Nephrol Dial Transplant (2003) 18: 1201-1208
© 2003 European Renal Association-European Dialysis and Transplant Association
A compartmental pharmacokinetic model of cyclosporin and its predictive performance after Bayesian estimation in kidney and simultaneous pancreas–kidney transplant recipients
1 Department of Clinical Pharmacy and Toxicology, 2 Department of Nephrology, 3 Centre for Human Drug Research and 4 Department of Clinical Chemistry, Leiden University Medical Center, Leiden, The Netherlands
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Abstract |
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Background. Therapeutic drug monitoring of cyclosporin A (CsA) is an obvious necessity because of its unpredictable absorption and narrow therapeutic window. The use of limited sampling models (LSMs) has improved the estimation of the systemic exposure [area under curve (AUC)] compared with C0h monitoring, but these equations are rigid and not reliable in patients with an abnormal absorption profile. We developed and validated a limited sampling (t=0, 2 and 3 h) strategy, based on a compartmental population pharmacokinetic (PK) model for CsA after kidney transplantation alone (KTA) and simultaneous pancreas–kidney transplant (SPKT) recipients, a group of patients with unpredictable absorption kinetics.
Methods. A two-compartment model with lag time and first-order absorption was calculated using a PK software package from data of 20 KTA and SPKT recipients and validated prospectively in 20 KTA and 20 SPKT recipients. Calculated population PK parameters were individualized for each of the remaining 40 patients based on their CsA dosing and on one or a combination of measured CsA blood concentrations using the Bayesian fitting method. AUCs were calculated from individualized PK parameters. AUCs were also calculated using previously published LSMs. Relationships between AUCs calculated by the models and the ‘golden standard’ AUC (trapezoidal rule) were investigated by Pearson correlation test.
Results and conclusions. A population two-compartment model is presented to reliably estimate the CsA AUC in KTA and SPKT recipients. The performance of the model to estimate the AUC is comparable to the performance of two published LSMs in KTA patients, but markedly better in SPKT patients. Combined with Bayesian fitting, the model is very flexible since sampling times are not rigid and can be varied as long as dosing and sampling times are recorded accurately. The model has already proven to be clinically useful and is currently used to further investigate CsA in an integrated pharmacokinetic/pharmacodynamic model.
Keywords: Bayesian; cyclosporin; kidney transplant; pharmacokinetics; simultaneous pancreas–kidney transplant
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Introduction |
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Since the introduction of cyclosporin A (CsA), it was apparent that defining the appropriate dose was problematic because of its poor and unpredictable absorption and narrow therapeutic window. Therapeutic drug monitoring (TDM) is therefore an obvious necessity and, by convention, dosing adjustments became targeted to trough levels (C0h), i.e. the CsA blood concentration immediately before the next scheduled dose. Although the correlation between C0h level and its efficacy to prevent acute rejection or chronic nephrotoxicity is poor, this parameter is still widely used to guide CsA dosing after transplantation [1,2]. Despite maintaining CsA trough levels within the therapeutic range, substantial groups of patients experience either acute rejection episodes or nephrotoxicity [3,4]. The CsA area under the drug concentration vs time curve (AUC) seems a better measure of systemic drug exposure and efficacy to prevent acute rejection episodes [5], but AUC monitoring has not gained popularity, largely because of the inconvenience of multiple blood samplings over a 12 h period and cost considerations.
Because AUC reflects systemic drug exposure, several groups have used sparse-sampling algorithms [limited sampling models (LSMs)] as a way of predicting AUCs without the need for large numbers of blood-level measurements [6,7]. Exposure during the first 4 h (AUC0–4h), the area of greatest inter- and intrapatient variability, is a reliable estimate of total drug exposure throughout the dosing interval (AUC0–12h) [8]. Recently, dosing based on a single drug level measurement, i.e. C2h, within this absorption phase has been associated with improved results after de novo heart, liver and kidney transplantation [9]. It should be stressed, however, that estimation of the true AUC will always be more reliable when more samples are taken. This may be particularly true, or even mandatory, in patients with an unpredictable absorption profile, such as diabetic recipients [10].
Compared with LSMs, a compartmental population pharmacokinetic model for CsA in renal transplant recipients combined with the maximum a posteriori Bayesian fitting method offers in clinical practice the important advantage of flexibility [11,12]. The exact sampling time is no longer an issue as long as the exact times of drug administration and blood drawing are recorded. In the present study we describe the development and prospective validation of such a model in non-diabetic patients who received a kidney transplant alone (KTA) and simultaneous pancreas–kidney transplant (SPKT) recipients.
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Subjects and methods |
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Patients
Sixty (32 KTA and 28 SPKT) transplant recipients (38 male, 22 female) treated with CsA-based immunosuppression were studied. Thirty patients were early (<3 months) post-transplantation, while the other 30 had been transplanted at least 3 months before the present study. All patients received the microemulsion formulation of CsA (Neoral; Novartis Pharmaceuticals, Basel, Switzerland) with prior dosing based on trough levels. Patients who used drugs known to interact with CsA pharmacokinetics were excluded. Patient characteristics are listed in Table 1
. Prior to and after the morning dose of CsA, blood was taken at t=0, 1, 2, 3, 4, 6, 8 and 12 h. Blood was drawn using an indwelling catheter and was collected in a vacutainer containing EDTA. Blood was stored at 4°C until analysis, usually the same day.
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Pharmacokinetics
Using the Kinpop module of the pharmacokinetic software package MW/Pharm version 3.33 (Mediware, Groningen, the Netherlands), a population two-compartment model with a lag time and first-order absorption pharmacokinetics was calculated from the CsA dosing and the blood concentration values of the first 20 patients (12 KTA and 8 SPKT recipients). This program uses an iterative two-stage Bayesian procedure and calculates means, medians and SDs of the pharmacokinetic parameters [11]. During the iterative two-stage Bayesian procedure, pharmacokinetic parameters were set to be distributed log-normally and bioavailability was fixed at 0.5.
The calculated mean population pharmacokinetic parameters were individualized for each of the remaining 40 patients (20 non-diabetic KTA and 20 SPKT recipients) based on their CsA dosing and one or a combination of measured blood concentrations (0 h; 1 h; 2 h; 3 h; 4 h; 0+1 h; 0+2 h; 0+3 h; 0+4 h; 2+4 h; 0+1+2 h; 0+1+3 h; 0+2+3 h; 1+2+3 h; 0+1+2+3 h; 0+1+2+4 h; 0+1+2+3+4+6+8+12 h) according to the maximum a posteriori (MAP) Bayesian fitting method [12], using the MW/Pharm computer program. By means of MAP Bayesian fitting any available information, i.e. ‘a priori’ population parameters, drug dosage regimen and measured blood concentrations can be used to estimate the ‘a posteriori’ pharmacokinetic parameters of the individual patients. These ‘a posteriori’ pharmacokinetic parameters of the individual patient are the maximum likelihood estimates obtained by MAP Bayesian fitting, minimizing the deviations of measured and predicted concentrations and of population pharmacokinetic parameters and pharmacokinetic parameters of the individual patient [12]. This approach is very flexible and it ensures an optimal use of available information, both from a population and from the individual patient. From the individualized pharmacokinetic parameters the area under the CsA blood concentration time curve (AUC0–12h) was calculated for each combination of measured blood concentrations.
The AUC0–12h of the 40 patients was also calculated using the two-point limited sampling strategy as described by Wacke et al. [7]:
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Drug analysis
Whole blood concentrations of CsA in the first 20 patients were determined by radioimmunoassay (RIA) (Cyclotrac; IncStar, Stillwater, MN). Because of a change of equipment, whole blood concentrations of CsA in the remaining 40 patients were determined by fluorescence polarization immunoassay (FPIA) (Axsym; Abbott Diagnostics, Abbott Park, IL).
Statistical analysis
Statistical analysis was performed three times. First, the KTA recipient group was investigated. Secondly, the SPKT recipient group was investigated. Finally, these two groups were analysed together.
The AUCs calculated by the different methods were compared with the golden standard AUC by linear regression analysis and Pearson correlation coefficient. Calculations were carried out by means of the SPSS software (version 9.0). Predictive performance of the different methods was also investigated by calculating the prediction precision and bias according to Sheiner and Beal [14]. Prediction bias was calculated as the mean prediction error (MPE), i.e. the mean of differences between the AUC according to the different methods and the golden standard AUC. Prediction precision was calculated as the mean absolute prediction error (MAPE), i.e. the mean of the absolute differences between the AUC according to the several different methods and the golden standard AUC. Smaller values for MPE and MAPE indicate less bias and greater precision.
The actual description of blood concentration in time by the model was investigated prospectively by calculating residuals between measured and predicted CsA blood concentrations in the 40 patients. The concentrations were predicted for each patient using either the whole data set or only limited sampling at t=0, 2 and 3 h after drug administration.
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Results |
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CsA pharmacokinetics was adequately described by a two-compartment model with a lag time. Pharmacokinetic parameters as calculated by Kinpop are listed in Table 2
. A representative example of Bayesian fitting based on measured CsA concentrations at t=0, 2 and 3 h is shown in Figure 1.
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In Figures 2
–4 the predictive performance in both KTA and SPKT recipients is shown for several methods of CsA TDM. In Figure 2A the relationship is plotted between trough levels and the AUC0–12h calculated using the trapezium method. Figures 2B and C, which show the relationships between systemic exposure and the AUC0–12h calculated according to the compartment model with blood concentration time points taken at 0 and 2 h (B) and 0, 2 and 3 h (C), illustrate that using the compartmental model the AUC0–12h is estimated well in both patient groups and that the predictive performance improves when more concentration time-points are used. Figures 3A and B show the relationship between the AUC0–12h calculated with the trapezium rule and the AUC according to the two published LSMs [6,7]. The variation of the actual AUC is less when estimating the AUC using any of the models, when compared with the estimation of the systemic exposure from the trough levels. Predictive performance differs between the models, which is predominantly caused by values obtained in SPKT recipients. In Figures 4A and B the relationships are shown between C2h and AUC0–4h and between C2h and AUC 0–12h, respectively. In Figure 4C the relationship between AUC0–4h and AUC0–12h calculated by the trapezoidal rule is shown. These figures illustrate that absorption profiling has a good predictive performance in KTA recipients, but it is significantly worse in SPKT recipients.
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Bias and precision of the different models are listed in Tables 3
and 4. In general, when using the compartmental model, bias as well as precision improve when the Bayesian estimations are made based on more blood concentration data with a bias of -2.2% and precision of 2.6% when based on all data, indicating that the model tends to slightly underestimate the AUC as determined by the trapezoidal rule. Bias and precision of the LSMs are comparable to bias and precision of the compartmental model, if the latter is used with limited sampling at two or more blood concentration data.
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In KTA recipients (Table 3
), bias and precision of the LSMs are comparable to bias and precision of the compartmental model if the latter is used with limited sampling at two or more blood concentration data. The best relationships were found with the blood concentration data 0+2 h, 0+1+3 h and 0+1+2+3 h when only data within 3 h after drug administration are taken into consideration.
In SPKT recipients (Table 4), it appears that the first LSM (1, 3) is less useful to estimate the AUC0–12h. Bias, precision and correlation of the compartmental model are also worse in several combinations of blood concentration data compared with KTA recipients. The best relationships are found with the blood concentration data 0+3 h, 0+2+3 h and 0+1+2+3 h when only data within 3 h after drug administration are taken into consideration. Bias and precision of these combinations are good and comparable to the good performance of the second LSM (2, 6).
When the performance of the models is validated on both KTA and SPKT recipients together (data not shown), the combinations of blood concentration data that best describe the systemic exposure are 0+2 h, 0+2+3 h and 0+1+2+3 h. The performance of LSM (2, 6) is very good; the performance of LSM (1, 3) seems less useful.
Figure 5 displays the residuals of the model as a function of time after the MAP Bayesian fitting procedure based on all concentrations and on limited sampling at t=0, 2 and 3 h in the 20 KTA and 20 SPKT recipients. In both groups the concentrations are scattered around the x-axis, indicating a good description of the blood concentrations by the model. The largest deviations from the measured concentrations are around t=1 h. The peak concentration measured is usually reached at 1 or 2 h. Limited sampling at t=0, 2 and 3 h causes somewhat more deviation from the measured concentrations. However, the residuals remain more or less distributed around 0 µg/l, especially at t=1 and 2 h. The residuals at the other time points do not appear to change during limited sampling at 0, 2 and 3 h. The residuals in the SPKT recipients are also scattered around the x-axis. However, the pattern is somewhat different, indicating different pharmacokinetics in this group.
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Discussion |
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At present, calcineurin inhibitors still constitute the cornerstone of immunosuppressive regimens for the prevention of allograft rejection in renal transplant recipients. Recent data have indicated that the long-term outcome of both cadaveric and live donor renal allografts has improved in the past decade, especially if acute rejection episodes could be prevented [15]. In healthy volunteers and stable renal transplant recipients, the CsA microemulsion formulation under the name Neoral has increased dose linearity with AUC and has resulted in a better correlation between C0h and AUC0–12h than cyclosporin gelcaps or Sandimmune [16]. However, in de novo transplant recipients, the interpatient variability of pharmacokinetic parameters is not different between these formulations during the first post-operative weeks and in clinical practice C0h has an equally poor correlation with AUC0–12h [17]. Conversely, AUC estimates correlate with early clinical events [18], but there is little information about the usefulness of AUC monitoring to improve long-term outcome [19].
Estimating the systemic exposure to CsA with LSMs, but also with C2h, is rigid. It is not allowed to deviate too much from the predefined time points. Moreover, once a time point is missed, a LSM formula becomes useless, since then one of the determinants in the formula is lacking. Deviations from predefined time points and missing of samples occur frequently in daily clinical practice. In contrast to the LSMs, these everyday problems are dealt with easily by a Bayesian fitting procedure. For example, the pharmacokinetic model can be used to calculate systemic exposure to CsA in a data set that consists of 0, 1.5 and 3.4 h time points instead of 0, 2 and 3 h or a data set that consists of only 2 and 3 h time points, illustrating the flexibility of the model and the clinical applicability.
The performance of the current population model to estimate the AUC0–12h was investigated using several sampling strategies. As expected, the estimation of the AUC0–12h always improves when the number of sampling points is increased, as more information is introduced. However, using the time points t=0, 2 and 3 h post-dose with the population model and MAP Bayesian fitting, the AUC was estimated with a mean accuracy of -2.3% and a mean precision of 8.3%. This is well within accepted and clinical relevant limits.
Using individualized population pharmacokinetic models, CsA exposure in renal transplant patients can be estimated well. However, intrapatient pharmacokinetics is known to change in the early period (6–8 weeks) after transplantation. The model was developed and validated in a population with varying time after transplantation. Consequently, the model is able to deal with the changes in pharmacokinetics after transplantation, mainly because this change has been incorporated into the range of the pharmacokinetic parameters. However, using the population pharmacokinetic model as described, the systemic exposure can be estimated, but actual prediction of the systemic exposure during a period of great changes in pharmacokinetics is not possible. In order to ensure an adequate systemic exposure, several approaches can be made. Either the estimation of the AUC of CsA is performed frequently in the early period after transplantation or a pharmacokinetic model is used in which factors specifically influencing this change in pharmacokinetics are incorporated. One of those factors is probably time after transplantation. However, clinically applicable pharmacokinetic models, in which time after transplantation has been incorporated, enabling the actual prediction of systemic exposure in a period of changing pharmacokinetics of CsA, are scarce. For our own approach, in which we thus estimate the AUC0–12h of CsA at a certain moment, we are currently investigating still the optimal frequency of drug monitoring, both short- and long-term after transplantation. In our prospective study we use every other week estimations of the AUC0–12h during the first 12 weeks after transplantation, which is followed by an estimation of the AUC0–12h every 3–6 months.
The study population consisted of both patients that received kidney transplant as well as SPKT recipients. Patients with insulin-dependent diabetes mellitus often suffer from (severe) gastrointestinal dysfunction and in these patients CsA pharmacokinetics is often variable and unpredictable [10]. Inclusion of these patients may have skewed the pharmacokinetic parameters of the population model, leading to deviation of predicted from measured CsA concentrations in the KTA patients. The advantage, however, is that the model is suitable to describe CsA pharmacokinetics in the population of interest, i.e. recipients with an abnormal absorption profile. The differences in CsA pharmacokinetics between KTA and SPKT recipients were adequately detected by the compartment model and by one of the previously described LSMs [6]. The performance of the other LSM was significantly worse [7], indicating that caution should be taken when monitoring CsA in various patient groups with defined sampling time-points. This is illustrated especially by the lack of correlation between C2h and AUC0–4h or AUC0–12h in SPKT recipients as compared with the patients without diabetes mellitus, who received a kidney transplant. In Figure 6, two clinical examples are given illustrating the above-mentioned issues and how the model deals with them.
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Although the drug is metabolized to at least 25 metabolites, blood concentrations of CsA after oral administration, as determined by the immunoassays, are adequately described by a two-compartment model with a lag time and first-order absorption pharmacokinetics. The model was superior to a one-compartment model, while an extra compartment did not add significantly to the description of the data. Fitting procedures by the calculation algorithm were improved by fixing the oral availability at 0.5. Absorption pharmacokinetics therefore is characterized mainly by the lag time and the absorption rate-constant. This may also explain why deviation of the CsA concentrations predicted by the model was largest at 1 h post-dose. A recent study by Debord et al. [20] has applied a gamma distribution model of absorption to the pharmacokinetics of cyclosporin in stable renal transplant recipients and indeed yielded a better fit during the absorption phase compared with a classical exponential model with lag-time. An underestimation of the Cmax using the latter model, however, was not observed in the current population with scattering of the residuals around zero at both 1 and 2 h after ingestion of the oral dose. Compared with the FPIA, the RIA method slightly overestimated the data in our laboratory. Recently, Keown et al. [9] pointed out that differences between assays may have consequences for trough-level-based monitoring, while these assays performed quite comparable during the absorption phase of CsA in renal transplant recipients. The presented pharmacokinetic model, however, is flexible enough to deal with the apparent differences. The model therefore performs adequately despite the immunoassay used.
Calcineurin-inhibitor trough levels are a poor indicator of drug exposure and drug exposure should be quantitated by means of more accurate methods. To prevent structural underimmunosuppression or graft dysfunction due to chronic calcineurin-inhibitor toxicity, a compartmental population pharmacokinetic model with maximum a posteriori Bayesian fitting method offers several advantages. The presented model is reliable and more flexible than LSMs and does not depend on exact blood sampling time-points. In addition, it can be used in transplant recipients with gastrointestinal dysfunction and even offers the possibility to integrate pharmacodynamic parameters [21]. These practical and theoretical advantages argue in favour of this approach for future therapeutic drug monitoring.
Conflict of interest statement. None declared.
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Notes |
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Correspondence and offprint requests to: S. C. L. M. Cremers, Department of Clinical Pharmacy and Toxicology, Leiden University Medical Center, PO Box 9600, NL-2300 RC Leiden, The Netherlands. Email: S.C.L.M.Cremers{at}lumc.nl
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References |
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Accepted in revised form: 20.12.02
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