Abstract
Purpose: The Calvert formula is a widely applied algorithm for the a priori dosing of carboplatin based on patients glomerular filtration rate (GFR) as accurately measured using the ^{51}CrEDTA clearance. Substitution of the GFR in this formula by an estimate of creatinine clearance or GFR as calculated by formulae using serum creatinine (S_{CR}; CockcroftGault, Jelliffe, and Wright) is, however, routine clinical practice in many hospitals. The goal of this study was to validate this practice retrospectively in a large heterogeneous adult patient population.
Experimental Design: Concentrationtime data of ultrafilterable platinum of 178 patients (280 courses, 3,119 samples) with different types of cancer receiving carboplatinbased chemotherapy in conventional and high doses were available. Data were described with a linear twocompartment population pharmacokinetic model. Relations between S_{CR}based formulae for estimating renal function and carboplatin clearance were investigated.
Results: None of the tested S_{CR}based estimates of renal function were relevantly related to the pharmacokinetic variables of carboplatin. Neither S_{CR} (median, 51; range, 18124 μmol/L) nor the estimated GFR using the three different formulae was related to carboplatin clearance.
Conclusions: Our data do not support the application of modifications of the Calvert formula by estimating GFR from S_{CR} in the a priori dosing of carboplatin in patients with relatively normal renal function (creatinine clearance, >50 mL/min). For targeted carboplatin exposures, the original Calvert formula, measuring GFR using the ^{51}CrEDTA clearance, remains the method of choice. Alternatively, in patients with normal renal function, a flat dose based on the mean population carboplatin clearance should be administered.
 carboplatin
 Calvert formula
 glomerular filtration
 serum creatinine
The platinum compound carboplatin is used in the treatment of several malignancies, often in combination chemotherapy regimens (1). Carboplatin is mainly eliminated by the kidneys. In patients with normal renal function, between 60% and 70% of an administered carboplatin dose is excreted into the urine within the first 24 hours of administration. The remainder of the drug binds irreversibly to proteins and tissue (1, 2). The free, ultrafilterable carboplatin fraction is considered pharmacologically active (3).
The use of carboplatin is mainly limited by myelosuppression. Carboplatin exposure, expressed as area under the plasma concentration versus time curve (AUC), has been related both to severity of thrombocytopenia and leukopenia as well as to therapeutic outcome (reviewed in refs. 4, 5). In highdose chemotherapy regimens with stem cell support, toxicities, such as nephrotoxicity, ototoxicity, central nervous system toxicity, and peripheral nervous system toxicity, have been associated with a higher carboplatin exposure (3, 6–11). By controlling carboplatin exposure in both conventional as well as highdose regimens, the incidence of side effects might be reduced.
Carboplatin clearance seems to be poorly correlated to body surface area (BSA), but it is linearly related to the glomerular filtration rate (GFR; refs. 12–15). Therefore, various dosing equations have been proposed to calculate a priori an appropriate dose for a target exposure of carboplatin in a patient with a known GFR (12, 16). The most simple and widely used formula to calculate the carboplatin dose was proposed by Calvert et al. (12), relating the ultrafilterable AUC to the GFR by Dose = AUC × (GFR + 25), with dose in mg, target AUC in mg/mL min (usually 57), and GFR in mL/min. The 25 mL/min is a constant included to account for nonrenal clearance (drug binding irreversibly to tissue or proteins). This formula has been developed using the clearance of ^{51}CrEDTA as an accurate measure of the GFR (4). This method is, however, expensive, invasive, involves radioactive compounds, requires multiple blood sampling at exact time points, and is not available in most treatment centers. Therefore, in many instances, the GFR is substituted by the estimated creatinine clearance (Cl_{CR}) as calculated with the CockcroftGault formula (17) or the Jelliffe formula (18). These formulae are based on measured serum creatinine (S_{CR}) in μmol/L, age in years, gender (1 if female, 0 if male), and BSA in m^{2} or weight in kg.
CockcroftGault (17):
Jelliffe (18):
Recently, Wright et al. (19) developed a method for estimating GFR based on the same variables.
Wright (19):
To evaluate the dosing accuracy of the Calvert formula using the above described substitutions of the GFR and to define patient characteristics influencing carboplatin pharmacokinetics, we did a large population pharmacokinetic study. We pooled pharmacokinetic data of carboplatin obtained from several studies, including both conventional as well as highdose chemotherapy regimens. The intention was to use as much data available of many different populations with various types of cancer treated with different schedules of carboplatin. The performance of a formula calculating carboplatin clearance based on S_{CR}, weight, age, and sex, as developed by Chatelut et al. (13), was also evaluated with our data set:
Materials and Methods
Patients. Pharmacokinetic data of ultrafilterable platinum were used as obtained in several previously published studies in which patients received carboplatin both in highdose as well as in conventionaldose regimens in combination with other chemotherapeutic agents (6, 20–23). Data were available of 178 patients (280 courses) of carboplatin (in total 3,119 samples). Of all patients in the data set, baseline patient characteristics and biochemical variables were available as summarized in Table 1 . All protocols were approved by the Committee of Medical Ethics of the Netherlands Cancer Institute, and written informed consent was obtained from all patients.
Pretreatment S_{CR} levels were estimated by the kinetic Jaffé method (Hitachi systems, Roche Diagnostics, Almere, the Netherlands) in three studies (21–23) and in the first 32 patients of one study (6), whereas in the resulting patients (6, 20) the compensated Jaffé method was used. Although the Jaffé method is nonspecific, the S_{CR} measurements in the compensated Jaffé method are corrected for measured pseudocreatinine chromogens by subtracting exactly 26 μmol/L from each S_{CR} concentration. Because every individual sample contains different amounts of pseudocreatinine chromogens, this is a nonspecific correction. However, it has been shown that results obtained with the compensated Jaffé method were comparable with those obtained with reference methods using highperformance liquid chromatography (24). Therefore, the noncompensated S_{CR} values in our data set were retrospectively adjusted by subtracting 26 μmol/L from the initial values.
Sampling and analyses. In all studies, the ultrafilterable plasma fraction was prepared immediately after blood sampling using the Amicon micropartition system with a YMT14 membrane (30 kDa; Millipore Corp., Bedford, MA). A volume of 0.5 mL plasma was transferred in the micropartition system and centrifuged at 2,500 × g for 20 minutes. Ultrafiltrate was stored at −20°C until analyses. Analyses of platinum in ultrafiltrate were done using flameless atomic absorption spectrometry as described previously (25). Accuracy and daytoday precision of this method were 93.9% to 103.3% and 1.5% to 10.2%, respectively. The number and time points of samples withdrawn in each study protocol are depicted in Table 1.
Population pharmacokinetics. A population pharmacokinetic model of carboplatin (measured as free platinum) was developed using the nonlinear mixed effect modeling program NONMEM (version V 1.1; GloboMax LLC, Hanover, MD; ref. 26). The firstorder conditional estimate method with INTERACTION was used after log transformation of the data (27).
Both interindividual variability (IIV) and interoccasion variability (IOV) were modeled with an exponential function. For example, variability in clearance Cl was estimated using the following: Cl_{ij} = Cl_{pop} × exp (η_{I} + κ_{j}), where Cl_{ij} represents Cl of the i^{th} individual on the j^{th} occasion, Cl_{pop} is the population value of Cl, η is the interindividual random effect with mean 0 and variance ω^{2}, and κ is the interoccasion random effect with mean 0 and variance π^{2} (28).
The difference between observed concentrations and their respective predictions resulting from measurement error and model misspecification (i.e., the residual or unexplained variability) was modeled with an exponential error model: ln(C_{obs ij}) = ln(C_{pred ij}) + ε_{ij}, where ε_{ij} is the residual error with mean 0 and variance σ^{2}, representing the difference between the natural logarithm of the j^{th} observed concentration in the i^{th} individual [ln(C_{obs ij})] and its respective prediction [ln(C_{pred ij})].
Four different models describing the possible relation between carboplatin clearance and S_{CR} were tested:
Cl_{pop} = theta(1)
Cl_{pop} = GFR + 25
Cl_{pop} = GFR + theta(1)
Cl_{pop} = theta(1) + (140 − age) × theta(2) × weight × theta(3)^{gender} / S_{CR}
(in which GFR was calculated using the Wright formula or replaced by Cl_{CR} using the CockcroftGault and the Jelliffe formula).
In model 1, no relation between S_{CR} and carboplatin clearance was assumed and this model was used as reference for the other models. Model 2 is the regularly applied Calvert formula in which the GFR is approximated by different S_{CR}based formulae. In model 3, the variable from the Calvert formula was reestimated on our data set. Model 4 was used to further analyze the possible relation between S_{CR}, determinants of S_{CR} (i.e., age, gender, and body size), and carboplatin pharmacokinetics in our data set. In this model, some of the variables of the CockcroftGault formula were reestimated. This model was used to test whether any relation between S_{CR} and carboplatin clearance existed in our data set after compensation for known determinants of creatinine production (age, body size, and gender).
Estimated values of Cl_{CR} >150 mL/min based on the different formulae used are physiologically unlikely. Therefore, we tested the unadjusted Cl_{CR} as covariate but also values >150 mL/min and >250 mL/min truncated to these values (29). We also tested for possible other determinants of carboplatin pharmacokinetics in our data set as pretreatment regimen (cisplatin or noncisplatincontaining regimen), study protocol, and the administration of multiple doses. A covariate was considered significantly associated with the pharmacokinetic variable of interest when the objective function value (OFV) decreased >7.8 (P < 0.005).
Results
Data were best described with a twocompartment model estimating firstorder elimination (Cl), volume of distribution (Vd), and the distribution rate constants k_{12} and k_{21}. IIV was estimated for Cl, Vd, k_{12}, and k_{21}, whereas IOV was estimated for Cl and k_{12}.
The observed carboplatin concentration was accurately predicted by the model (Fig. 1 ). Furthermore, the weighted residuals did not vary according to the predicted concentration or time (Figs. 2 and 3 ), indicating that the model accurately described the data. Covariance between Cl and Vd was estimated. Population pharmacokinetic variables obtained from the total carboplatin data set are summarized in Table 2 .
Of the four models tested, model 1 in which no relation between S_{CR} and carboplatin clearance was assumed showed a better fit than models 2 and 3 (the original Calvert formula in which GFR is estimated by S_{CR}based formulae and a model in which the variable of the Calvert formula was reestimated on our data set; Table 3 ). Model 4 (the Calvert formula with GFR estimated by the CockcroftGault formula and all variables reestimated on our data set) showed a significant improvement of fit (ΔOFV = −24.6; df, 2; P < 0.001). This model yielded the following equation:whereas the original Calvert formula (using CockcroftGault to calculate Cl_{CR}) was
This shows that, in the reestimated equation, the intercept is 4.6 times higher and the slope is six times smaller than in the Calvert formula (using CockcroftGault to calculate Cl_{CR}), indicating that the relation between carboplatin pharmacokinetics and S_{CR} and determinants of S_{CR} is much weaker than suggested by substituting the CockcroftGault estimate of Cl_{CR} in the original Calvert formula. This is also shown in Fig. 4AC .
No differences in pharmacokinetics could be shown between the different study protocols and treatment regimens. A total of 16 patients with refractory germ cell cancer (35 courses) had received cisplatin pretreatment of daily 20 mg/m^{2} cisplatin during 5 days for four courses (6). In addition, one patient with metastatic ovarian cancer (6) had been pretreated with cisplatin. Pretreatment with platinumbased therapy, however, had no significant effect on carboplatin clearance. In addition, no difference in carboplatin clearance was found after multiple courses of carboplatin. Evaluation of relations between pretreatment regimen, protocol and multiple courses, and pharmacokinetic variables using a univariate procedure did not result in a significant correlation.
Figure 4AC shows that the expected relation between carboplatin clearance and Cl_{CR} (as calculated using the CockcroftGault or the Jelliffe formula) or GFR (as calculated using the Wright formula) using truncation to 250 mL/min was not significant. Similar results were obtained when the upper limits were not truncated or truncated to 150 mL/min. In addition, no relation was found between carboplatin clearance and S_{CR} (Fig. 5 ) not even when only the patients with physiologic values of Cl_{CR} were included in the analyses. The performance of the Chatelut formula in predicting carboplatin clearance in our population was also poor as shown in Fig. 6 .
These results question the value of the variables S_{CR}, weight, BSA, gender, and age in predicting individual pharmacokinetics of carboplatin in our population. Carboplatin dosing formulae based on these patient characteristics are thus not predictable of carboplatin exposure in this population.
Discussion
In our study, no significant relation between carboplatin pharmacokinetics and patient characteristics could be detected with a population pharmacokinetic analysis in a large patient population. Because carboplatin dosing based on patients' S_{CR}, age, gender, weight, and height is widely applied in clinical oncology, the accuracy of this practice should be questioned.
The predominant determinant of carboplatin clearance is the GFR. It has been shown that, when GFR was estimated using radioisotopes, a strong relation with carboplatin clearance exists (12). However, these methods are expensive, inconvenient, and not universally available. Cl_{CR} is widely accepted as a simple measure of GFR, although it systematically overestimates GFR because creatinine is not solely filtered by the glomerulus but is also secreted by the proximal tubule. Cl_{CR} can be measured by collection of timed urine, which is also labor intensive and often prone to error. Therefore, simple formulae have been introduced to estimate Cl_{CR} based on S_{CR}, age, gender, weight, and length (17, 18). It has, however, also been shown that S_{CR}, as used in these formulae, is a poor indicator of glomerular function and, thus, carboplatin clearance. It is an insensitive measure of early glomerular impairment and is also dependent on nonrenal factors, especially creatinine production, which itself is dependent on muscle mass. Fluctuations in the endogenous creatinine production may therefore cause erroneous results in estimation of renal function. In addition, the methodologic difficulties inherent in the measurement of S_{CR} reduce the accuracy of the method (30). The enzymatic methods of S_{CR} have been shown to give more reliable results than the widely used Jaffé alkaline picrate colorimetric methods, which are complicated by the measurement of noncreatinine chromogens (19). The use of different assays for S_{CR} may therefore result in systematically different results between studies.
In contrast to our results, many authors have reported relations between S_{CR}, age, gender, weight, height, and carboplatin pharmacokinetics (11, 13, 31–33). In the studies in which a correlation was found between S_{CR} and carboplatin clearance (13, 31), also patients with (moderate) renal insufficiency were included while in our study, renal function was adequate in all patients (Cl_{CR}, >50 mL/min, as calculated using the CockcroftGault formula), which is the result of the inclusion criteria of the different protocols. This is probably an important explanation for our different results. Variability in carboplatin clearance in our population was small (IIV, 19.1% and IOV, 9.52%; Table 2), which may also be caused by the inclusion of patients with relatively normal renal function.
Without a clear correlation between S_{CR} and carboplatin clearance, substituting GFR in the Calvert formula with an estimation of Cl_{CR} or GFR based on S_{CR} measurements (using the CockcroftGault, the Jelliffe, or the Wright equations) is therefore also prone to errors. This may explain the lack of relation between Cl_{CR} or GFR and carboplatin clearance in our study. Moreover, it should be questioned whether these equations should be applied in our patient population because of the large number of patients with very low measured S_{CR} values (Fig. 5) and concomitant extremely high physiologic unlikely estimated Cl_{CR} or GFR values (Fig. 4AC) seen in our population. In the work of Kirkpatrick et al. (29), S_{CR} values <60 μmol/L were set at 60 μmol/L in patients receiving gentamicin because it was thought that low values of S_{CR} may reflect decreased production rather than enhanced clearance. In our population, S_{CR} values were <60 μmol/L in more than half the patients probably due to the disease condition of these patients. In these patients, estimated Cl_{CR} or GFR values were therefore above the physiologic meaningful upper limit of 150 mL/min. Applying the Calvert formula with these estimates of Cl_{CR} or GFR may result in inaccurate predictions of the carboplatin exposure.
These low S_{CR} values were not only the result of the subtraction of 26 μmol/L but were also directly observed. Moreover, these low S_{CR} values were seen in samples from all the different study protocols. Therefore, the observed low S_{CR} values are not due to the different protocols used to measure S_{CR}.
Substitution of the Cl_{CR} estimates of GFR from the CockcroftGault formula and the Jelliffe formula into the Calvert formula has become routine practice in many centers. Although the Calvert formula, with GFR calculated using the ^{51}CrEDTA clearance, is a superior method of dosing carboplatin than the traditional BSA method (34), the use of this formula with inaccurate substitutions of the GFR is not. The same is true for the application of the Chatelut formula. Studies evaluating the performance of the Chatelut formula (35, 36) or the Calvert formula using the CockcroftGault (13, 35–39), Jelliffe (35, 37), or Wright (37) equations in predicting carboplatin exposures indeed reported poor precisions (percentage root mean squared error, 1743%). The authors, however, did not establish the dosing precision if doses would have been based on BSA or if a flat dose would have been administered. The variation in carboplatin exposure in our population after administration of a flat dose would be ∼21% () calculated from the observed variation in carboplatin clearance within our patient population (IIV, 19.1% and IOV, 9.52%; Table 2). Therefore, in our population, the performance of the dosing formulae in approaching a fixed carboplatin exposure is not better than of a flat dose based on the mean carboplatin population clearance.
In summary, the current data do not support the general use of estimates of renal function by the CockcroftGault, Jelliffe, or Wright formulae, based on S_{CR} measurements, to select the dose of carboplatin using the Calvert formula for patients with relatively normal renal function. The original Calvert formula, using the clearance of ^{51}CrEDTA as an accurate measure of the GFR, remains the method of choice. When targeted carboplatin exposures are desired and radioisotope methods are not available, we propose to base the carboplatin dose in patients with a Cl_{CR} >50 mL/min (as calculated with the CockcroftGault formula, with S_{CR} measured using the compensated Jaffé method) on the mean carboplatin population clearance of this study (8.33 L/h = 138.8 mL/min) using the following general formula:
Thus, in case an AUC of 5 mg/mL min is desired, the appropriate dose for carboplatin would be 5 mg/mL min × 138.8 mL/min = 694.2 mg (=695 mg). In the future, alternative approaches for estimating renal function using promising markers of GFR, such as cystatin C, may prove suitable and applicable in routine clinical practice for estimating accurate a priori carboplatin doses (40).
Footnotes

Grant support: Dutch Cancer Society project NKI 20012420, 20053418.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Note: C. Ekhart and M.E. de Jonge contributed equally to this work.
 Accepted July 18, 2006.
 Received May 16, 2005.
 Revision received June 23, 2006.