参数。结果以二室模型拟合伏立康唑的药动学过程,得PPK参数为Vss为(46.58±19.35)L,CL为(4.76±2.64)L/h,k10为(0.187±0.006)h-1k,12为(4.97±0.02)h-1,k21为(0.895±0.308)h-1。结论此PPK模型能够较准确地描述伏立康唑在临床患者静脉输注的药动学特征,其预测能力尚待进一步评估。     

非线性混合效应模型法估算癫痫患者卡马西平的群体药动学参数

目的:建立癫痫患者卡马西平(CBZ)的群体药动学(PPK)模型。方法:采集我院服用CBZ的270例门诊癫痫患者的稳态血药浓度数据(共316个样本)以及患者相关资料数据。应用非线性混合效应模型(NONMEM)法估算癫痫患者CBZ的PPK参数值,建立PPK模型。并运用自举法(Bootstrap)验证模型的可靠性。结果:年龄(AGE)、每日服药剂量(DKG)、体质量(BW)均为CBZ清除率(CL)的影响因素。最终模型:当AGE≤14岁时,CL(L/h)=[2.55+0.013×(AGE-15)]×(DKG/0.011)0.443×(BW/40)0.392;AGE>14岁时,CL(L/h)=2.55×(DKG/0.011)0.443×(BW/40)0.392。表观分布容积(Vd)=85L。经Bootstrap法验证,本模型稳定、可靠。结论:用NONMEM软件成功建立我院癫痫患者服用CBZ的PPK模型。根据本院癫痫患者的PPK模型,结合患者DKG、BW和合并用药可估算其CL,优化临床个体化用药方案。     

用NONMEM法建立西酞普兰群体药代动力学模型

目的建立中国人西酞普兰(抗抑郁药)的群体药代动力学(PPK)模型,为临床个体化给药提供参考。方法用群体药代动力学方法,对西酞普兰生物等效性研究中23例受试者的血药浓度和临床资料进行分析,用NON-MEM软件求算西酞普兰的PPK参数值,建立西酞普兰的PPK模型,并进行模型验证。结果经NONMEM法处理,所有因素中,年龄、体重以及CYP2C19基因型对中央隔室清除率有显著性的影响;体重对分布容积有显著性的影响。年龄和体重的增加对清除率影响分别为-0.39L·h-1.a-1和0.18L.h-1·kg-1。结论用NONMEM软件拟合获得的西酞普兰群体药代动力学最终模型,经验证稳定可靠。     

Propagation of Population Pharmacokinetic Information Using a Bayesian Approach: Comparison with Meta-Analysis

We investigated the propagation of population pharmacokinetic information across clinical studies by applying Bayesian techniques. The aim was to summarize the population pharmacokinetic estimates of a study in appropriate statistical distributions in order to use them as Bayesian priors in consequent population pharmacokinetic analyses. Various data sets of simulated and real clinical data were fitted with WinBUGS, with and without informative priors. The posterior estimates of fittings with non-informative priors were used to build parametric informative priors and the whole procedure was carried on in a consecutive manner. The posterior distributions of the fittings with informative priors where compared to those of the meta-analysis fittings of the respective combinations of data sets. Good agreement was found, for the simulated and experimental datasets when the populations were exchangeable, with the posterior distribution from the fittings with the prior to be nearly identical to the ones estimated with meta-analysis. However, when populations were not exchangeble an alternative parametric form for the prior, the natural conjugate prior, had to be used in order to have consistent results. In conclusion, the results of a population pharmacokinetic analysis may be summarized in Bayesian prior distributions that can be used consecutively with other analyses. The procedure is an alternative to meta-analysis and gives comparable results. It has the advantage that it is faster than the meta-analysis, due to the large datasets used with the latter and can be performed when the data included in the prior are not actually available.     

Population Pharmacokinetic Analysis of Mizolastine and Validation from Sparse Data on Patients Using the Nonparametric Maximum Likelihood Method

A population analysis of the kinetics of mizolastine was performed from concentrations on 449 allergic patients, using the nonparametric maximum likelihood method (NPML). A two-compartment open model with zero-order absorption was used to describe the kinetics of mizolastine after oral administration. A heteroscedastic variance model was assumed for the error. To explain the kinetic variability, eight covariates were introduced in the analysis: gender, pharmaceutical dosage form, age, body weight, serum creatinine concentration, creatinine renal clearance, plasma levels of hepatic transaminases ASAT and ALAT. Their relationships to the kinetic parameters were studied by means of the estimated distribution of each kinetic parameter conditional on different levels of each covariate. An important interindividual kinetic variability was found for all parameters. Moreover, several kinetic parameters among which the duration of absorption were found to be influenced by pharmaceutical dosage form and gender. Body weight and creatinine renal clearance were found to have a little influence on the oral clearance and the smallest disposition rate constant. This population analysis was validated on a separate group of 247 other patients. For each observed concentration of this sample, a predictive distribution was computed using the individual covariates. Predicted concentrations and standardized prediction errors were deduced. The mean and variance of the standardized prediction errors were, respectively, 0.21 and 2.79. Moreover, in the validation sample, the predicted cumulative distribution function of each observed concentration was computed. Empirical distribution of these values was not significantly different from a uniform distribution, as expected under the assumption that the population model estimated by NPML is adequate.     

Performance of an Iterative Two-Stage Bayesian Technique for Population Pharmacokinetic Analysis of Rich Data Sets

Purpose To test the suitability of an Iterative Two-Stage Bayesian (ITSB) technique for population pharmacokinetic analysis of rich data sets, and to compare ITSB with Standard Two-Stage (STS) analysis and nonlinear Mixed Effect Modeling (MEM). Materials and Methods Data from a clinical study with rapacuronium and data generated by Monte Carlo simulation were analyzed by an ITSB technique described in literature, with some modifications, by STS, and by MEM (using NONMEM). The results were evaluated by comparing the mean error (accuracy) and root mean squared error (precision) of the estimated parameter values, their interindividual standard deviation, correlation coefficients, and residual standard deviation. In addition, the influence of initial estimates, number of subjects, number of measurements, and level of residual error on the performance of ITSB were investigated. Results ITSB yielded best results, and provided precise and virtually unbiased estimates of the population parameter means, interindividual variability, and residual standard deviation. The accuracy and precision of STS was poor, whereas ITSB performed better than MEM. Conclusions ITSB is a suitable technique for population pharmacokinetic analysis of rich data sets, and in the presented data set it is superior to STS and MEM. An erratum to this article can be found at     

Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model

Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).     

Diazepam Pharamacokinetics from Preclinical to Phase I Using a Bayesian Population Physiologically Based Pharmacokinetic Model with Informative Prior Distributions in Winbugs

Modelling is an important applied tool in drug discovery and development for the prediction and interpretation of drug pharmacokinetics. Preclinical information is used to decide whether a compound will be taken forwards and its pharmacokinetics investigated in human. After proceeding to human little to no use is made of these often very rich data. We suggest a method where the preclinical data are integrated into a whole body physiologically based pharmacokinetic (WBPBPK) model and this model is then used for estimating population PK parameters in human. This approach offers a continuous flow of information from preclinical to clinical studies without the need for different models or model reduction. Additionally, predictions are based upon single parameter values, but making realistic predictions involves incorporating the various sources of variability and uncertainty. Currently, WBPBPK modelling is undertaken as a two-stage process: (i) estimation (optimisation) of drug-dependent parameters by either least squares regression or maximum likelihood and (ii) accounting for the existing parameter variability and uncertainty by stochastic simulation. To address these issues a general Bayesian approach using WinBUGS for estimation of drug-dependent parameters in WBPBPK models is described. Initially applied to data in rat, this approach is further adopted for extrapolation to human, which allows retention of some parameters and updating others with the available human data. While the issues surrounding the incorporation of uncertainty and variability within prediction have been explored within WBPBPK modeling methodology they have equal application to other areas of pharmacokinetics, as well as to pharmacodynamics.     

Analytical Expressions for Combining Population Pharmacokinetic Parameters from Different Studies

We provide a set of formulas that allow the combination of separately performed analyses of population pharmacokinetic (PK) studies, without any further computational effort. More specifically, given the point estimates and uncertainties of two population PK analyses, the formulas provide the point estimates and uncertainties of the combined analysis, including the mean population values, the between-subject variability, and the residual variability. To derive the formulas we considered distributional assumptions applicable for the conjugate priors of the Bayesian problem of “unknown mean and variance.” In order to demonstrate the approach, the formulas were applied to an example involving the results of fitting two real experimental datasets. The formulas presented offer an easy-to-use method of combining different analyses particularly applicable to a combination of literature information.     

用NONMEM法建立癫痫患者丙戊酸群体药代动力学模型

目的建立丙戊酸（VPA）在癫痫患者中的群体药代动力学（PPK）模型,考察固定效应因素对VPA清除率（CL/F）的影响。方法回顾性收集贵州省人民医院111名癫痫患者VPA稳态血药浓度数据及相应的人口学、合并用药及CYP2A6基因型等资料,随机将患者分成建模组（74名）及验证组（37名）,使用建模组数据通过非线性混合效应模型（NONMEM）程序建立VPA的PPK模型。使用验证组数据来验证模型的准确度和精密度,比较基础模型和最终模型的平均预测误差（MPE）、平均绝对误差（MAE）、平均根方差（RMSE）。结果建立的最终模型包含了日用药剂量（DDO）及CYP2A6基因型,模型方程为：CL/F=0.363.DDO0.525.1.29GENECYP2A6。最终模型有更好的精密度及准确度,基础模型MPE、MAE、RMSE值为-10.631、4.40、22.55,最终模型相应值为-6.11、9.06、14.17。结论本研究初步建立癫痫患者VPA的PPK模型,VPA清除率随日给药剂量的增大而增大,CYP2A6野生型（CYP2A6＊1/＊1）组患者较CYP2A6突变型（CYP2A6＊1/＊4、CYP2A6＊4/＊4）组患者有更高的VPA清除率。     

用NONMEM法建立癫痫患者丙戊酸群体药代动力学模型

目的 建立丙戊酸(VPA)在癫痫患者中的群体药代动力学(PPK)模型,考察固定效应因素对VPA清除率(CL/F)的影响.方法 回顾性收集贵州省人民医院111名癫痫患者VPA稳态血药浓度数据及相应的人口学、合并用药及CYP2A6基因型等资料,随机将患者分成建模组(74名)及验证组(37名),使用建模组数据通过非线性混合效应模型(NONMEM)程序建立VPA的PPK模型.使用验证组数据来验证模型的准确度和精密度,比较基础模型和最终模型的平均预测误差(MPE)、平均绝对误差(MAE)、平均根方差(RMSE).结果 建立的最终模型包含了日用药剂量(DDO)及CYP2A6基因型,模型方程为:CL/F=0.363·DD00.525·1.29GENECYP2A6.最终模型有更好的精密度及准确度,基础模型MPE、MAE、RMSE值为- 10.63、14.40、22.55,最终模型相应值为-6.11、9.06、14.17.结论 本研究初步建立癫痫患者VPA的PPK模型,VPA清除率随日给药剂量的增大而增大,CYP2A6野生型(CYP2A6*1/*1)组患者较CYP2A6突变型(CYP2A6* 1/*4、CYP2A6* 4/*4)组患者有更高的VPA清除率.     

Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters

Population pharmacokinetic (PPK) analysis usually employs nonlinear mixed effects models using first-order linearization methods. It is well known that linearization methods do not always perform well in actual situations. To avoid linearization, the Monte Carlo integration method has been proposed. Moreover, we generally utilize asymptotic confidence intervals for PPK parameters based on Fisher information. It is known that likelihood-based confidence intervals are more accurate than those from the usual asymptotic confidence intervals. We propose profile likelihood-based confidence intervals using Monte Carlo integration. We have evaluated the performance of the proposed method through a simulation study, and analyzed the erythropoietin concentration data set by the method.     

A three-step approach combining bayesian regression and NONMEM population analysis: Application to midazolam

NONMEM, the only available supported program for population pharmacokinetic analysis, does not provide the analyst with individual subject parameter estimates. As a result, the relationship between pharmacokinetic parameters and demographic factors such as age, gender, and body weight cannot be sought by plotting demographic factors vs. kinetic parameters. To overcome this problem, we devised a three-step approach. In step 1, an initial NONMEM analysis provides the population pharmacokinetic parameters without taking into account the demographic factors. Step 2 consists of individual bayesian regressions using the measured drug concentrations for each subject and the population pharmacokinetic parameters obtained in step 1. The bayesian parameter estimates of the individual subject can be plotted against the demographic factors of interest. From the scatter plots, it can be seen which are the demographic factors that appear to affect the pharmacokinetic parameters. In step 3, the NONMEM analysis is resumed, and the demographic factors found in step 2 are entered into the NONMEM regression model in a stepwise manner. This method was used to analyze the pharmacokinetics of midazolam in 64 subjects from 714 plasma concentrations and 11 demographic factors. CL (elimination clearance) and V₁ were found to be a function of body weight. Age and liver disease were found to decrease CL. Of the 11 demographic factors recorded for each patient, none was found to influence V_ss or intercompartmental clearance.Supported in part by the Swiss National Science Foundation (Dr. Maitre) and the National Institute on Aging Grant R01-AG03104 (Dr. Stanski). Presented in abstract form at the Annual Meeting of the American Society for Clinical Pharmacology and Therapeutics, Nashville, TN, March 1989.     

用群体药代动力学模型实现抗生素个体化给药

目的:介绍群体药代动力学模型在抗生素调整剂量上的应用。方法:群体药代动力学模型以及药代动力学(PK)-药效动力学(PD)模型的基本概念、建立步骤、应用特点以及国内外发展现状。并通过两个举例说明剂量调试方法。结果与结论:群体药代动力学和TDM监测紧密联系用于临床抗感染治疗,PK-PD模型的应用有利于临床药学的剂量设计和剂量调整,为不同患者群体的抗感染治疗的最合理解释。     

Estimating Bias in Population Parameters for Some Models for Repeated Measures Ordinal Data Using NONMEM and NLMIXED

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

Bayesian反馈法估算静脉输注伏立康唑的群体药动学参数

目的 用Bayesian反馈法估算临床患者静脉输注伏立康唑的群体药动学(PPK)参数.方法　收集静脉输注给药不同时间后的血样,采用HPLC法测定伏立康唑血药浓度,用Bayesian反馈法估算PPK参数.结果 以二室模型拟合伏立康唑的药动学过程,得PPK参数为Vss为(46.58±19.35)L,CL为(4.76±2.6...     

Bayesian Population Pharmacokinetic and Pharmacodynamic Analyses Using Mixture Models

Population studies of the pharmacokinetics or pharmacodynamics or drugs help us learn about the variability in drug disposition and effects, information that can be used to treat future patients at safe and effective doses. We present a new approach to population modeling based on a weighted mixture of normal distributions having random weights and means. This method allows estimation of underlying continuous population distributions without prespecifying the parametric form or shape of these probability distributions. Additionally, this method can carry out nonparametric regression of pharmacokinetic or dynamic parameters on patient covariates while estimating the underlying distributions. Two examples illustrate the method and its flexibility.     

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.