Monte Carlo法用于新生儿阿米卡星的群体药动学分析和认证(英文)

目的:用Monte Carlo算法编制群体药动学分析程序并认证该方法估计药动学参数和预测血药浓度的能力.方法:用阿米卡星作为模型药物,对来自42名新生儿共142对血药浓度时间数据进行分析;根据Sheiner等提出的群体药动学思想,我们编制了估计群体参数和个体参数的程序,目标函数最小值以Monte Carlo算法求得,方法的认证采用经典药动学 程序3p87作为对照,预测能力通过计算预测血药浓度的均方根误差(RMSD)和偏性(BIAS)来考察.结果:我们自编的程序运行稳定;本法提取的群体参数与3p87得到的一致,学习样本与认证样本的预测浓度与实测浓度显著相关(相关系数分别为0.995和0.990),预测误差大多数小于1 mg/L,认证样本RMSD和BIAS分别为0.58和-0.07 mg/L.结论:本法估计参数准确,预测血药浓度能力令人满意.     

An evaluation of an optimal sampling strategy for meropenem in febrile neutropenics

Optimal sampling design with nonparametric population modeling offers the opportunity to determine pharmacokinetic parameters for patients in whom blood sampling is restricted. This approach was compared to a standard individualized modeling method for meropenem pharmacokinetics in febrile neutropenic patients. The population modeling program, nonparametric approach of expectation maximization (NPEM), with a full data set was compared to a sparse data set selected by D-optimal sampling design. The authors demonstrated that the D-optimal sampling strategy, when applied to this clinical population, provided good pharmacokinetic parameter estimates along with their variability. Four individualized and optimally selected sampling time points provided the same parameter estimates as more intensive sampling regimens using traditional and population modeling techniques. The different modeling methods were considerably consistent, except for the estimation of CL(d) with sparse sampling. The findings suggest that D-optimal sparse sampling is a reasonable approach to population pharmacokinetic/pharmacodynamic studies during drug development when limited sampling is necessary.     

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 VSS or intercompartmental clearance.     

Robust Population Pharmacokinetic Experiment Design

The population approach to estimating mixed effects model parameters of interest in pharmacokinetic (PK) studies has been demonstrated to be an effective method in quantifying relevant population drug properties. The information available for each individual is usually sparse. As such, care should be taken to ensure that the information gained from each population experiment is as efficient as possible by designing the experiment optimally, according to some criterion. The classic approach to this problem is to design “good” sampling schedules, usually addressed by the D-optimality criterion. This method has the drawback of requiring exact advanced knowledge (expected values) of the parameters of interest. Often, this information is not available. Additionally, if such prior knowledge about the parameters is misspecified, this approach yields designs that may not be robust for parameter estimation. In order to incorporate uncertainty in the prior parameter specification, a number of criteria have been suggested. We focus on ED-optimality. This criterion leads to a difficult numerical problem, which is made tractable here by a novel approximation of the expectation integral usually solved by stochastic integration techniques. We present two case studies as evidence of the robustness of ED-optimal designs in the face of misspecified prior information. Estimates from replicate simulated population data show that such misspecified ED-optimal designs recover parameter estimates that are better than similarly misspecified D-optimal designs, and approach estimates gained from D-optimal designs where the parameters are correctly specified.     

Estimating inestimable standard errors in population pharmacokinetic studies: the bootstrap with Winsorization.

A simulation study was performed to determine how inestimable standard errors could be obtained when population pharmacokinetic analysis is performed with the NONMEM software on data from small sample size phase I studies. Plausible sets of concentration-time data for nineteen subjects were simulated using an incomplete longitudinal population pharmacokinetic study design, and parameters of a drug in development that exhibits two compartment linear pharmacokinetics with single dose first order input. They were analyzed with the NONMEM program. Standard errors for model parameters were computed from the simulated parameter values to serve as true standard errors of estimates. The nonparametric bootstrap approach was used to generate replicate data sets from the simulated data and analyzed with NONMEM. Because of the sensitivity of the bootstrap to extreme values, winsorization was applied to parameter estimates. Winsorized mean parameters and their standard errors were computed and compared with their true values as well as the non-winsorized estimates. Percent bias was used to judge the performance of the bootstrap approach (with or without winsorization) in estimating inestimable standard errors of population pharmacokinetic parameters. Winsorized standard error estimates were generally more accurate than non-winsorized estimates because the distribution of most parameter estimates were skewed, sometimes with heavy tails. Using the bootstrap approach combined with winsorization, inestimable robust standard errors can be obtained for NONMEM estimated population pharmacokinetic parameters with > or = 150 bootstrap replicates. This approach was also applied to a real data set and a similar outcome was obtained. This investigation provides a structural framework for estimating inestimable standard errors when NONMEM is used for population pharmacokinetic modeling involving small sample sizes.     

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.     

Optimisation of sampling windows design for population pharmacokinetic experiments

This paper describes an approach for optimising sampling windows for population pharmacokinetic experiments. Sampling windows designs are more practical in late phase drug development where patients are enrolled in many centres and in out-patient clinic settings. Collection of samples under the uncontrolled environment at these centres at fixed times may be problematic and can result in uninformative data. Population pharmacokinetic sampling windows design provides an opportunity to control when samples are collected by allowing some flexibility and yet provide satisfactory parameter estimation. This approach uses information obtained from previous experiments about the model and parameter estimates to optimise sampling windows for population pharmacokinetic experiments within a space of admissible sampling windows sequences. The optimisation is based on a continuous design and in addition to sampling windows the structure of the population design in terms of the proportion of subjects in elementary designs, number of elementary designs in the population design and number of sampling windows per elementary design is also optimised. The results obtained showed that optimal sampling windows designs obtained using this approach are very efficient for estimating population PK parameters and provide greater flexibility in terms of when samples are collected. The results obtained also showed that the generalized equivalence theorem holds for this approach.     

Inter-study variability in population pharmacokinetic meta-analysis: when and how to estimate it?

Population pharmacokinetic analysis is being increasingly applied to individual data collected in different studies and pooled in a single database. However, individual pharmacokinetic parameters may change randomly from one study to another. In this article, we show by simulation that neglecting inter-study variability (ISV) does not introduce any bias for the fixed parameters or for the residual variability but may result in an overestimation of inter-individual (IIV) variability, depending on the magnitude of the ISV. Two random study-effect (RSE) estimation methods were investigated: (i) estimation, in a single step, of the three-nested random effects (inter-study, inter-individual and residual variability); (ii) estimation of residual variability and a mixture of ISV and IIV in the first step, then separation of ISV from IIV in the second. The one-stage RSE model performed well for population parameter assessment, whereas, the two-stage model yielded good estimates of IIV only with a rich sampling design. Finally, irrespective of the method used, ISV estimates were valid only when a large number of studies was pooled. The analysis of one real data set illustrated the use of an ISV model. It showed that the fixed parameter estimates were not modified, whether an RSE model was used or not, probably because of the homogeneity of the experimental designs of the studies, and suggest no study-effect in this example.     

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.     

Bayesian estimation of cyclosporin exposure for routine therapeutic drug monitoring in kidney transplant patients

AIMS: AUC-based monitoring of cyclosporin A (CsA) is useful to optimize dose adaptation in difficult cases. We developed a population pharmacokinetic model to describe dose-exposure relationships for CsA in renal transplant patients and applied it to the Bayesian estimation of AUCs using three blood concentrations. METHODS: A total of 84 renal graft recipients treated with CsA microemulsion were included in this study. Population pharmacokinetic analysis was conducted using NONMEM. A two-compartment model with zero-order absorption and a lag time best described the data. Bayesian estimation was based on CsA blood concentrations measured before dosing and 1 h and 2 h post dose. Predictive performance was evaluated using a cross-validation approach. Estimated AUCs were compared with AUCs calculated by the trapezoidal method. The Bayesian approach was also applied to an independent group of eight patients exhibiting unusual pharmacokinetic profiles. RESULTS: Mean population pharmacokinetic parameters were apparent clearance 30 l h(-1), apparent volume of distribution 79.8 l, duration of absorption 52 min, absorption lag time 7 min. No significant relationships were found between any of the pharmacokinetic parameters and individual characteristics. A good correlation was obtained between Bayesian-estimated and experimental AUCs, with a mean prediction error of 2.8% (95% CI [-0.6, 6.2]) and an accuracy of 13.1% (95% CI [7.5, 17.2]). A good correlation was also obtained in the eight patients with unusual pharmacokinetic profiles (r(2) = 0.96, P < 0.01). CONCLUSIONS: Our Bayesian approach enabled a good estimation of CsA exposure in a population of patients with variable pharmacokinetic profiles, showing its usefulness for routine AUC-based therapeutic drug monitoring.     

Comparison of different reduced sampling approaches for the estimation of pharmacokinetic parameters for long half-life drugs in patients with renal or hepatic impairment

OBJECTIVE: To compare 3 different reduced sampling approaches (truncated area, population and Bayesian; sampling schedule till 48 or 72 hours) with the extensive sampling for the estimation of pharmacokinetic parameters for long half-life drugs in healthy subjects and in patients with renal or hepatic impairment. METHODS: Two drugs (extensively metabolized or extensively excreted) whose half-lives were greater than 30 hours were used in this analysis. Pharmacokinetic parameters such as maximum plasma concentration, clearance and half-life were estimated in healthy subjects and in patients using the above-mentioned 3 reduced sampling approaches and then compared with the extensive sampling. RESULTS: The truncated area method failed to detect the same magnitude of difference in pharmacokinetic parameters between healthy subjects and patient populations that was determined using extensive sampling. On the other hand, the population or Bayesian approach provided the same magnitude of difference in pharmacokinetic parameters between the 2 populations that was observed with extensive sampling. CONCLUSION: This study indicates that the truncated area method may be a less suitable method to accurately characterize the pharmacokinetics of a long half-life drug either in healthy subjects or in patients with renal or hepatic impairment compared to a population or Bayesian approach.     

Optimal sampling strategy development methodology using maximum a posteriori Bayesian estimation

Maximum a posteriori Bayesian (MAPB) pharmacokinetic parameter estimation is an accurate and flexible method of estimating individual pharmacokinetic parameters using individual blood concentrations and prior information. In the past decade, many studies have developed optimal sampling strategies to estimate pharmacokinetic parameters as accurately as possible using either multiple regression analysis or MAPB estimation. This has been done for many drugs, especially immunosuppressants and anticancer agents. Methods of development for optimal sampling strategies (OSS) are diverse and heterogeneous. This review provides a comprehensive overview of OSS development methodology using MAPB pharmacokinetic parameter estimation, determines the transferability of published OSSs, and compares sampling strategies determined by MAPB estimation and multiple regression analysis. OSS development has the following components: 1) prior distributions; 2) reference value determination; 3) optimal sampling time identification; and 4) validation of the OSS. Published OSSs often lack all data necessary for the OSS to be clinically transferable. MAPB estimation is similar to multiple regression analysis in terms of predictive performance but superior in flexibility.     

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.     

Evaluation of methods for estimating population pharmacokinetic parameters. III. Monoexponential model: Routine clinical pharmacokinetic data

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual kinetic variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting a pharmacokinetic model to individual data. Population pharmacokinetic parameters have traditionally been estimated by doing this separately for each individual, and then combining the individual parameter estimates, the Standard Two Stage (STS) approach. Another approach, NONMEM, appropriately pools data across individuals and is therefore less dependent on individual parameter estimates. This study provides further evidence of NONMEM's validity and usefulness by comparing both approaches on simulated routine-type pharmacokinetic data arising from a monoexponential model. The estimates of population parameters (notably those describing interindividual variability) provided by the STS method are poorer than those provided by NONMEM, especially when there is considerable residual error. Further, NONMEM's estimates of population parameters do not require that the data be restricted to special types of routine data such as those obtained only at steady state, or only at peak or trough, nor do the estimates improve with such data. NONMEM's estimates do improve, however, when a data set is enhanced by the addition of single-observation-per-individual type data. Thus, population parameters can be estimated efficiently from data that simulate real clinical pharmacokinetic conditions.     

Influence of Inter-Animal Variability on the Estimation of Population Pharmacokinetic Parameters in Preclinical Studies

Abstract

Single response population (1 sample / animal) simulation studies were carried out (assuming a 1 compartment model) to investigate the influence of inter-animal variability (in clearance (σ_Cl) and volume (σ_v)) on the estimation of population pharmacokinetic parameters. NONMEM was used for parameter estimation. Individual and joint confidence intervals coverage for parameter estimates were computed to reveal the influence of bias and standard error (SE) on interval estimates. The coverage of interval estimates, percent prediction error and correlation analysis were used to judge the efficiency of parameter estimation. The efficiency of estimation of Cl and V was good, on average, irrespective of the values of σ_Cl and σ_v Estimates of σ_Cl and σ_v were biased and imprecise. Small biases and high precision resulted in good confidence intervals coverage for Cl and V. SE was the major determinant of confidence intervals coverage for the random effect parameters, σ_Cl and σ_v and the joint confidence intervals coverage for all parameter estimates. The usual confidence intervals computed may give an erroneous impression of the precision with which the random effect parameters are estimated because of the large standard errors associated with these parameters. Conservative approach to data interpretation is required when biases associated with σ_Cl and σ_v are large.     

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.     

Extended quasi-likelihood is useful for analyzing intra-individual variability in pharmacokinetic regression models

The method of maximum extended quasi-likelihood (MEQL) can be viewed as an estimation method in the framework of generalized linear models. The method was applied to a pharmacokinetic problem in which the pharmacokinetic model was a nonlinear function of its parameters. The behavior of the method toward the estimation of a variance function was numerically compared with those of the generalized least squares (GLS) and extended least squares methods. In general, the MEQL and GLS methods were equally better. However, the MEQL estimator often showed smaller mean squared errors for the scaling parameter than the other two estimators. Such a generally comparable but partially distinct property of the MEQL method, as compared with the GLS method, is useful to pharmacokinetic analysis.     

Simulation for population analysis of Michaelis-Menten elimination kinetics

A simulation study was conducted to compare the cost and performance of various models for population analysis of the steady state pharmacokinetic data arising from a one-compartment model with Michaelis-Menten elimination. The usual Michaelis-Menten model (MM) and its variants provide no estimate of the volume of distribution, and generally give poor estimates of the maximal elimination rate and the Michaelis-Menten constant. The exact solution to the Michaelis-Menten differential equation (TRUE) requires a precise analysis method designed for estimation of population pharmacokinetic parameters (the first-order conditional estimation method) and also considerable computational time to estimate population mean parameters accurately. The one-compartment model with dose-dependent clearance (DDCL), in conjunction with the first-order conditional estimation or Laplacian method, ran approximately 20-fold faster than TRUE and gave accurate population mean parameters for a drug having a long biological half-life relative to the dosing interval. These findings suggest that the well-known MM and its variants should be used carefully for the analysis of blood concentrations of a drug with Michaelis-Menten elimination kinetics, and that TRUE, in conjunction with a precise analysis method, should be considered for estimating population pharmacokinetic parameters. In addition, DDCL is a promising alternative to TRUE with respect to computation time, when the dosing interval is short relative to the biological half-life of a drug. This work was supported in part by the Epilepsy Research Foundation, the Nakatomi Foundation, and a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan.     

Non-compartmental estimation of pharmacokinetic parameters in serial sampling designs

Pharmacokinetic studies are commonly analyzed using a two-stage approach where the first stage involves estimation of pharmacokinetic parameters for each subject separately and the second stage uses the individual parameter estimates for statistical inference. This two-stage approach is not applicable in sparse sampling situations where only one sample is available per subject. Nonlinear models are often applied to analyze pharmacokinetic data assessed in such serial sampling designs. Modelling approaches are suitable provided that the form of the true model is known, which is rarely the case in early stages of drug development. This paper presents an alternative approach to estimate pharmacokinetic parameters based on non-compartmental and asymptotic theories in the case of serial sampling when a drug is given as an intravenous bolus. The statistical properties of estimators of the pharmacokinetic parameters are investigated and evaluated using Monte Carlo simulations.     

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.