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Antimicrobial Agents and Chemotherapy, December 2005, p. 4934-4941, Vol. 49, No. 12
0066-4804/05/$08.00+0 doi:10.1128/AAC.49.12.4934-4941.2005
Copyright © 2005, American Society for Microbiology. All Rights Reserved.
Emma V. Herrera,2,
Alfonso Dominguez-Gil,1,3 and
María José García1*,
Department of Pharmacy and Pharmaceutical Technology, University of Salamanca, Salamanca, Spain,1 Faculty of Chemical Sciences, University of Puebla, Puebla, Mexico,2 Pharmacy Service, University Hospital, Salamanca, Spain3
Received 22 March 2005/ Returned for modification 30 June 2005/ Accepted 27 September 2005
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The empirical use of VAN in persistently febrile neutropenic patients remains controversial (16, 46). Currently, the prevalent opinion is for a restrictive use of glycopeptides, i.e., only for patients whose infection requires them, based on the microbiological data and a rigorous clinical evaluation of the patient. From a practical standpoint, this postulate implies, first, a rational antibiotic selection based on potential pathogens and, second, optimal use, including the drug dose and duration of therapy (36). In this sense, the population approach and pharmacodynamic criteria have become available as tools in individualized antimicrobial therapy, leading to increased efficacy and reduced selection of resistance (13). In order to apply such a strategy in everyday clinical practice, the precise pharmacokinetic (PK)-pharmacodynamic index determining efficacy and its target value as well as population PK parameters obtained from specific cohorts (oncology, intensive care unit, etc.) must be known or estimated (19, 40, 45).
A specific glycopeptide-treated population benefiting from this approach could be patients with hematological malignancies, owing to their high risk of developing life-threatening bacterial infections and the need for higher-than-expected dosages (9, 17, 34, 35). However, little is known about the VAN pharmacokinetics in these patients since only one population PK analysis has been published (17). The methodological and sampling size constraints of this work suggested the need for studies aimed at improving our knowledge about the PK behavior of this drug in this particular group of patients. Other populations of patients with nonhematological diseases, mainly pediatric, treated with VAN have been appropriately characterized using the most usual and suitable population approach of mixed-effect modeling implemented in the NONMEM program.
On this basis, the information obtained should provide specific PK parameters to estimate appropriate dosage guidelines, which are not clearly defined for this high-risk population.
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15-year-old) inpatients with an underlying hematological malignancy admitted to the Hematology Unit of the University Hospital of Salamanca (Spain) from 1989 to 1999 on VAN therapy for suspected or documented infection caused by gram-positive bacteria were chosen retrospectively for the analysis. After a detailed examination of their medical reports (clinical history), some patients were excluded on the basis of two criteria: (i) the lack of the necessary data concerning the patients' demographic, physiopathological, and clinical status (11 patients) and (ii) hospitalization in the intensive care unit during VAN therapy (six patients). According to previous criteria, a total of 348 treatments corresponding to 274 patients were available. Owing to intraindividual physiopathological changes, if the time period between two successive treatments in the same patient was more than 1 month we considered each as an individual course of VAN for population analysis, according to our previous experience for this kind of patient (37). Two hundred twenty-four patients received only one course of VAN therapy, and the remaining 50 patients received from two to six courses. Informed consent and ethical approval were unnecessary because the study involved a retrospective collection of routine clinical data coming from therapeutic drug monitoring (TDM). However, since additional patient information was needed for this study, approval was obtained from the Institutional Review Board of the University Hospital of Salamanca. Initial VAN dosage regimens were chosen by attending physicians according to a specifically designed nomogram for hematological patients, taking into account the patients' age, weight, and renal function (17). VAN was administered by intermittent intravenous infusion over 0.5 to 1 h at doses ranging from 200 to 3,900 (1,535 ± 280) mg/day, the dosage interval ranging from 6 to 48 h.
Data acquisition. PK data were collected in a database by the clinical pharmacokinetic service of our hospital. Dosing and sampling times were always recorded by nursing staff. The accuracy of the records was further assessed by a clinical pharmacist belonging to the clinical pharmacokinetic service.
From these PK reports, the following data were obtained: patient identification, TDM dates, and the characteristics of VAN therapy. On the day of each VAN TDM, the following data were retrieved from the patients' medical records: age, weight, body surface area, serum creatinine (SCR), hemoglobin, albumin, and time postchemotherapy. The categorical variables collected were gender (GEN); hematological diagnosis; Eastern Cooperative Oncology Group (ECOG) performance status according to the standards of the Eastern Cooperative Oncology Group (15); stage of antineoplastic treatment; and the presence or absence of autologous bone marrow grafting, neutropenia (absolute neutrophil count of <500/mm3), and hypoalbuminemia (serum albumin concentration of <3.5 g/dl). Concurrent antibiotic therapy with amikacin and amphotericin was also recorded. Creatinine clearance (CLCR) was estimated as a function of individual variables such as total body weight (TBW), height, age, body surface area, GEN, and SCR. Estimations following the formulas of Cockcroft and Gault (10), Jelliffe (23), Tsubaki et al. (44), and Levey et al. (27) were made for each patient.
According to statistical criteria (power of 0.8) and desired clinical representativeness we selected a minimum number of 200 patients to build the model (index set). To obtain this figure, a period of approximately 7 years (30 patients/year) was necessary, and to externally validate the model another 50 patients (validation set) were required. Patient assignment to the index and validation groups was chronological (three-fourths and one-fourth of the evaluated time, respectively). Data acquisition for the validation set was accomplished after the final population analysis, so only significant covariates were recorded. To prevent the potential introduction of bias into the prediction analysis, only two items of VAN serum data per patient were obtained in the validation group.
Table 1 summarizes the demographic and clinical characteristics of the patients included in the study.
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TABLE 1. Demographic and clinical data of the patient population
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FIG. 1. Distribution of VAN concentrations in relation to the number of doses and sampling times in the index (boldface) and validation data sets.
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Pharmacokinetic and statistical analysis. (i) Pharmacokinetic modeling. A population PK method based on a nonlinear mixed-effect modeling approach was used (NONMEM program, version V; double precision, level 1.1) (4). The first-order conditional estimation was used throughout. To determine the most suitable compartmental model, we first fitted data for VAN concentrations versus time to both one- and two-compartment models, with first-order elimination, specified to NONMEM by ADVAN1-TRANS2 or ADVAN3-TRANS4 routines, respectively. The fixed-effect PK parameters estimated directly with these model specifications were total body clearance (CL) and distribution volume (V) for the former and CL, distribution volume of the central compartment (V1), intercompartment clearance, and distribution volume of the peripheral compartment (V2) for the latter. Bayesian PK estimates for individual subjects were obtained by specification of the POSTHOC option to NONMEM.
Both additive and exponential-error models were tested to describe interindividual variability:
j =
' + 
j and
j =
'exp (
j), where
j is the estimate for a PK parameter in the jth individual as predicted by the model,
' is the population mean of the PK parameter, and 
j represents the random variable with zero mean and variance
2. Covariance was also estimated. It should be noted that the first-order method used in this analysis approximates the exponential error model as a proportional error model. The terms for interindividual variability were included only for CL, V, and V1.
Residual variability, including intraindividual variability, measurement error, and model misspecification, was estimated using both additive and exponential error models: Cij = C'ij +
and Cij = C'ijexp (
), where Cij and C'ij are the observed and predicted VAN concentrations for the jth individual at time i, respectively, and
is the additive error (with zero mean and variance
2).
(ii) Model building. Assumptions about the population model (one versus two compartments and additive versus exponential error models) were evaluated according to the objective function value (OFV) produced by NONMEM, which was the first criterion of selection. The Akaike criterion (2) and visual inspection of the distribution of weighted residual plots were also used.
To elucidate the preliminary relationships between a PK parameter obtained using a Bayesian maximum a posteriori estimation and covariates, a graphic approach to exploratory data analysis and the stepwise generalized additive model (GAM) implemented in Xpose were used (24).
Inclusion of a fixed-effect parameter in the basic model quantifies the relationship between a PK parameter and a covariate and allows it to be known whether that covariate significantly improves the ability of the model to predict the observed concentration-time profile. The OFV difference between two hierarchical models is asymptotically
2 distributed, with degrees of freedom (df) equal to the difference in the number of parameters between the two models, and should be at least 3.84 (if df = 1) in order to achieve the desired level of significance of
= 0.05. Other diagnostic criteria for the retention of a covariate in the model were a reduction in unexplained interindividual variability for the associated PK parameter; an improvement in the graphic diagnostic model, evaluated by randomly distributed weighted residuals; a closer relationship between predicted and observed concentrations; and the criterion that the 95% confidence interval, estimated using standard errors, should not include zero value. Additionally, the percent estimation error of fixed and random parameters should not be higher than 25 and 50%, respectively (3). The full model thus generated was then subjected to backwards elimination, where each model parameter was fixed to zero value, using a more stringent criterion of statistical significance (
= 0.01).
(iii) Validation of the population pharmacokinetic model. The population parameters obtained with the index data set were used to estimate values with NONMEM individual parameters in the validation data set. From these individual parameters, a priori (i.e., without individual serum data) VAN serum concentrations were estimated (the "simul" NONMEM option) at the same times as those actually observed and compared in order to know their predictive performance according to standard procedures (42).
Additionally, standardized prediction errors were estimated in order to evaluate whether the regression model was correct and the parameters estimated were unbiased (47). The clinical suitability of the predictions was defined as the percentage of attainment within ±20% of the predicted value.
The ADAPT II software (11) was used for Monte Carlo simulation of 1,000 subjects in order to graphically delineate variability in VAN pharmacokinetic profile for a standard dosage. For patients with the typical mean characteristics of the population studied (TBW = 65 kg and CLCR = 90 ml/min), receiving a dose of 1,000 mg/12 h administered in 60-min intermittent infusions, simulations were performed using the mean parameter vector and covariance matrices estimated with the models selected.
In order to visually compare the VAN pharmacokinetic profiles, graphic simulations were performed with Pharmacokinetics System software, as described previously (1, 18, 32, 33, 49, 52)
Summary statistics and differences between the index and validation groups were obtained with the SPSS program (v. 10.0.7) (43).
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Comparison of the one- and two-compartment models according to the diagnostic criteria specified above in Materials and Methods revealed a slightly lower value of the OFV for the latter model (4,502.68 versus 4,495.44). However, there were no obvious differences in the scatter plots between the two models, and the Akaike criterion (2) was better for the simpler model (8,462.46 versus 8,454.46). Additionally, the mean parameter values obtained with the two-compartment model were unrealistic for both the central and peripheral distribution volumes (50.4 and 100.0 liters, respectively). Accordingly, the one-compartment model was assumed to adequately describe serum VAN concentrations in view of the good correlation between the individual predicted and measured concentration data (r = 0.943 and no statistical differences with the identity line as reflected by the 95% confidence interval of the constant, 0.59 to 0.09, and slope, 0.98 to 1.02) In this model, the interindividual and residual errors were best described by exponential and additive structures, respectively. The population parameters estimated for this model are depicted in Table 2. A striking observation is the large estimation error in the CV on V. Since the data analyzed were obtained mostly at steady state, it is not surprising that the estimates pertaining to interindividual variability in V are less precise and more biased than those pertaining to clearance. The covariate analysis was then examined on the basis of this structural model.
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TABLE 2. Population pharmacokinetic parameters of VAN estimated from the basic model
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Table 3 summarizes the main models tested with NONMEM according to this preliminary analysis. The proposed final VAN population model, summarized in Table 4, is defined by the following relationships: CL (liters/h) = 1.08 x CLCR(Cockcroft and Gault)(liters/h); CVCL = 28.16% and V (liters) = 0.98 x TBW; CVV = 37.15%;
= 3.52 mg/liter.
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TABLE 3. Summary of principal covariate models tested in population model building (one-compartment structure)a
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TABLE 4. Population pharmacokinetic parameters of VAN estimated from the final model
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was unacceptable (34.5%) and therefore this covariate was removed from the model. However, in view of (i) these results, (ii) the above-discussed limitation of NONMEM in detecting nonnormal distributions, (iii) the suspicion of a modified kinetic profile in leukemic patients, and (iv) the availability of a significant proportion of AML patients (n = 79), we decided to characterize VAN kinetics behavior specifically in this subpopulation. In AML patients the variables accounting for CLCR (TBW, GEN, age, and SCR) were better VAN clearance predictors than CLCR (OFV difference = 14.56, P < 0.01). However, other diagnostic criteria (lower unexplained variability and parameter estimation errors) as well as the presumed greater use of CLCR in clinical practice supported the exchangeability with respect to an alternative simplified model, which included only this later covariate. The equations defining such population models, designated AML-1 and AML-2, were as follows: AML-1, CL (liters/h) = 0.49 x TBW x SCR0.87 x age0.49; CVCL = 23.3%; CL was multiplied by 1.08 if the patient was male; V (liters) = 1.06 x TBW; CVV = 24.2%;
= 3.25 mg/liter; AML-2, CL (liters/h) = 1.17 x CLCR; CVCL = 21.6%; V (liters) = 0.97 x TBW; CVV = 24.8%;
= 3.20 mg/liters. Validation. A priori predicted VAN concentrations in the validation data set from the proposed general population model afforded a mean prediction error of 0.82 ± 4.83 mg/liter. The bias for the AML-1 and AML-2 models was 1.95 ± 4.48 mg/liter and 0.33 ± 4.11 mg/liter, respectively. The predictive performance of the models was also evaluated by calculating the mean and standard deviation of the standardized prediction errors. The values obtained were 0.13 ± 1.47 mg/liter, 0.33 ±1.26 mg/liter, and 0.04 ± 1.39 mg/liter for the general, AML-1, and AML-2 models, respectively. The 95% confidence interval included a zero value for all of them, and standard deviations were close to unity, which are necessary conditions for a model to be considered acceptable. The proportion of measured concentrations predicted accurately was 37.9, 33.3, and 39.6% for the general, AML-1, and AML-2 models, respectively.
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Understanding the variability associated with pharmacokinetics and identifying subpopulations with special features can provide clinicians with relevant information for dosage individualization. Since no precise evaluation of VAN population PK exists for patients with hematological malignancies, we designed this study to characterize PK parameters, the covariates affecting their variability, and unexplained residual and interindividual variabilities. Sparse VAN serum concentration data obtained from routine monitoring were used to estimate the population parameters. Limited sample acquisition in the clinical setting usually permits only one-compartmental models, although it is well accepted that VAN PK characteristics are more realistically described by a two-compartment model. However, in spite of the poor design these TDM data can provide results more representative of the population studied if a large number of patients are analyzed. All samples for VAN peak concentrations were drawn at least 2 hours after the end of the infusion, so the data are one compartment in nature. The available information did not allow the distributive phase to be described adequately.
The mean values (expressed in a homogeneous system of units to allow comparisons) obtained for VAN clearance and V in this study using NONMEM (1.19 ml/min/kg of body weight and 1.05 liters/kg) are slightly higher than the values reported in other studies using standard approaches (two-stage methods with a one-compartment model) in other adult populations (6,7, 14, 25, 28, 29, 38, 39). Also, the mean values accounting for the effect of renal function and TBW on VAN clearance and V, respectively, were higher than the ranges quoted for this antibiotic in other adult populations (26, 30, 50). The greater volume of distribution observed can be attributed to the pathophysiology of malignancy, although postdistribution sampling times and the one-compartment pharmacokinetic model used in the analysis could also have been responsible. For the purposes of comparison, the one-compartment pharmacokinetic parameters from different studies are summarized in Table 5. The magnitude of the differences (26to 42%) is the main argument against the use of pharmacokinetic data from the general population instead of from the population of interest.
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TABLE 5. One-compartment pharmacokinetic parameters (mean ± standard deviation) of VAN from different studies versus this study (boldface)
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To our knowledge, no previous VAN studies using NONMEMhave been conducted specifically with patients with hematological malignancies, which hinders critical comparison of our results with others. For this antibiotic, five studies using mixed-effect models have been published previously (21, 22, 41, 50, 51).Methodological issues (patient age, sample size, and PK analysis) mean that only one of them (50) can be compared with our final model. This comparison revealed that the coefficients of the linear relationship between CL and CLCR (1.08) and V (0.98) in our model were greater than those obtained by those authors, suggesting enhanced VAN clearance and V in patients with hematological malignancies. Such notions are consistent with those reported for aminoglycoside antibiotics in the same kind of patients (5, 12, 33, 53). The underlying mechanism explaining enhanced disposition in this patient population could be related to two hypotheses: possible changes in renal function induced by the cancer and the fact that CLCR is a surrogate index of the glomerular filtration rate, although the tubular secretion of VAN should at least partially contribute to its renal excretion (20).
Figure 2 shows mean VAN profiles in a standard patient (male, 65 kg in weight, with a CLCR of 90 ml/min, receiving a conventional dosage regimen of 1,000 mg/12 h) simulated according to the population models developed in this study versus a general model for the adult population (1). The significantly lower serum concentrations predicted with our models in hematological patients owing to the higher V and CL values estimated are noteworthy. According to our final model, a typical patient would require a mean dosage of 45 mg/kg/day (50% higher than that conventionally used) in order to attain an area under the curve of 500 mg/liter · h. Dosage intervals of 6, 8, or 12 h can be used depending on desired fluctuations in serum levels. Dosage recommendations based on peak target concentrations should be adapted to the one-compartment model as we have previously established (18). Such a target should be 19 to 21 mg/liter as opposed to the generally cited 30 to 40 mg/liter.
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FIG. 2. Simulated mean VAN serum profiles in a standard patient (male, 65 kg, 50 years old, with a CLCR of 90 ml/min, receiving 1,000 mg/12 h), according to two population models developed in this study (general model for patients with hematological malignancies and model customized for AML diagnosis) in comparison with the one-compartment model implemented in the AbbottBase Pharmacokinetics System software (PKS) for adult populations.
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The main results obtained in population PK analysis and their interpretation are dependent on the study design. Critical factors are the total number of patients, the representativeness of the covariates analyzed, and sampling strategies. The population models, both general and AML specific, constructed from the analysis of 1,004 and 301 VAN serum samples, respectively, underscore the representativeness of our sample of patients and broaden the generality of our results to similar hematological populations. However, previous validation is necessary to certify their reliability and appropriateness for the target population receiving this drug. The results obtained for external validation in a subset of 59 (24 with AML diagnosis) patients confirmed the good predictive performance of our models and suggest that they would constitute a useful clinical tool for a priori individualizing VAN therapy. Moreover, more than one of three (37.9%) a priori predictions lies within ±20% of the predicted concentrations. This therapeutic precision seems to be more than twofold for this model in comparison with a general model implemented in the AbbottBase Pharmacokinetics System software (16.1%). It is clear that having an a priori dosing method achieving target concentrations without bias and as close as those desired is an important issue when TDM is controversial. In fact, the more reliable the dosing method, the less TDM that is required. However, as seen in Fig. 3 for the general and AML-2 models, the magnitude of the interindividual and residual variabilities involves a broad range of expected VAN serum concentrations for a fixed-dosage regimen, which could justify TDM of this drug in hematological patients.
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FIG. 3. Typical (thick line) vancomycin population profiles including interindividual plus residual variabilities (thin lines) from the general and AML-2 models for a standard patient (male, 65 kg, 50 years old, and with a CLCR of 90 ml/min) receiving 1,000 mg/12 h.
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In conclusion this study proposes and validates VAN pharmacokinetic models specifically designed for patients with hematological malignancies in general and customized for AML patients in particular. Although these models will be useful for initial dosage selection and Bayesian forecasting of VAN therapy, our proposals should be evaluated prospectively in comparison with alternative models (i.e., nomograms specifically derived for this patient population) and should be correlated with clinical and microbiological outcomes to determine their relevance in clinical practice.
Equal contribution as first author of paper. ![]()
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