Experimental Design and Efficient Parameter Estimation in Preclinical Pharmacokinetic Studies

Monte Carlo simulation technique used to evaluate the effect of the arrangement of concentrations on the efficiency of estimation of population pharmacokinetic parameters in the preclinical setting is described. Although the simulations were restricted to the one compartment model with intravenous bolus input, they provide the basis of discussing some structural aspects involved in designing a destructive (quantic) preclinical population pharmacokinetic study with a fixed sample size as is usually the case in such studies. The efficiency of parameter estimation obtained with sampling strategies based on the three and four time point designs were evaluated in terms of the percent prediction error, design number, individual and joint confidence intervals coverage for parameter estimates approaches, and correlation analysis. The data sets contained random terms for both inter- and residual intra-animal variability. The results showed that the typical population parameter estimates for clearance and volume were efficiently (accurately and precisely) estimated for both designs, while interanimal variability (the only random effect parameter that could be estimated) was inefficiently (inaccurately and imprecisely) estimated with most sampling schedules of the two designs. The exact location of the third and fourth time point for the three and four time point designs, respectively, was not critical to the efficiency of overall estimation of all population parameters of the model. However, some individual population pharmacokinetic parameters were sensitive to the location of these times.     

Estimation of Population Pharmacokinetic Parameters of Saquinavir in HIV Patients with the MONOLIX Software

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020–1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.     

Population Pharmacokinetic Modelling to Support the Evaluation of Preclinical Pharmacokinetic Experiments with Lorlatinib

The effect of transporters and enzymes on drug pharmacokinetics is increasingly evaluated using genetically modified animals that have these proteins either knocked-out or their human orthologues transgenically expressed. Analysis of pharmacokinetic data obtained in such experiments is typically performed using non-compartmental analysis (NCA), which has limitations such as not being able to identify the PK parameter that is affected by the genetic modification of the enzymes or transporters and the requirement of intense and homogeneous sampling of all subjects. Here we used a compartmental population pharmacokinetic modeling approach using PK data from a series of genetically modified mouse experiments with lorlatinib to extend the results and conclusions from previously reported NCA analyses. A compartmental population pharmacokinetic model was built and physiologically plausible covariates were evaluated for the different mouse strains. With the model, similar effects of the strains on the area under the concentration-time curve (AUC) from 0 to 8 hours were found as for the NCA. Additionally, the differences in AUC between the strains were explained by specific effects on clearance and bioavailability for the strain with human expressing CYP3A4. Finally, effects of multidrug efflux transporters ATP-binding cassette (ABC) sub-family B member 1 (ABCB1) and G member 2 (ABCG2) on brain efflux were quantified. Use of compartmental population PK modeling yielded additional insight into the role of drug-metabolizing enzymes and drug transporters in mouse experiments compared to the NCA. Furthermore, these models allowed analysis of heterogeneous pooled datasets and the sparse organ concentration data in contrast to classical NCA analyses.     

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.     

基于遗传算法的药动学参数估算

目的:利用遗传算法全局和局部搜索力强的优势,进行非线性药动学参数估算。方法:以最小二乘法建立目标函数,拟合一室模型血管外给药的药-时数据。结果:遗传算法与传统经典方法拟合的药动学参数无显著性差异(P>0.05),通过算例验证了其处理非线性药动学问题的有效性。结论:遗传算法适用于估算非线性药室模型的药动学参数。     

Prediction of Pharmacokinetic Parameters and the Assessment of Their Variability in Bioequivalence Studies by Artificial Neural Networks

Purpose. The methodology of predicting the pharmacokinetic parameters (AUC, c_max, t_max) and the assessment of their variability in bioequivalence studies has been developed with the use of artificial neural networks. Methods. The data sets included results of 3 distinct bioequivalence studies of oral verapamil products, involving a total of 98 subjects and 312 drug applications. The modeling process involved building feedforward/backpropagation neural networks. Models for pharmacokinetic parameter prediction were also used for the assessment of their variability and for detecting the most influential variables for selected pharmacokinetic parameters. Variables of input neurons based on logistic parameters of the bioequivalence study, clinical-biochemical parameters, and the physical examination of individuals. Results. The average absolute prediction errors of the neural networks for AUC, c_max, and t_max prediction were: 30.54%, 39.56% and 30.74%, respectively. A sensitivity analysis demonstrated that for verapamil the three most influential variables assigned to input neurons were: total protein concentration, aspartate aminotransferase (AST) levels, and heart-rate for AUC, AST levels, total proteins and alanine aminotransferase (ALT) levels, for c_max, and the presence of food, blood pressure, and body-frame for t_max. Conclusions. The developed methodology could supply inclusion or exclusion criteria for subjects to be included in bioequivalence studies.     

MATLAB软件在非线性药动学参数估算中的应用

目的:利用MATLAB软件拟合非线性药动学参数。方法:采用MATLAB软件的非线性回归拟合二室模型血管外给药的药-时数据。结果:MATLAB非线性算法与3p97软件拟合得到的药动学参数一致,通过实例验证了其处理非线性药动学问题的有效性。结论:MATLAB回归分析计算准确、方便、简单,并能显示直观的拟合曲线图,适用于估算非线性药室模型的药动学参数。     

丙戊酸钠对卡马西平药代动力学的影响

目的：考察丙戊酸钠对卡马西平药代动力学的影响。方法：6名健康志愿分别口服单剂量卡马西平片以及卡马西平和丙戊酸钠片，采用荧光偏振免疫法测定卡马西平血药浓度，经3p97程序处理，计算卡马西平的药代动力学参数以及丙戊酸钠对卡马西平药代动力学参数的影响。结果：合用丙戊酸钠后，卡马西平的Ke,CL/F明显增加，而T1/2Ke,AUC0-1明显减小（P＜0．05）。结论：丙戊酸钠可加速卡马西平的排泄，使卡马西平的半衰期缩短，生物利用度减小。     

丙戊酸钠对卡马西平药代动力学的影响

目的:考察丙戊酸钠对卡马西平药代动力学的影响。方法:6名健康志愿者分别口服单剂量卡马西平片以及卡马西平和丙戊酸钠片,采用荧光偏振免疫法测定卡马西平血药浓度,经3p97程序处理,计算卡马西平的药代动力学参数以及丙戊酸钠对卡马西平药代动力学参数的影响。结果:合用丙戊酸钠后,卡马西平的Ke,CL/F明显增加,而T_(1/2Ke),AUC_(0-t)明显减小(P<0.05)。结论:丙戊酸钠可加速卡马西平的排泄,使卡马西平的半衰期缩短,生物利用度减小。     

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。     

应用1stOpt软件求算磺胺噻唑药物动力学参数

目的:应用1stOpt(First Optimization)软件求算磺胺噻唑钠(sulfathiazole sodium,ST)药动学参数。方法:以文献磺胺噻唑静脉注射血药浓度数据为例,应用1stOpt软件求算药动学参数。结果:分别应用1stOpt方法与MATLAB方法求得的药动学参数十分接近,2种方法拟合磺胺噻唑静脉注射血药浓度—时间曲线的残差平方和相差不足1%,说明2种方法得到的拟合公式差异微小。结论:1stOpt可用于求算药动学参数,并具有无需提供参数初值,计算"代码"编写简易、快捷的特点。     

Population Pharmacokinetic Model of the Pregabalin-Sildenafil Interaction in Rats: Application of Simulation to Preclinical PK-PD Study Design

Purpose  

Preliminary evidence has suggested a synergistic interaction between pregabalin and sildenafil for the treatment of neuropathic pain. The focus of this study was to determine the influence of sildenafil on the pharmacokinetics (PK) of pregabalin with the objective of informing the design of a quantitative pharmacodynamic (PD) study.     

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。     

Population Pharmacokinetic Measures,Their Estimation and Selection of Sampling Times

In pharmacokinetic (PK) studies, including bioavailability assessment, various population PK measures, such as area under the curve (AUC), maximal concentration (C _max ) and time to maximal concentration (T _max ) are estimated. In this paper we compare a model-based approach, where parameters of a compartmental model are estimated and the explicit formulae for PK measures are used, and a model-independent approach, where numerical integration algorithms are used for AUC and sample estimates for C _max and T _max . Since regulatory agencies usually require the model-independent estimation of PK measures, we focus on the empirical approach while using the model-based approach and corresponding measures as a benchmark. We show how to “split” a single sampling grid into two or more subsets, which substantially reduces the number of samples taken for each patient, but often has little effect on the precision of estimation of PK measures in terms of mean squared error (MSE). We give explicit formulae for the MSE of the empirical estimator of AUC for a simple example and discuss how costs may be taken into account.     

Assuming Peripheral Elimination: Its Impact on the Estimation of Pharmacokinetic Parameters of Muscle Relaxants

For anesthetic drugs undergoing nonorgan-based elimination, there is a definite trend towards using pharmacokinetic (PK) models in which elimination can occur from both central (k₁₀ ) and peripheral compartments(k₂₀ ). As the latter cannot be assessed directly, assumptions have to be made regarding its value. The primary purpose of this paper is to evaluate the impact of assuming various degrees of peripheral elimination on the estimation of PK parameters. For doing so, an explanatory model is presented where previously published data from our laboratory on three muscle relaxants, i.e., atracurium, doxacurium, and mivacurium, are used for simulations. The mathematical aspects for this explanatory model as well as for two specific applications are detailed. Our simulations show that muscle relaxants having a short elimination half-life are more affected by the presence of peripheral elimination as their distribution phase occupies the major proportion of their total area under the curve. Changes in the exit site dependent PK parameters (Vd_ss ) are also mostly significant when k₂₀ is smaller than k₁₀ . Although the physiological processes that determine drug distribution and those affecting peripheral elimination are independent, the two are mathematically tied together in the two-compartment model with both central and peripheral elimination. It follows that, as greater importance is given to k₂₀ , the rate of transfer from the central compartment (k₁₂ ) increases. However, as a result of a proportional increase in the volume of the peripheral compartment, peripheral concentrations remain unchanged whether or not peripheral elimination is assumed. These findings point out the limitations of compartmental analysis when peripheral elimination cannot be measured directly.     

Impact of Anti-Drug Antibodies in Preclinical Pharmacokinetic Assessment

The administration of human biotherapeutics is often associated with a higher incidence of immunogenicity in preclinical species. The presence of anti-drug antibodies (ADAs) in the test samples can affect the accurate measurement of therapeutic protein (TP) in bioanalytical methods designed to support pharmacokinetic (PK) and toxicokinetic (TK) assessments. The impact can vary depending on the bioanalytical method platform and study dosing design. The goal of this study is to evaluate the impact of ADA response on the bioanalytical methods in support of PK/TK and the associated study data interpretation. Sprague Dawley rats were administered with four weekly doses of 50 mg/kg TP, a humanized monoclonal antibody. The TP in serum samples was measured using three bioanalytical methods that quantified bound and/or unbound TP to ADA. The ADA response in the animals was classified into negative, low, medium, and high based on the magnitude of the response. The presence of ADA in samples led to discrepant TP measurements between the methods, especially at time points where the TP concentrations were low. This could be due to ADA interference to the accurate measurement of ADA-bound TP concentrations. The TP concentration at last time point (C _last) was reduced by 82.8%, 98.6%, and 99.8%, respectively, for samples containing low, medium, and high levels of ADA. The interfering effects of the ADA on bioanalytical methods and exposure were evident as early as 2 weeks post-dosing. This modeling approach can provide the better understanding of ADA impact on PK exposure in multiple doses.     

Designing Cross-Sectional Population Pharmacokinetic Studies: Implications for Pediatric and Animal Studies

Abstract

Sampling constraints and ethical concerns are two of the issues that prompt the conduct of pediatric/animal cross-sectional pharmacokinetic studies. A simulation study was carried out to investigate the effect of optimization of design features (arrangement of concentrations (n) in time and sample size (N)) on the accuracy and precision of parameter (especially intersubject/interanimal variability) estimation in cross-sectional population pharmacokinetic studies involving drugs administered by single or multiple intravenous bolus input(s). Drugs exhibiting one and two compartment (i.e., 1 CMT and 2 CMT) pharmacokinetics were investigated using N of 20 to 100 and 30 to 150, respectively, n was optimized, using the profile (block) randomized sampling design, for accurate and precise estimation of population pharmacokinetic parameters. N of 50 and 80 was found to be adequate for the estimation of clearance (CL) and its variability ((ω^CL) needed for dosage optimization) for the 1 CMT and 2 CMT drugs, respectively. Estimates of ω^V (1 CMT), and most of the parameters of the drug exhibiting 2 CMT pharmacokinetics were biased and imprecise. the bootstrap resampling of weighted residuals was found to provide only a limited (= 15%) bias correction in the estimation of ω^V and this may not be an adequate correction for the study setting. Cross-sectional pharmacokinetic study was not useful in the estimation of population pharmacokinetic parameters of highly variable drugs. However, it was found to be useful in the estimation of the relevant population pharmacokinetic parameters required for dosage optimization of non-highly variable drugs in the pediatric/animal population.     

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.