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Antimicrobial Agents and Chemotherapy, December 2004, p. 4718-4724, Vol. 48, No. 12
0066-4804/04/$08.00+0 DOI: 10.1128/AAC.48.12.4718-4724.2004
Copyright © 2004, American Society for Microbiology. All Rights Reserved.
Albany College of Pharmacy,1 Albany Medical Center,2 Ordway Research Institute, New York State Department of Health, Albany, New York,4 Colleges of Pharmacy and Medicine, University of Illinois at Chicago, Chicago, Illinois3
Received 17 June 2004/ Returned for modification 8 August 2004/ Accepted 8 September 2004
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8 mg/liter. The 4-h piperacillin administration interval had a superior pharmacodynamic profile and provided target attainment rates exceeding 95% for MICs of
16 mg/liter. This study indicates that piperacillin-tazobactam should have utility for empirical therapy of hospital-onset infections. |
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Piperacillin-tazobactam is an acylureido-penicillin-beta-lactamase inhibitor combination and is frequently used in the empirical treatment of hospital-acquired infections. Similar to other beta-lactam antibiotics, piperacillin-tazobactam exhibits time-dependent killing and the T > MIC appears to be the best outcome predictor (7, 8). Because a majority of infections are treated empirically, it is necessary to achieve a T > MIC equal to 50% of the dosing interval (50% T > MIC) against the most likely pathogens, including those with only moderate susceptibility. Although the pharmacokinetics (PK) of piperacillin-tazobactam are well described, its pharmacodynamic profile or ability to achieve 50% T > MIC in its targeted patient populationpatients with hospital-related infectionsagainst the array of MICs encountered in clinical practice has not been extensively characterized (6, 15-18, 20, 22, 27, 28).
There is also a debate about the PK model that most accurately describes the elimination of piperacillin. Although piperacillin PK have been most frequently described as linear, some authors have recently argued that piperacillin exhibits nonlinear PK and studies have documented evidence for fluctuating clearance with increasing concentrations (3-5, 34, 35). Piperacillin is primarily excreted through the kidneys by glomerular filtration. Piperacillin is also eliminated by active tubular secretion, and this active secretion process may be saturable.
The primary objectives of this investigation were to describe the PK of piperacillin in the presence of tazobactam and to characterize its pharmacodynamic profile. Through population PK modeling, the PK model that best characterizes its clearance was determined. Once the optimal PK model was identified, Monte Carlo simulationusing the mean parameter vector and full covariance matrix from the population modelwas used to characterize the pharmacodynamic profile of currently recommended piperacillin-tazobactam dosing regimens against the array of MICs encountered clinically. Specifically, the Monte Carlo simulation profiled the likelihood of attaining a free-piperacillin 50% T > MIC at each MIC between 0.25 and 32 µg/ml for each regimen examined. We did not examine the pharmacodynamic profile of tazobactam because current doses of tazobactam in the piperacillin-tazobactam formulation have been shown to be sufficient for an antibacterial effect when the target is attaining a free-drug concentration exceeding the MIC for 50% of the dosing interval (31).
The second objective was to compare the piperacillin-tazobactam target attainment rates between hospitalized patients and healthy subjects. Monte Carlo simulations of antibiotic target attainment rates frequently use healthy-subject PK data, and this practice may provide a conservative estimate of antibiotic target attainment rates (20, 21). Piperacillin-tazobactam is primarily used in patients with hospital-related infections, and this patient population typically has a lower glomerular filtration rate than that of healthy subjects. Although it is advisable to use the PK data from the population of interest, the impact of using healthy-subject data to estimate target attainment rates for piperacillin in the presence of tazobactam has not been extensively described.
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TABLE 1. PK studies of piperacillin-tazobactam in hospitalized patients
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(NPAG) program of Leary et al. (23). To determine which PK model most accurately describes the elimination pathways for piperacillin, models were parameterized as two-compartment models with zero-order infusion and with elimination from the central compartment modeled as a Michaelis-Menten (MM) process, as a MM process in parallel with first-order elimination, or as a first-order elimination process only. The models with zero-order input and MM with or without a parallel first-order elimination term were evaluated because of a recent study by Vinks et al. (35). Population PK modeling for the MM model and a parallel first-order-MM model was performed with the BIGNPAG program of Leary et al. The general differential equations for the models are dX(1)/dt = R(t) [((Vmax · V/(Km · V + X(1)) ( kel + kcp) · X(1) + kpc · X(2)] and dX(2)/dt = kcp · X(1) kpc · X(2), where Km is the MM constant and the concentration in the central compartment for a half-maximal effect (milligrams per liter), Vmax is the maximum elimination rate (milligrams per hour), X(1) is the amount of drug in the central compartment (milligrams), X(2) is the amount of drug in the peripheral compartment (milligrams), kel is the first-order elimination rate constant (per hour), kcp and kpc are first-order intercompartmental transfer rate constants (per hour), V is the volume of the central compartment (liters), and R(t) is the time-delimited zero-order rate (piecewise input function) of drug input into the central compartment (milligrams per hour).
The inverse of the estimated assay variance was used as the first estimate for weighting in the PK modeling throughout. Weighting was accomplished by making the assumption that total observation variance was proportional to assay variance. Assay variance was determined on a between-days basis. The analysis was performed with adaptive
, a scalar that multiplies the polynomial described above and is optimized with each cycle to produce the best approximation to the homoscedastic assumption.
Upon attaining convergence, maximal a-posteriori probability (MAP) Bayesian estimates for each patient were obtained by using the population-of-one utility within NPAG and BIGNPAG. For each model, the mean, median, and modal values were used as measurements of the central tendency of the population parameter estimates and were evaluated in the MAP Bayesian analysis. Scatter plots were examined for individual patients and for the population as a whole. Goodness of fit was assessed by regression with an observed-predicted plot, coefficients of determination, and log-likelihood values. Predictive performance evaluation was based on weighted mean error and the bias-adjusted weighted mean squared error.
Monte Carlo simulation of hospitalized-patient data. The mean parameter vector and covariance matrix from the population PK models were embedded in the PRIOR subroutine of the ADAPT II package of the programs of D'Argenio and Schumitzky (ADAPT II User's Guide, Pharmacokinetics/Pharmacodynamics System Analysis Software; Biomedical Simulations Resource, Los Angeles, Calif.) (10, 11). The population simulation without process noise option was used. A 10,000-subject Monte Carlo simulation was performed for standard 0.5-h infusions of 3 g of piperacillin administered every 4 or 6 h. Both normal and log-normal distributions were evaluated. These were discriminated on the ability to recreate the original mean parameter values and corresponding standard deviations from the population analyses.
The parameter values from the optimal distributions were used to simulate steady-state concentrations and to generate plasma concentration-time curves for each dosing regimen. The PK data for piperacillin were adjusted for 30% protein binding of piperacillin to reflect unbound drug concentrations in the data analysis (2). For each regimen examined, the fraction of simulated subjects who achieved 50% T > MIC was calculated for the range of piperacillin MICs (in the presence of tazobactam) from 0.25 to 32 µg/ml. Systat for Windows (version 10.2) was used for all data transformations.
Population PK modeling and Monte Carlo simulation of healthy-subject data. The optimal PK model identified in the population PK analysis of hospitalized-patient data was used to characterize the PK and pharmacodynamic profile of piperacillin for healthy subjects. Population PK modeling and Monte Carlo simulation were performed as already described for hospitalized patients. The data were drawn from a previously published investigation of 12 healthy male subjects administered piperacillin-tazobactam at 3.375 g every 6 h and 4.5 g every 8 h. The subjects ranged in age from 23 to 40 years (mean, 25 years) and in weight from 60.4 to 96.3 kg (mean, 78.4 kg). Their creatinine clearance values ranged from 94.1 to 134.1 ml/min/1.73 m2 (28).
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TABLE 2. Piperacillin population PK parameter estimates for hospitalized patients obtained by NPAG and BIGNPAG analysesa
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TABLE 3. Predictive performance of piperacillin population models
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2 distribution with the appropriate number of degrees of freedomrevealed statistically significant differences between the parallel first-order-MM model and the linear model, the parallel first-order-MM model and the MM model, and the MM model and the linear model (P < 0.05). In contrast, the r2 and bias and precision measurements were better for the linear model relative to those of the MM model and the parallel first-order-MM model. The best-fit regression lines for the observed-predicted plots were highly satisfactory for all three models, but the slope and intercept of the regression line most closely approached a slope of 1 with a small y intercept for the linear model relative to the other models. The observed-predicted plot for the linear model showed a best-fit regression line of observed = 1.032 x predicted + 0.31. For the MM and parallel first-order-MM models, the observed-predicted plots showed best-fit regression lines of observed = 1.041 x predicted + 3.69 and observed = 1.053 x predicted + 3.20, respectively. Overall, the measurements of bias and precision, observed-predicted plots, and r2 values were highly acceptable for all three models and all three models were appropriate candidates for the Monte Carlo simulation evaluation. Monte Carlo simulation of hospitalized-patient data. We performed a 10,000-subject Monte Carlo simulation for the linear model, the MM model, and the parallel first-order-MM model. Log-normal distributions were selected for the population simulation for all three models on the basis of the ability to recapitulate the original mean parameter values and the corresponding standard deviations (Table 4). The Monte Carlo simulations recreated the original mean parameter values extremely well for both the linear model and the parallel first-order-MM model. For the MM model, considerable differences were observed between the original and simulated means and standard deviations of Vmax and K21.
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TABLE 4. Mean parameter values from the 10,000-subject Monte Carlo simulation for piperacillin population modelsa
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FIG. 1. Distribution of piperacillin concentrations at the pharmacodynamic target, the 50% time point for a 6-h dosing interval (h 3 after initiation of infusion). Shown are the raw data scaled to a piperacillin dose of 3 g (A), a 10,000-subject Monte Carlo simulation with the linear-clearance model (B), a 10,000-subject Monte Carlo simulation with the MM model (C), and a 10,000-subject Monte Carlo simulation with the parallel first-order-MM model (D). All concentrations were corrected for an assumed protein binding of 30%.
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8 mg/liter and was 72.7% at 16 mg/liter. Piperacillin administration every 4 h (18 g/day) had a superior pharmacodynamic profile and provided target attainment rates exceeding 95% for MICs of
16 mg/liter.
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FIG. 2. Comparison of target attainment profiles of 3.375 g of piperacillin-tazobactam administered every 6 or 4 h as a 0.5-h infusion for hospitalized patients.
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TABLE 5. Piperacillin population mean PK parameter estimates for healthy subjects obtained by NPAG analysisa
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1 mg/liter (Fig. 3) and dropped precipitously with increasing MICs. For a 4-h dosing interval (0.5-h infusion), 50% T > MIC attainment exceeded 95% for MICs of
8 mg/liter and was 72% at 16 mg/liter. Compared to the simulated pharmacodynamic profile of hospitalized patients, the use of healthy-subject PK data underestimated the target attainment rate of 50% T > MIC for piperacillin.
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FIG. 3. Comparison of target attainment profiles of 3.375 g of piperacillin-tazobactam administered every 6 or 4 h as a 0.5-h infusion for healthy subjects.
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Monte Carlo simulation was used to estimate target attainment rates for piperacillin in the presence of tazobactam. Monte Carlo simulation has been integrated with accepted pharmacodynamic models to compare antimicrobials and determine their abilities to achieve critical dynamic endpoints (1, 12, 13, 15, 20-22, 32). It is a mathematical technique in which parameter values are randomly drawn from a multivariate distribution. These randomly selected values allow the characterization of drug concentration-time profiles for a large number of simulated subjects. In essence, Monte Carlo simulation is a technique that incorporates the variability in PK among potential patients (variability between patients) when predicting antibiotic exposures and allows calculation of the probability of obtaining a critical target exposure for the range of possible MICs.
The Monte Carlo simulations demonstrated that piperacillin-tazobactam is a suitable agent for the empirical treatment of hospital-acquired infections. Standard piperacillin-tazobactam doses administered every 6 h provided high target attainment rates for MICs of
8 (piperacillin) and 4 (tazobactam) mg/liter when hospitalized-patient data were used. The population utility of this dose and schedule(s) can be ascertained by taking an expectation (weighted average) over the MIC distribution for target pathogens (Escherichia coli, Klebsiella pneumoniae, etc.). In clinical situations in which the MICs are expected to be
16 (piperacillin) and 4 (tazobactam) mg/liter, the results of the Monte Carlo simulations indicate that is preferable to administer piperacillin-tazobactam every 4 h to ensure a higher probability of achieving 50% T > MICthe dynamic endpoint of maximal bactericidal activity. It is important to note that the Monte Carlo results indicate that the probability of achieving 50% T > MIC for piperacillin-tazobactam every 4 h is >95% for MICs of
16 (piperacillin) and 4 (tazobactam) mg/liter and is <80% for higher MICs. In situations in which the MICs are suspected or known to be
32 (piperacillin) and 4 (tazobactam) mg/liter, caution should be exercised when using piperacillin-tazobactam.
The linear-clearance model was used in the Monte Carlo simulation. There is a debate about the PK model that best describes the clearance of piperacillin in the presence of tazobactam (3-5, 34, 35). The measurements of bias and precision and the r2 values indicate that all three models are appropriate candidates for the Monte Carlo simulation evaluation. However, it is also clear that the best model by log likelihood is the parallel first-order-MM model. This is not surprising, given that the parallel first-order-MM model is an expansion of the MM and linear models and log-likelihood values improve with addition of terms to the model.
The goal of this study, however, was to determine the probability of obtaining 50% T > MIC for standard piperacillin-tazobactam dosing regimens against the array of MICs encountered in clinical practice. Visual comparison of the distribution of the piperacillin concentrations at the pharmacodynamic endpointthe midpoint of a 6-h dosing interval (i.e., h 3)between the simulated populations and raw data revealed that the linear model was most reflective of the raw data at the pharmacodynamic endpoint. We felt that the linear model, therefore, was the most appropriate model for the Monte Carlo simulation, in which the goal was to elucidate the pharmacodynamic adequacy of currently approved piperacillin-tazobactam dosing regimens. Compared to the raw data, both MM models produced a distribution of simulated h 3 concentration data that differed substantially from the shape of the concentration distribution of the raw data for h 3. Specifically, both MM models overestimated the clearance rate of piperacillin and provided conservative estimates of piperacillin concentrations at 50% of the 6-h dosing interval.
For the comparison of the raw and population data, the raw data were scaled to a 3-g dose. By scaling the raw data, there is an assumption that the rate of excretion and the concentration vary in direct proportion. This is contrary to MM kinetics, where drug clearance changes in a nonlinear fashion with increasing concentrations, most notably at concentrations exceeding the Km (26). Most (n = 115) of the patients were scaled from 2 to 3 g (Table 1). If the MM assumption was essential, scaling would only provide a conservative estimate of piperacillin clearance and concentrations would actually be much higher because of the decreased clearance with escalating drug input. As previously mentioned, the range of piperacillin concentrations at the pharmacodynamic targetthe midpoint of a 6-h dosing intervalis much greater for the actual data than the range of concentrations for the simulated MM models.
Furthermore, only 24 of the 138 patients had a single piperacillin concentration that exceeded the Km of the MM model and only 14 patients had a single piperacillin concentration that exceeded the Km of the parallel first-order-MM model. This indicates that serum piperacillin concentrations do not frequently exceed the Km values and the contribution of the MM portion of clearance would be expected to be pseudolinear in the patient population we examined. This reason and the better measurements of bias and precision drove our decision to use the simpler linear model for the Monte Carlo simulation.
While Vinks and colleagues published an MM model for this drug, there are several reasons for the dissimilar findings (35). First, their patient population was a specialized population (cystic fibrosis patients) that may have different Km and Vmax values for the anion-selective pumps in their renal tubules. Wang et al. found that the renal clearance of ticarcillin, a related acylureido-penicillin derivative, was enhanced in cystic fibrosis patients because of the greater affinity of the renal secretory system for these drugs (36). This notion is further supported by the different Km and Vmax values observed between studies. In the present study, the observed mean Km and Vmax values for the MM model were 307.03 ± 147.4 and 812.75 ± 801.64, respectively, which are substantially different from the observed mean Km and Vmax values (92.3 ± 85.6 and 2,284 ± 1,046) in the study of Vinks et al. Second, the observed differences in the clearance models between studies may be secondary to the different infusion methods (intermittent versus continuous). In the study of Vinks et al., it was only with a continuous-infusion mode of administration that the benefits of the MM model were manifested (35). The nonlinear behavior of piperacillin in non-cystic fibrosis patients, therefore, may not become as evident with intermittent infusion as with continuous infusion, especially with continuous-infusion steady-state concentrations exceeding the Km. Examination of the clearance of continuous-infusion piperacillin in non-cystic fibrosis patients is needed to clarify this issue.
Comparison of the target attainment rates of hospitalized patients and healthy subjects revealed that the healthy-subject data underestimated target attainment rates for piperacillin and illustrates the importance of using PK data from the target patient population when possible. Frequently, Monte Carlo simulations rely on PK data from healthy subjects because of the dearth of data on the population of interest (1, 20-22). Even the NCCLS frequently relies on healthy-subject data to assess the viability of MIC breakpoints. When possible, PK data should be derived from the population of interest (1, 12, 22, 30, 32, 33).
In summary, 3.375 g of piperacillin-tazobactam given intravenously every 6 h performed well, achieving excellent target attainment rates for MICs of
8 (piperacillin) and 4 (tazobactam) mg/liter. Use of 3.3375 g of piperacillin-tazobactam every 4 h extended the range to 16 (piperacillin) and 4 (tazobactam) mg/liter, respectively, indicating that piperacillin-tazobactam should have utility for empirical therapy of hospital-onset infections.
This study also greatly benefited from the gracious critical reviews of Johan W. Mouton and Alexander A. Vinks.
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