Evaluation of Bayesian predictability of vancomycin concentration using population pharmacokinetic parameters in pediatric patients

The objective of this study was to evaluate the Bayesian predictability of vancomycin (VCM) pharmacokinetics in Japanese pediatric patients using one-compartment population pharmacokinetic (PPK) parameters, which we reported previously. The validity of the PPK model was evaluated by bootstrap method and cross validation method, and the Bayesian predictive performance was examined. The predictive performance of the PPK model for premature patients was also examined. The cross validation method showed the predictability to be acceptable for practical use, especially for predicting trough concentration using other trough data. However, for the external premature patient data, this PPK model did not seem to be adequate. A theoretical approach using a simulation technique was also examined to evaluate the predictive performance. The results suggested that the predictability at the peak was not necessarily good at all sampling times and the predictability at the trough was better when a later time point was used. The optimal sampling time for prediction of VCM concentration in pediatric patients is discussed.     

基于群体药物代谢动力学模型的万古霉素给药方案优化研究进展

万古霉素为糖肽类抗菌药,是临床上用于耐甲氧西林金黄色葡萄球菌感染的一线用药。大量研究表明,万古霉素的PK/PD参数AUC0~24 h/MIC≥400与其临床疗效密切相关。但是,万古霉素在不同人群中的药物代谢动力学行为差异较大,因此,通过群体药物代谢动力学模型来实施万古霉素的优化给药尤为重要。本文对近年来万古霉素在不同群体中药物代谢动力学模型研究进展和基于PPK给药方案的优化研究进展综述如下,以期为临床万古霉素的合理使用提供依据。     

Individualizing vancomycin dosage regimens: one- versus two-compartment Bayesian models

The absolute and relative predictive performances of one- and two-compartment Bayesian forecasting models were evaluated and compared. Initial population parameters were derived from 25 adult patients with stable renal function and who were being treated for presumed or documented gram-positive infections. The performance of each model was compared using these population parameters with and without steady-state or non-steady-state feedback concentrations to predict future peak and trough concentrations in an additional 20 patients. Both models tended to underpredict vancomycin peak and trough concentrations obtained at steady state. The use of a two-compartment model resulted in statistically less bias and more precise predictions of vancomycin peak concentrations when either population parameters or non-steady-state concentrations were used for future predictions. No difference in model performance was observed when steady-state concentrations were used to predict future steady-state concentrations. The results of this evaluation demonstrate that the two-compartment Bayesian model is less biased and more precise in determining future vancomycin serum concentrations given only population parameters or non-steady-state feedback information. No difference in model performance could be discerned when steady-state concentrations were used as feedback information.     

万古霉素群体药代动力学模型在临床应用中的预测性能的评估

目的评估万古霉素群体药代动力学(PPK)模型在临床应用中的预测性能。方法收集广西医科大学第一附属医院静脉应用万古霉素治疗的成人住院患者,根据万古霉素PPK模型,通过贝叶斯反馈法求出给定剂量下的稳态谷浓度和稳态峰浓度个体预测值,与实测值比较,评估模型的预测效能。结果共纳入271例患者697个血药浓度值,其中稳态谷浓度417个,稳态峰浓度280个。谷浓度和个体预测值均值分别为(11.85±7.14)和(11.08±6.81)mg·L^-1,峰浓度和个体预测值均值分别为(18.42±9.61)和(17.61±7.37)mg·L^-1。谷浓度的平均预测误差、平均相对预测误差、平均绝对误差和均方根误差分别为-0.77 mg·L^-1,-2.53%,1.63 mg·L^-1和2.38 mg·L^-1,峰浓度的平均预测误差、平均相对预测误差、平均绝对误差和均方根误差分别为-0.81 mg·L^-1,1.53%,2.28 mg·L^-1和3.32 mg·L^-1,相对预测误差在±30%以内的血药浓度值约占92%。结论建立的万古霉素PPK模型在临床应用中具有较高的预测性能,可用于指导万古霉素的个体化给药。     

Bayesian estimation of pharmacokinetic parameters of vancomycin in patients with decreasing renal function

In clinical settings, decrease of renal function is frequently observed in patients treated with vancomycin (VCM). In this study, mutable covariates models (MCMs) were constructed to analyze the pharmacokinetics (PK) of VCM with Bayesian estimation, considering time-dependent decreases in creatinine clearance in 23 patients with decreasing renal function. The predicted mean percentage error (MPE) of VCM concentrations analyzed with a conventional fixed covariates model (FCM) was -19.1%, whereas the MPE was improved to 2.5% by applying MCM. Furthermore, a probable lag time between fluctuations in VCM clearance (CL(VCM) ) and serum creatinine (S(cr) ) was analyzed by MCM, MCM(Lag1d) , and MCM(Lag2d) , which considered lag times of 0, 1, and 2 days, respectively. Compared with FCM, all MCMs improved fitness with the significantly decreased root mean square percentage error (RMSPE) and MPE. However, RMSPE and MPE analyzed with MCM were not significantly different from those with MCM(Lag1d) and MCM(Lag2d) , indicating that lag times between alterations in CL(VCM) and S(cr) were obscure in these patients. Collectively, these results suggest that PK parameters of VCM were more accurately calculated by MCMs than by conventional FCM, and that VCM dosages calculated by FCM would be overestimated by approximately 20% in patients with decreasing renal function.     

基于群体药动学模型的万古霉素个体化给药软件研制及应用

目的:研发基于建立的成人和老年群体药动学(population pharmacokinetics,PPK)模型的万古霉素(vancomycin,VCM)个体化给药软件。方法:根据已建立的成人和老年VCM的PPK模型信息,运用MyEclipse、SQL Server、JRE等工具软件研发VCM给药软件。软件开发方案包括需求分析,概要设计,详细设计,软件编码,软件测试以及软件维护和二次开发。结果:研制的VCM给药软件可实现感染患者信息输入和管理,软件通过接口调用非线性混合效应模型(NONMEM)软件,不仅能预测多种具体VCM给药方案下的血药浓度,供临床医师制定初始用药方案参考,而且能结合已有的血药浓度监测信息和贝叶斯反馈法更精准地预测血药浓度,辅助临床医师进一步优化给药方案。软件应用于VCM血药浓度解读,药师向临床做出剂量调整建议。采纳建议组患者复查的血药浓度均达到目标血药浓度范围。结论:本研究基于VCM的PPK模型研制的给药软件能快速方便地辅助成人和老年感染患者VCM的个体化给药。     

Evaluation of Bayesian estimation of pharmacokinetic parameters

The validity of pharmacokinetic parameters estimated by the maximum a posteriori probability (MAP) Bayesian method was investigated by simulation studies. A 1-compartment model with bolus intravenous administration was used as a pharmacokinetic model, and the coefficients of variation for the parameters and residual error were set at 30% and 10%, respectively. The accuracy of the posterior modes of pharmacokinetic parameters estimated by the MAP Bayesian method was assessed by the difference between the true value and the estimated value. The results showed that the accuracy of the Bayesian estimation depended on sampling times and on the differences between the prior means and individual true parameter values. For assessing the reliability and accuracy of the Bayesian estimation, the authors suggest using the whole posterior distribution of the pharmacokinetic parameters to describe the 95th percentile range for predicted blood concentration profiles. The authors believe that the proposed procedures provide helpful information for evaluating the Bayesian estimation of pharmacokinetic profiles.     

老年患者万古霉素群体药代动力学模型验证

目的:利用已发表的成人万古霉素群体药代动力学模型对本院使用万古霉素的老年患者治疗药物监测数据进行拟合;探讨已发表的模型对不同临床机构的适用性,选择较为适合本院老年患者的万古霉素群体药代动学模型。方法:分析已发表的成人万古霉素群体药代动力学模型,提取人口学信息及模型参数,将模型参数固定后,利用NONMEM 7.3.0.(Icon Development Solution,USA)软件及PDx-Pop Version 5软件进行拟合,并用RStudio软件作图。根据实测浓度-预测浓度(DV-PRED)图及可视化预测检验(VPC)评估拟合效果。结果:共收集2014-2015年42例老年患者88个稳态谷浓度点,年龄范围为66~93岁;共检索到15个成人万古霉素群体药代动力学模型,一房室模型6个,二房室模型9个。对一房室模型进行拟合,模型拟合图形显示模型2、5及6的拟合效果较好,其中模型5为老年人模型。结论:可以尝试利用拟合结果良好的模型在本院进行前瞻性临床实践,并逐步建立本院老年患者的万古霉素群体模型。     

APriori lithium dosage regimen using population characteristics of pharmacokinetic parameters

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

Comparison of serum sampling methods for determining vancomycin dosage regimens

The predictive ability of a four-point sampling method versus a two-point sampling method for vancomycin was assessed in 11 patients with various staphylococcal infections. All steady-state predictions were based on first-dose pharmacokinetic parameters. The mean vancomycin serum concentrations achieved at 4 and 8 h postinfusion were not significantly different from the predicted concentrations derived from either the four- or two-point method. Also, there was no significant difference between the two methods in predictive ability or accuracy. Both methods underpredicted the steady-state concentration to the same degree, 2.9 micrograms/ml at 4 h and 3.1 micrograms/ml at 8 h, which would appear to be clinically acceptable. A one-compartment pharmacokinetic model, which uses two serum concentrations, appears to be adequate for adjusting vancomycin regimens.     

Evaluation of Bayesian predictability of vancomycin concentration in patients with various degrees of renal function.

To assess the usefulness of the population pharmacokinetic parameters of vancomycin (VCM) based on a two-compartment model in Japanese adult patients, predictability by a Bayesian method was evaluated using a concentration time course after single dosing to 22 patients with various degrees of renal function. Using one or two points from the observed data for each patient, the concentrations predicted by a Bayesian method were compared with the observed data for each sampling time. The patients were separated into five groups based on their renal functions indicated by creatinine clearance, and the mean prediction error (MPE) and root mean squared error (RMSE) were calculated for each group as measures of accuracy and precision, respectively. In both one- and two-point methods, the absolute MPE values at each sampling time in the elimination phase were less than 2.5 microg/ml, and the RMSE values were also small. No clear differences were found in MPE and RMSE among the groups. In the distribution phase, the MPE and RMSE were somewhat greater, and RMSE in some groups was around 15 microg/ml when trough data was used to predict the peak concentration. Also, the theoretical RMSE using this population parameter setting could well explain the observed RMSE. These results confirmed this population parameter setting is useful for at least predicting concentration in the elimination phase after single dosing, and the predictability was independent of renal function.     

A priori lithium dosage regimen using population characteristics of pharmacokinetic parameters

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

A Bayesian method based on clotting factor activity for the prediction of maintenance warfarin dosage regimens

A Bayesian algorithm, employing a population pharmacokinetic-pharmacodynamic model, for the effective and rapid prediction of warfarin maintenance dosing requirements was developed. The algorithm was evaluated prospectively in five healthy volunteers who were given a 15-mg single dose of racemic warfarin. Based on previous population pharmacokinetic and pharmacodynamic parameters and factor VII response measurements taken during the first 48 hours, dosage regimens to achieve a subtherapeutic degree of anticoagulation (50% of normal) were determined. Three factor VII response measurements were sufficient to determine dosing requirements in the five volunteers. The advantage of the algorithm is that it does not require warfarin concentration measurements and uses non-steady-state data.     

迭代二步法估算阿米卡星的群体药动学参数

目的：用迭代二步法估算阿米卡星的群体药动学参数。方法：收集58例呼吸系统感染病人静脉滴注阿米卡星的临床血药浓度监测数据,用荧光偏振免疫法测定阿米卡星血药浓度。用迭代二步法估算阿米卡星的群体及个体药动学参数。比较性别、年龄、体重、肌酐清除率等因素对药动学参数的影响。结果：性别对药动学参数无影响,CL与CLcr呈正相关,Vd与体重呈正相关。结论：迭代二步法能较好地估算出阿米卡星的群体及个体药动学参数,用于优化给药方案及预测血药浓度可满足临床需要。     

Evaluation of population pharmacokinetic models for amikacin dosage individualization in critically ill patients

Objectives The aim of this study was to evaluate the reliability for dosage individualization and Bayesian adaptive control of several literature‐retrieved amikacin population pharmacokinetic models in patients who were critically ill. Methods Four population pharmacokinetic models, three of them customized for critically‐ill patients, were applied using pharmacokinetic software to fifty‐one adult patients on conventional amikacin therapy admitted to the intensive care unit. An estimation of patient‐specific pharmacokinetic parameters for each model was obtained by retrospective analysis of the amikacin serum concentrations measured (n = 162) and different clinical covariates. The model performance for a priori estimation of the area under the serum concentration‐time curve (AUC) and maximum serum drug concentration (C_max) targets was obtained. Key findings Our results provided valuable confirmation of the clinical importance of the choice of population pharmacokinetic models when selecting amikacin dosages for patients who are critically ill. Significant differences in model performance were especially evident when only information concerning clinical covariates was used for dosage individualization and over the two most critical determinants of clinical efficacy of amikacin i.e. the AUC and C_max values. Conclusions Only a single amikacin serum level seemed necessary to diminish the influence of population model on dosage individualization.     

基于NONMEN法建立万古霉素新生儿群体药动学模型

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

万古霉素个体化用药的方法学评价

万古霉素是目前治疗耐甲氧西林金黄色葡萄球菌（MRSA）感染的首选药物，在临床广泛应用，其治疗窗窄，不良反应严重，药动学个体差异大，因此万古霉素的个体化用药非常重要。越来越多的方法被用于万古霉素的个体化用药方案的调整，本文对目前常用的方法进行了总结和评价。     

Comparison of antibiotic dosage regimens using pharmacokinetic and microbiologic factors

A pharmacokinetic meta-analysis was performed for 33 antibiotics used in treating infections caused by microorganisms for which the antibiotics are considered to be agents of first choice or primary alternatives. The pharmacokinetic indices assessed were the following components of the steady-state blood concentration-time profile: the magnitude of the peak antibiotic serum concentration at steady state compared with the minimum inhibitory concentration (CSSmax/MIC) and the intensity index, a dimensionless term that reflects the contribution of the peak serum antibiotic concentration and the duration that this concentration is above the MIC. Substantial differences in CSSmax/MIC and intensity-index values were observed among antibiotics within an antibiotic class for individual microorganisms and for groups of microorganisms. Piperacillin, amikacin, and tetracycline showed the best mean performances of the ureido penicillins, aminoglycosides, and tetracyclines, respectively. For the cephalosporins, cefadroxil displayed the highest mean values of the first-generation cephalosporins; cefuroxime and cefotetan showed the greatest measures for the second-generation agents; and all third-generation cephalosporins demonstrated very high mean performance indices. Meta-analysis of pharmacokinetic performance factors is a useful technique for making intergroup and intragroup comparisons of antibiotics.     

Evaluation of methods for estimating population pharmacokinetic parameters II. Biexponential model and experimental pharmacokinetic data

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters have been estimated either by fitting all individuals' data together as though there were no individual kinetic differences, the naive pooled data (NPD) approach, or by fitting each individuals' data separately and then combining the individual parameter estimates, the two stage (TS) approach. A third approach, NONMEM, takes a middle course between these. This study provides further evidence of NONMEM's validity by comparing, using simulation, the three approaches on three types of data sets corresponding to three typical types of pharmacokinetic studies. The estimates of population parameters provided by the NPD method are poorer than those provided by either of the other methods. The estimates provided by the TS method are adequate for mean values and for residual variability, but not for interindividual kinetic variability. NONMEM's estimates are as good as those of the TS method for mean parameters and for residual variability, and considerably better for interindividual variability. The latter estimates are still not acceptable in an absolute sense. This is probably due, not to an intrinsic fault of the method (as it is in the case of the TS approach), but to an insufficient number of individuals being studied.This work was supported in part by NIH Grants GM26676 and GM26691.     

新生儿万古霉素群体药动学模型建立的必要性评价

目的:观察研究万古霉素在新生儿中的临床应用及血药谷浓度达标情况,评价新生儿万古霉素群体药动学模型建立的必要性。方法:回顾性收集苏州市立医院本部新生儿科2011年7月-2014年8月使用万古霉素的病史材料,对其感染部位、病原学检查、疗程、疗效、合并用药、血药浓度监测结果进行统计与分析。结果:入选71例患儿,90.14%为多部位混合感染,最常见的是呼吸道合并血流感染(43.66%);病原学送检率100%,首次培养阳性率80.28%,以葡萄球菌属为主(87.67%);万古霉素首次用药后血药谷浓度达标(10~20 mg·L^-1)率28.17%,未达标患者中有43.14%进行剂量调整,调整后达标率50%;万古霉素总临床有效率为90.14%,血药谷浓度未达标组的临床有效率为42.25%,达标组有效率为47.62%;首次经验性用药未进行剂量调整组万古霉素疗程为(13.41±4.41)d,经验性剂量调整组为(18.73±9.52)d(P=0.00188)。结论:万古霉素治疗新生儿感染疗效确切,但经验性用药后血药谷浓度达标率低,未达标者临床疗效差,经验性多次调整万古霉素用法显著延长患儿治疗时间,因此有必要建立新生儿万古霉素群体药动学模型以实现个体化给药治疗。