A population pharmacokinetic model for cefuroxime using cystatin C as a marker of renal function

Abstract

Aims

Since cefuroxime mainly is excreted by renal filtration, dosing is currently based on serum creatinine (Scr) or creatinine clearance (CLcr). However, it has been suggested that cystatin C (CysC) is superior to Scr as a marker of renal function. The aim of this prospective study was to develop a population model that describes the pharmacokinetics of cefuroxime and to investigate the usefulness of CysC as a covariate of the model parameters.

Methods

Ninety-seven patients were studied (CLcr range 6.5–115 ml min⁻¹). Blood samples (n = 407) for the determination of cefuroxime were withdrawn according to a sparse data sampling schedule and analysed by liquid chromatography mass spectrometry. The population analysis was performed in NONMEM.

Results

A two-compartment model described the data well. The biomarkers Scr, CLcr and CysC were evaluated as covariates on clearance (CL). The model that included CysC generated the best fit. In the final population model CL was a function of CysC and body weight, whereas V₁ was only a function of body weight. Final parameter estimates (relative standard errors) were 6.00 (3.2%) l h⁻¹, 11.4 (5.3%) l and 5.11 (11%) l for CL, V₁ and V₂, respectively.

Conclusions

Based on the results of the present study, and because CysC is practical to use in the clinic, it is suggested that individual dosing of cefuroxime may be based on CysC rather than on Scr or CLcr. Furthermore, our final population model may be useful as a tool when designing new dosing schedules for cefuroxime.

Introduction

Cefuroxime is a second-generation cephalosporin that has been used worldwide for over two decades against a variety of bacterial infections. In Sweden it is the most widely used parenteral cephalosporin. Like other β-lactam antibiotics, cefuroxime shows time-dependent killing, i.e. the longer time the bacteria are exposed to concentrations above the minimum inhibitory concentration (time above MIC) the better the killing achieved [1, 2]. Like most cephalosporins, cefuroxime has a wide therapeutic range and there is no acute need to individualize dosing. However, unnecessarily high dosing should be avoided to minimize ecological disturbances, e.g. the selection of Clostridium difficile and the development of antibiotic resistance, as well as costs. Most hospitalized patients are elderly with age-related impaired renal function, which requires individualization of dosing to prevent over-use of antibiotics.

Since time above MIC is important for outcome during treatment with cephalosporins, it is crucial to describe not only its elimination pharmacokinetics but also its distribution and redistribution, as these will influence the amount of time the bacteria are exposed to concentration above MIC. Although the pharmacokinetics of intravenously administered cefuroxime have been described previously, there are few data on its distribution pharmacokinetics, and only a small number of subjects have been studied [3, 4].

Cefuroxime is eliminated mainly by renal excretion (more than 90% is excreted unchanged in the urine) and the clearance of the drug is proportional to renal function [5–8]. Therefore, dosing of cefuroxime has been based on either serum creatinine (Scr) or creatinine clearance (CLcr) [9]. However, Scr is not an optimal renal function biomarker and tends to over-estimate glomerular filtration rate [10], particularly in patients with very poor renal function.

Any compound used as an endogenous marker of glomerular filtration rate should be generated at a constant rate and be eliminated only by glomerular filtration [11]. Cystatin C (CysC) is an endogenous protease inhibitor that is produced in all nucleated cells [12] and seems to undergo extensive glomerular filtration [13]. A meta-analysis has shown that CysC is superior to Scr in the prediction of renal function [14]. Furthermore, recent reports have indicated that plasma concentrations of drugs that are renally cleared may be better predicted using CysC than using either Scr or CLcr [15, 16]. For this reason it might be expected that CysC would be a better marker for the elimination of cefuroxime compared with Scr and CLcr. However, no pharmacokinetic model that includes CysC as a covariate of the disposition parameters of cefuroxime or any other anti-infective agent has been published.

The aim of this prospective study was to develop a population model that describes the pharmacokinetics of cefuroxime and to investigate the usefulness of cystatin C as a covariate of the pharmacokinetic model parameters.

Methods

Patients

The study was conducted between March 2002 and March 2004 at the Departments of Infectious Diseases and Nephrology, Uppsala University Hospital, Uppsala, Sweden and the Department of Nephrology at Karlstad Central Hospital, Karlstad, Sweden. The study was approved by the Swedish Medical Products Agency and the ethics committees of Uppsala University and Örebro University. All included patients signed written informed consent before inclusion.

In total, 97 patients with symptoms and signs indicating bacterial infection believed to be susceptible to treatment with cefuroxime were included, regardless of their renal function. However, in order to study patients with a broad range of renal capacity, some recruitment was from wards treating patients with impaired renal function. Patients on haemodialysis, chronic inflammatory diseases or who had had treatment with cefuroxime within the previous 2 weeks were excluded. Data on demographics [age, sex, body weight (WT)] and Scr and CysC were recorded on the day of recruitment. Scr and CysC were determined on a second occasion approximately 24 h after the start of cefuroxime treatment. Creatinine clearance was calculated using the formula by Cockcroft and Gault [17], where . The units for WT, age and Scr are kg, years and µmol l⁻¹, respectively. For men k = 1.23 and for women k = 1.04. Values of CLcr in the study population ranged between 6 and 115 ml min⁻¹. Patient characteristics are listed in Table 1.

Table 1.

Demographics of the patient population

CLcr (ml min−1)	>80	41–80	21–40	<20
Dose (mg) nonsepsis	750 × 3	750 × 3	750 × 2	750 × 1
Dose (mg) sepsis	1500 × 3	750 × 3	750 × 2	750 × 1
n	20	40	27	10
Males/females	16 : 4	25 : 15	13 : 14	1 : 9

	Median	Range	Median	Range	Median	Range	Median	Range
Creatinine (mmol l−1)	97	69–131	101	61–177	127	97–350	295	110–1160
Cystatin C (mg l−1)	1.12	0.743–1.5	1.18	0.727–3.78	2.05	0.978–6.06	4.51	2.15–6.18
Body weight (kg)	85	60–115	74	54–107	70	50–100	68	35–137
Age (years)	56	24–75	74	35–90	82	44–95	78	67–94

Treatment and sample collection

The dosing regimen for cefuroxime for patients with normal renal function (CLcr > 80 ml min⁻¹) was 1500 mg three times daily for patients suspected of suffering from severe sepsis and 750 mg three times daily for patients with other diagnoses. Based on preliminary pharmacokinetic analyses, a dosing schedule for patients with impaired renal function had been developed, with the aim that these patients should be exposed to concentration above the MIC for at least as long as patients with normal renal function and receiving standard dosing (unpublished data). The dosing schedule is presented in Table 1.

Cefuroxime was administered as an intravenous injection over 5–15 min. Blood samples of 5 ml were withdrawn predose and at five different time points from 1 to 72 h after the start of treatment according to a flexible sparse data sampling schedule, designed to cover the main part of the concentration–time profile (see Table 2). To characterize the distribution pharmacokinetics of cefuroxime, three additional samples were withdrawn 5–40 min after the dose in a subgroup of 12 patients (n = 2, 2, 4 and 4 in the CLcr intervals <20, 21–40, 41–80 and >80, respectively). The samples were centrifuged at 2000 g for 10 min and serum was stored at −20 °C until analysis.

Table 2.

Sampling schedule for blood samples for analysis of cefuroxime

	Sampling time post dose (h)
Patient 1	0	2	5	12	24	72
Patient 2	0	3	6	8	20	72
Patient 3	0	1	4	16	30	72
Patient 4	Repeat from patient 1

Drug and biochemical analysis

Concentrations of cefuroxime were determined using a mass spectrometry method described elsewhere [18]. The protein from 100 µl serum was precipitated with 200 µl acetonitrile and cefotaxime was added as the internal standard. After centrifugation, 50 µl of the supernatant was diluted in 450 µl mobile phase and 10 µl was injected onto a Zorbax SB-CN column and detected by tandem mass spectrometry. The method was linear over the range 0.025–50 µg ml⁻¹. Samples that contained concentrations higher than 50 µg ml⁻¹ were diluted 1 : 4 with medical-free human serum before re-analysis. The within-run precision was <9.4% and the accuracy was <± 7.1%. The between-run variations (presented as relative standard deviations) were at 0.2 mg l⁻¹, 4 mg l⁻¹, 40 mg l⁻¹ and 160 mg l⁻¹, 10%, 4.8%, 2.5% and 2.8%, respectively.

Creatinine was analysed on an Advia 1650 instrument (Bayer Corp., Tarrytown, NY, USA). The imprecision of the method was 3% at 89 and 167 µmol l⁻¹. The assays were performed in the Department of Clinical Chemistry, Uppsala University Hospital, Uppsala.

Cystatin C measurements were performed with latex enhanced reagent (N Latex Cystatin C; Dade Behring, Deerfield, IL, USA) using a Behring BN ProSpec analyser (Dade Behring). The imprecision of the method was 4.8% at 0.56 mg l⁻¹ and 3.7% at 2.85 mg l⁻¹. The assays were performed in the Department of Clinical Chemistry, Uppsala University Hospital, Uppsala. Glomerular filtration rate (GFR) in ml min⁻¹ was calculated (in mg ml⁻¹) from the CysC results using the equation GFR = 77.24·CysC^−1.2623[19].

All assays were performed independently without prior knowledge of other patient data.

Data analysis

The pharmacokinetic modelling was performed using mixed effects modelling within the NONMEM program version VIβ[20] using first-order conditional estimation with log-transformed data. The search for appropriate models was guided by the objective function value (OFV), a measurement of goodness of fit estimated by NONMEM, as well as by graphical inspection within the Xpose program version 3.11 [21]. For hierarchical models an OFV drop of 3.83, 6.63 and 10.83 units designates an improved fit at P < 0.05, P < 0.01 and P < 0.001, respectively, for a one-parameter difference [22]. The structural and stochastic models were developed first. One-, two- and three-compartment models, using ADVANS 1, 3 and 11 and TRANS 2 and 4, were considered. Inter-individual variability (IIV) was assessed on all pharmacokinetic parameters and in addition correlations between those terms were evaluated. To characterize accurately the residual variability in the model, combined additive and proportional error models were tested. Thereafter, the significant covariates were included as described below. Finally, interoccasion variability (IOV) was assessed as described by Karlsson and Sheiner [23] and tested on the parameters for which an IIV term was significant. Each evaluated parameter was retained in the model if the inclusion resulted in a drop of at least 10.83 in OFV.

Covariates available in the analysis are specified in Table 1. In addition to the use of the renal function biomarkers in the covariate analysis, different relationships of these markers were evaluated. Since the relationship between CysC and renal function has been described by the equation GFR = 77.237 · CysC^−1.2623, this relationship was included in the analysis [19]. The following covariates for renal function were hence tested on CL: Scr, 1/Scr, CLcr, CysC, 1/CysC and 77.237 · CysC^−1.2623. The rationale for testing the inverse of Scr and CysC is that these markers are inversely correlated with kidney function. Covariate effects were centred around the median population value and added one at a time to the model. Relationships tested initially were linear and if such an inclusion resulted in a significantly improved model fit nonlinear relationships, in terms of piecewise linear splines, were also evaluated for the covariate in question. The biomarkers of renal function and functions of these were expected to be strongly correlated and therefore only the covariate giving the highest drop in OFV was used and the remaining covariates for renal function were not re-evaluated. Furthermore, since Scr and CysC were measured on two different occasions during the study period, they were considered in the model in different ways. The first alternative was to use the first measurement during the entire study period. The second alternative was to use the first measurement until the next measurement was obtained and thereafter use the second covariate value. The third alternative was to use a linear function between the two measurements and thereafter use the second measurement of the renal biomarker. In three of the patients no body weight measurement was available and the median value for the population was used instead. In 11 of the patients the second measurement of CysC and Scr was missing and thus only the first value was used.

The covariates age, body weight and sex were independently assessed with respect to all the pharmacokinetic parameters in the model, and ranked according to the drop in OFV associated with their inclusion. Variables were then stepwise tested in the model, in descending order. When the inclusion of no more covariates caused a drop in OFV of more than 10.83, a backwards deletion was carried out, retaining only covariates associated with an increase in the OFV of more than 10.83 on their exclusion.

Results

A total of 427 serum samples for the determination of cefuroxime were available for the pharmacokinetic analysis. The drug was detectable in none of the samples collected prior to the start of treatment. A few protocol deviations were detected during the data analysis. Some samples had to be excluded due to uncertainty regarding the time that had elapsed after dose administration (n = 14), and a few data points where considered erroneous due to unrealistically high concentrations of cefuroxime in the samples (n = 4). In total 18 out of 427 samples were excluded from the analysis and the final dataset consisted of 409 cefuroxime concentrations from 97 individuals. The majority of the samples were collected within the first 24 h after the start of therapy (n = 321, Figure 1A–D).

Figure 1.

(A–D) Observed (○) and model predicted (line) cefuroxime concentration–time profiles during the first 24 h of treatment for groups with different renal function

A linear two-compartment model (ADVAN3 TRANS4) described the data well (Figures 2A, B and 3). Before the candidate covariates were considered in the model, the most favourable interindividual variability structure was obtained when IIV was allowed on clearance (CL), the central volume of distribution (V₁) and the peripheral volume of distribution (V₂). Allowing IIV on intercompartment clearance did not offer any further improvement. Different variance/covariance structures of IIV were assessed, but the model did not benefit from any block. The residual error was adequately described by only a proportional component.

Figure 2.

(A, B) Observed cefuroxime concentrations vs. model predicted concentrations. Left panel: population model prediction; right panel: individual population model prediction

Figure 3.

Weighted residuals vs. time

Inclusion of the factor 1/CysC generated a drop in OFV of 154.0 units compared with the model without covariates. When CLcr or 1/Scr were integrated in the model, a decrease of 131.4 units and 75.4 units, respectively, was obtained (Table 3). The IIV decreased from 70.2% to 29.7, 33.8 and 46.8%, respectively, when 1/CysC, CLcr or 1/Scr were included. Moreover, it was found that using the first measurement alone of any of the renal function markers was sufficient and that no further information about the clearance of cefuroxime was obtained when taking the second value into consideration. The model fit was further improved when CL and V₁ were allowed to covary with body weight. Finally, it was found to be beneficial to allow IOV on CL. The parameter estimates in the final model are listed in Table 4 and the observed vs. model predicted concentration is presented in Figure 2A, B. Weighted residuals vs. time are displayed in Figure 3.

Table 3.

Inclusion of covariates on CL

CL covariate	ΔOFV*
Creatinine	−22.9
Creatinine clearance	−131.4
1/Creatinine	−75.9
Cystatin C	−92.4
1/Cystatin C	−154.0
77.237 · Cystatin C−1.2623	−153.3

^*Difference in objective function value compared with structural model without covariate.

Table 4.

Parameter estimates in the final model^*

Parameter	Estimate	Inter individual variability (%)	Inter occasion variability (%)	1/cystatin C (% mg−1 l−1)	Body weight (% kg−1)
CL (l h−1)	6.00 (3.2)	27 (20)	16 (52)	143 (3.7)	1.08 (27)
V1 (l)	11.4 (5.3)	18 (60)	– –	– –	0.97 (23)
V2 (l)	5.11 (11)	48 (36)	– –	– –	– –
Q (l h−1)	3.65 (21)	– –	– –	– –	– –
Proportional error (%)	15.5 (15)	– –	– –	– –	– –

Standard errors of the estimates are in parentheses.

^*In the final population model CL and V₁ are implemented as CL (l h⁻¹) = 6.00 · (1 + 1.43 · [1/CysC (mg l⁻¹) − 0.758]) · (1 + 0.0108 · [WT (kg) − 74]) and V₁ (l) =11.4 · (1 + 0.0097 · [WT (kg) − 74]) l.

Discussion

Although cefuroxime is a drug with minimal dose-limiting toxicity, being an antibiotic, there are reasons to avoid unnecessarily high doses, namely, to minimize ecological disturbances and the risk of bacterial resistance development, and to reduce the cost of treatment. For drugs with a narrow therapeutic index, therapeutic drug monitoring may be necessary during the entire treatment period. However, for nontoxic drugs such as cefuroxime, it may be sufficient to select the dosing only at the start of treatment, based on patient characteristics that covary with its pharmacokinetics.

‘Gold standards’ for the estimation of renal function are measurements of clearance of exogenous substances such as inulin, iohexol, ⁵¹Cr-EDTA, ^99mTC-labelled diethylenetriamine pentaaceticacid (DTPA) or ¹²⁵I-labelled iothalamate. However, these measurements are both expensive and time-consuming and are often not applicable in routine clinical practice. However, CysC is simple and inexpensive to measure and is superior to Scr in prediction of renal function [7]. Thus, in the present study the relationship between CysC and the pharmacokinetics of cefuroxime was investigated.

Previous studies have indicated that renal function correlates more strongly with CysC than with Scr or CLcr [14]. There are recent reports on the ability of CysC, in relation to Scr and CLcr, to predict drug elimination [15, 16]. The plasma concentration of digoxin, which is mainly excreted unchanged in the urine, was found to be correlated more strongly with CysC than with Scr [15]. In addition, the CL of topotecan, an anticancer agent, approximately 50% of which is eliminated through the kidneys, is better predicted by CysC than by either Scr or CLcr [16]. In the present analysis, inclusion of the reciprocal of CysC as a covariate on the CL of cefuroxime resulted in a substantial decrease in the objective function value. By including this factor in the population model, a better fit was obtained compared with when Scr was incorporated. Concentrations of Scr have been shown to be dependent on the method used for measuring them [24]. Thus, the present method of quantification of Scr may influence the results with regard to the usefulness of Scr as a predictor of the pharmacokinetics of cefuroxime. Nevertheless, based on the present data, individualization of dose based on CysC rather than Scr may be recommended. Furthermore, although the difference in model fit after inclusion of either CysC or CLcr was not large, incorporation of the former did result in a better fit. This, and the finding that 1/CysC is a simple measurement to use on the ward, favours dose individualization of cefuroxime using CysC rather than Scr or CLcr, although further patient studies are needed to confirm this suggestion.

The values of CL and total volume of distribution obtained in the present study (6 l h⁻¹ and 16 l, respectively) are in accordance with those previously reported (0.8–9 l h⁻¹ and 12–30 l, respectively) [3, 7, 25, 26]. The final population model in the present analysis is superior to the pharmacokinetic models derived previously in the sense that significant covariates have been incorporated. The data on which the model was developed are derived from a markedly larger population, n = 97, compared with the 5–26 individuals included in previous studies [3, 7, 25, 26]. The present population also consisted of patients with a wide range of renal capacity. Moreover, the final population model contains information about covariates that are important for the prediction of not only the elimination but also the distribution of cefuroxime, an element that is particularly valuable in a model that describes the pharmacokinetics of a drug that shows time-dependent killing. Thus, the final pharmacokinetic model in the present study may be a useful tool in the development of improved dosing strategies for cefuroxime.

In summary, cystatin C was found to be markedly better than serum creatinine and at least as good as creatinine clearance for the prediction of cefuroxime clearance. Thus, dosing of cefuroxime should perhaps be based on cystatin C rather than on the other two indices of renal function. Furthermore, as the present data were obtained from a large population of patients with a wide range of renal functions, the final model might be a useful tool in the development of improved dosing strategies for cefuroxime.