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We determined the population pharmacokinetics of vancomycin (VAN) using the glomerular filtration rate (GFR) estimated from the serum cystatin C concentration. We examined the predictive performance of the trough serum VAN concentration for determination of the initial dose by using a new model for the analysis of the population pharmacokinetic parameters. Data for 86 patients were used to estimate the values of the population pharmacokinetic parameters. Analysis with a nonlinear mixed-effects modeling program was done by using a one-compartment model. Data for 78 patients were used to evaluate the predictive performance of the new model for the analysis of population pharmacokinetic parameters. The estimated GFR values determined by using Hoek's formula correlated linearly with VAN clearance (VAN clearance [ml/min] = 0.825 × GFR). The mean volume of distribution was 0.864 (liters/kg). The interindividual variability of VAN clearance was 19.8%. The accuracy of the prediction determined by use of the new model was statistically better than that determined by use of the Japanese nomogram-based model because the 95% confidence interval (−3.45 to −1.38) of the difference in each value of the mean absolute error (−2.41) did not include 0. Use of the serum cystatin C concentration as a marker of renal function for prediction of serum VAN concentrations may be useful.
Vancomycin (VAN) has been widely used for the treatment of methicillin-resistant Staphylococcus aureus (MRSA) infections. It is mainly eliminated via the kidneys and has a narrow therapeutic range; high doses cause nephrotoxicity, particularly if it is used in combination with an aminoglycoside antibiotic (6, 28). The area under the blood concentration-time curve (AUC)/MIC is the pharmacodynamic parameter that best correlates with a successful outcome after the use of VAN (20, 27). Therefore, it is believed that therapeutic drug monitoring (TDM) is appropriate for VAN therapy (3, 16, 18, 29).
The initial VAN dosage regimen is usually selected by use of a nomogram that uses the serum creatinine concentration as a marker of renal function. Our previous studies indicated that the nomogram that uses the serum creatinine concentration does not accurately predict the serum VAN trough concentration, particularly in elderly individuals (33). This is probably caused by using the serum creatinine concentration as a marker of renal function because this leads to an overestimation of the glomerular filtration rate (GFR) (17). A more accurate marker of GFR is needed for the appropriate use of VAN because renal function is one of the most important factors affecting the clearance of VAN.
It has been reported that the serum cystatin C concentration is a better marker of renal function than the serum creatinine concentration (5). A recent meta-analysis demonstrated that the serum cystatin C concentration is superior to the serum creatinine concentration for use for the detection of an impaired GFR (7). Some studies reported that the serum cystatin C concentration is a better marker of drug clearance than the serum creatinine concentration (15, 23). Recently, we have shown that the serum cystatin C concentration is a better marker for determination of the initial dose in VAN therapy. In a previous study, GFR was estimated on the basis of the serum cystatin C concentration in place of the creatinine clearance, which is the parameter usually used to determine the population pharmacokinetics of VAN (32). However, a means of population pharmacokinetic analysis that uses the serum cystatin C concentration as a marker of renal function is lacking.
We approached the population pharmacokinetic analysis of VAN using the serum cystatin C concentration and a one-compartment model for adult patients infected with MRSA. Covariate selection revealed that total body weight (TBW) affected the volume of distribution, whereas renal function (estimated from GFR by use of the serum cystatin C concentration) affected VAN clearance. We also compared the predictive performance of the trough serum VAN concentration for determination of the initial dose with that of the use of the nomogram and the serum creatinine concentration.
The present study was conducted in accordance with the guidelines of the Declaration of Helsinki. Approval was obtained from advisory boards of the Clinical Ethics Committees of Ehime University Hospital (Toon, Japan) and Matsuyama Citizens' Hospital (Matsuyama, Japan).
For the analysis of the pharmacokinetics of VAN and the relationship of the pharmacokinetics of VAN to the cystatin C concentration, 164 inpatients who had MRSA infections and who were receiving VAN treatment at Ehime University Hospital and Matsuyama Citizens' Hospital were recruited for the study. Each patient submitted written consent agreement before recruitment. We excluded patients with disseminated intravascular coagulation and/or multiple-organ failure, as well as those who had undergone hemodialysis or hemofiltration. Clinical data (body weight, height, age, serum creatinine concentration) were collected from the medical records of the recruited patients.
Blood samples were collected from each patient when his or her blood VAN concentration was considered to have reached steady state. For example, in the case of a patient whose elimination half-life of VAN was assumed to be 12 h on the basis of his or her estimated GFR, blood collection was at least 2 days after the first treatment with a 1-week VAN dosage regimen. Samples were collected just before the intravenous infusion of VAN (trough sample) and/or generally 1 to 8 h after the completion of the infusion (nontrough sample). For the latter, blood was collected from some patients 19 h after the completion of the infusion, due to clinical requirements. In the present study, blood samples collected within 1 h after the completion of the infusion were excluded to avoid a complex pharmacokinetic analysis (21, 35). The blood samples collected were subjected to VAN concentration determination as described below. The serum VAN concentration determined was recorded along with the amount dosed, the time of administration, and the time of blood collection. VAN was administered at a concentration of 500 to 1,500 mg by intravenous infusion over 1 to 2 h to patients at dosing intervals of 6 to 48 h.
The blood samples were used to determine the serum VAN concentration (μg/ml) by a fluorescence polarization immunoassay method with a TDx assay system (Abbott Laboratories, Chicago, IL). If the blood sample was the first one from a patient, the cystatin C concentration (mg/liter) was also determined by immunonephelometry with N Latex cystatin C (Dade Behring Diagnostics, Marburg, Germany) and a Behring BN ProSpec analyzer (Dade Behring Diagnostics). The coefficient of variation of the cystatin C determination method was 4.1%.
Among the 164 patients recruited, 86 patients underwent trough and nontrough blood collections (group A). The VAN concentration data for group A (181 data points) were used to estimate the population means of the values for the VAN pharmacokinetic parameters, as described below. Blood sample were collected from another 78 patients only at the trough time point (group B). Their concentration data (88 data points) were used to evaluate the result of the population pharmacokinetic analysis carried out with the concentration data from group A. There were no differences in the characteristics (including renal function) of the patients in groups A and B (Table (Table1).1). We checked for a normal or nonnormal distribution using the JMP 8J statistical analysis software package (SAS Institute Incorporated, Chicago, IL).
GFR was estimated in two ways. In addition to the conventional manner in which is estimated on the basis of the serum creatinine concentration and the formula of Cockcroft and Gault (4), it was estimated on the basis of the serum cystatin C concentration with Hoek's formula, described below (8, 14). Our previous studies demonstrated that Hoek's formula is the most effective method for adjusting the dosage of VAN (31).
where Ccys denotes the serum cystatin C concentration (mg/liter), and BSA is body surface area (m2). H and W denote height (cm) and weight (kg), respectively. The unit of measurement for the GFR derived from equation 1 is ml/min/1.73 m2.
The serum concentration profile of VAN in group A was analyzed by use of the one-compartment model described below and by taking inter- and intraindividual variabilities into consideration (21, 35). The total body clearance (CL; ml/min) of VAN and its volume of distribution (V; liters/kg) were then characterized as a function of GFR. Subsequently, because GFR was estimated in two ways, as described above, the adequacies of the pharmacokinetic model that used the GFR derived with the serum creatinine concentration and the pharmacokinetic model that used the GFR derived with the serum cystatin C concentration for determination of the VAN concentration profile were compared.
where C(t) denotes the serum VAN concentration (μg/ml) at time t, and t is the time (h) that elapsed after the completion of the infusion. R is the VAN infusion rate (μg/h). The infusion period (h) is designated T. If it is assumed that the serum VAN concentration is at steady state, the trough concentration (Ctrough; i.e., the concentration measured just before the infusion period) can be considered a constant. Therefore, equation 3 can be expressed by using Ctrough, as follows:
To evaluate the relationship between the VAN concentration profile and renal function, equation 4 is further arranged as described below, in which the inter- and intraindividual variabilities are taken into consideration:
where θ1, θ2, θ3, and θ4 are the parameters whose population means are to be determined in this study on the basis of the VAN concentration profiles. The relationships between CL and GFR and between V and GFR were set according to various reports on the pharmacokinetics of VAN (32, 35). In the analysis, if the value calculated for the parameter θ1, θ2, θ3, or θ4 was insignificant and it was rationally considered to be equal to 0, the corresponding parameter was removed from equation 6 or 7. The subscripts j and i indicate the jth value for the ith patient. The interindividual variabilities of the total body clearance and the volume of distribution are designated η1 and η2, respectively, and intraindividual variability is designated . The analysis was carried out with the nonlinear mixed-effects modeling program (NONMEM, version V; GloboMax, Ellicott City, MD) (22), in which the equations for the analysis were prepared with the $PRED description.
After determination of the population means of the θ parameters, the serum VAN concentration of each patient in group B was predicted by a Bayesian method and by using equations 5 to 7 and the GFR value obtained on the basis of the cystatin C concentration determined with Hoek's formula. The predicted concentrations (Cpred) were then compared with the corresponding measured values (Cmeas), and the prediction errors were evaluated (30). The mean error (ME) and mean absolute error (MAE) were calculated by using the following equations to evaluate the prediction bias and precision, respectively. If the 95% confidence intervals of ME and MAE do not include 0, the prediction is judged to be significantly biased.
where N is the total number of samples.
The VAN concentration can be calculated on the basis of the serum creatinine concentration by using a nomogram provided by a pharmaceutical company (35). The nomogram-based predicted values were also compared with the values predicted by the use of equation 5.
The relationship between the serum VAN concentration and renal function was examined with 181 data points from the patients in group A. The renal function of each patient was estimated on the basis of his or her serum cystatin C concentration by the use of Hoek's formula. In the preliminary analysis, the calculated values for the parameters θ2 and θ3 were 6.75 × 10−15 and 5.20 × 10−11, respectively, and were insignificant compared with those for the parameters θ1 and θ4. Therefore, parameters θ2 and θ3 in equations 6 and 7 were judged to be negligible and were set equal to 0 for the VAN pharmacokinetic analysis. This modification did not influence the pharmacokinetic analysis. In the analysis, the population means of the parameters explaining the relationship between the serum VAN concentration profile and renal function were determined (Table (Table2).2). The individual estimated VAN clearances and their variabilities are shown in Fig. Fig.11.
After carrying out the pharmacokinetic analysis and determining the population means of the parameters as described above, the prediction performance was evaluated by using the medical data for the patients in group B. That is, the VAN trough concentration of each patient was predicted from his or her serum cystatin C concentration, and it was then compared with the corresponding observed VAN concentration. The VAN trough concentration for each patient in group B was also predicted in a nomogram-based manner, and its prediction performance was evaluated. The correlation coefficient between the prediction and the observation was improved from 0.14 to 0.75 when the prediction was determined by the Bayesian method with the population means determined in this study (Fig. (Fig.2).2). An improved prediction performance seemed to result from a reduction of the prediction error in patients aged ≥70 years (Fig. 2B and C). The improvement was reflected in the calculated values of ME and MAE, whereby the values from the current analysis were significantly smaller than those from the nomogram-based prediction (Table (Table3).3). The accuracy of the prediction on the basis of the current analysis was shown to be statistically better than that of the nomogram-based prediction, as judged by the fact that the 95% confidence interval of the MAE determined by using the Japanese nomogram-based model minus the MAE determined by using our model (ΔΜΑΕ) did not include 0 (95% confidence interval, −3.45 to −1.38; Table Table33).
In clinical practice, creatinine clearance as a standard marker of GFR was estimated by the Cockcroft-Gault equation, but estimates of renal function obtained by this method are not accurate. Many reports state that the serum cystatin C concentration is an ideal endogenous marker of GFR (7, 10, 11, 15, 34). We therefore designed the present study to characterize population pharmacokinetic parameters, interindividual variability, and intraindividual variability.
We obtained serum VAN concentration data from routine monitoring to estimate the population pharmacokinetic parameters. It is well known that the pharmacokinetic characteristics of VAN are better described by a two-compartment model, but the limited availability of samples in clinical practice permits analysis by use of only a one-compartment model. Despite the limited design, these TDM data can provide results more representative of those for a population study because we analyzed many patients. All samples used for VAN peak concentration determinations were obtained at least 1 h after the end of administration, which aided analysis by use of the one-compartment model. The available information did not allow the distributive phase to be described adequately (2).
The mean VAN clearance and volume of distribution in our new model (group A) were 0.875 × GFR (ml/min) and 0.864 (liter/kg), respectively. For another Japanese adult population, the mean VAN clearance and volume of distribution were 0.797 × creatinine clearance (ml/min) and 60.7 liters, respectively (35). There was not much difference in clearance between the two populations. Nonrenal clearance was not detected in either study. This probably caused a wide range of GFRs (16 to 145 ml/min) in this population, which correlates well with the VAN clearance. It has been reported that the nonrenal clearance of VAN should not be ignored in patients with a severely reduced GFR (12, 19, 24), so data for these patients may not be eligible for this model.
The volume of distribution in this study (46.7 liters; mean weight, 54 kg) was lower than that determined by use of the Japanese nomogram-based model. The lower volume of distribution is caused by the differences in the pharmacokinetic models. Other studies performed by use of a one-compartment pharmacokinetic model obtained values of 0.54 to 0.98 liters/kg (1, 9, 26). There were no differences in the volumes of distribution between the other studies.
The interindividual variability of the VAN clearance in our new model was lower than that in the Japanese nomogram-based model (19.8% versus 38.5%). The intraindividual variability of the new model was lower than that of the Japanese nomogram-based model (12.7% versus 23.7%).
This observation could be attributed to the superior diagnostic sensitivity and accuracy of cystatin C because there was a good linear relationship between VAN clearance and the estimated GFR (Fig. (Fig.1).1). The predictive error of the serum VAN concentration determined by use of the Japanese nomogram-based model was considerably better than that determined by use of the new model, particularly for elderly individuals (Fig. (Fig.2B2B).
In clinical practice, the initial dose of VAN therapy is determined by the use of only population pharmacokinetic parameters and not the serum VAN concentration. We predicted the serum VAN concentrations in the setting of determination of the initial dose at steady state for group B by use of the new model and the Japanese nomogram-based model. The negative ME (−0.90) suggested that the new model underpredicted the trough serum VAN concentration, but the bias was only slight. The ME of the Japanese nomogram-based model (−3.31) was considerably lower than that of the new model. The accuracy of the prediction obtained by use of the new model was statistically better than that obtained by use of the Japanese nomogram-based model. These results suggest that the serum cystatin C concentration is a good marker for the prediction of serum VAN concentrations. This finding is in agreement with the findings of studies of other drugs eliminated by the kidneys (13, 32).
Our work focused on prediction of the trough values, which we assumed correlated with the AUC. We could not estimate the AUC using the sampling strategy and the pharmacokinetic model because we collected data as part of routine monitoring. Therefore, future research should be aimed at estimating the AUC and evaluating the clinical effect.
We confirmed the good predictive performance of our model. We suggest that the new model may be a useful clinical tool for determination of the initial dose of VAN therapy. Determination of the serum cystatin C concentration may be more appropriate for establishing the dosage regimens for drugs that are mainly eliminated by the kidneys.
No support was received for the production of this article.
Published ahead of print on 23 November 2009.