Bayesian estimation of cyclosporin exposure for routine therapeutic drug monitoring in kidney transplant patients

doi:10.1111/j.1365-2125.2005.02200.x

Journal List > Br J Clin Pharmacol > v.59(1); Jan 2005

Br J Clin Pharmacol. 2005 January; 59(1): 18–27.

doi: 10.1111/j.1365-2125.2005.02200.x.

PMCID: PMC1884958

Bayesian estimation of cyclosporin exposure for routine therapeutic drug monitoring in kidney transplant patients

Hélène Bourgoin,¹ Gilles Paintaud,¹ Matthias Büchler,² Yvon Lebranchu,² Elisabeth Autret-Leca,¹ France Mentré,³ and Chantal Le Guellec¹

¹Departments of Pharmacology, University Hospital of Tours, 37044 Tours cedex 9

²Departments of Nephrology, University Hospital of Tours, 37044 Tours cedex 9

³INSERM E0357, Department of Epidemiology, Biostatistic and Clinical Research, Bichat University Hospital, 75877 Paris, France

Correspondence Professor Gilles Paintaud, Department of Pharmacology, C.H.R.U. de Tours, 2 boulevard Tonnellé, 37044 Tours cedex 9, France. Tel: + 33 2474 76008 Fax: + 33 2474 76011 E-mail: paintaud/at/med.univ-tours.fr

Received February 19, 2004; Accepted June 3, 2004.

Abstract

Aims

AUC-based monitoring of cyclosporin A (CsA) is useful to optimize dose adaptation in difficult cases. We developed a population pharmacokinetic model to describe dose-exposure relationships for CsA in renal transplant patients and applied it to the Bayesian estimation of AUCs using three blood concentrations.

Methods

A total of 84 renal graft recipients treated with CsA microemulsion were included in this study. Population pharmacokinetic analysis was conducted using NONMEM. A two-compartment model with zero-order absorption and a lag time best described the data. Bayesian estimation was based on CsA blood concentrations measured before dosing and 1 h and 2 h post dose. Predictive performance was evaluated using a cross-validation approach. Estimated AUCs were compared with AUCs calculated by the trapezoidal method. The Bayesian approach was also applied to an independent group of eight patients exhibiting unusual pharmacokinetic profiles.

Results

Mean population pharmacokinetic parameters were apparent clearance 30 l h⁻¹, apparent volume of distribution 79.8 l, duration of absorption 52 min, absorption lag time 7 min. No significant relationships were found between any of the pharmacokinetic parameters and individual characteristics. A good correlation was obtained between Bayesian-estimated and experimental AUCs, with a mean prediction error of 2.8% (95% CI [−0.6, 6.2]) and an accuracy of 13.1% (95% CI [7.5, 17.2]). A good correlation was also obtained in the eight patients with unusual pharmacokinetic profiles (r² = 0.96, P < 0.01).

Conclusions

Our Bayesian approach enabled a good estimation of CsA exposure in a population of patients with variable pharmacokinetic profiles, showing its usefulness for routine AUC-based therapeutic drug monitoring.

Keywords: Bayesian estimation, cyclosporin, population pharmacokinetics, renal transplant recipients

Introduction

Cyclosporin (CsA) is characterized by both a substantial inter and intra-individual pharmacokinetic variability and a narrow therapeutic index. This may lead to treatment failure due to insufficient immunosuppression, and to side-effects due to excessive immunosuppression [1–3]. Various factors have been shown to be associated with the pharmacokinetic variability of the Sandimmun® formulation, including liver and pancreatic function, food intake and gastro-intestinal motility. The microemulsion formulation (Neoral®) is characterized by a better absorption profile but CsA pharmacokinetics are still influenced by individual factors such as concomitant drug treatment [4–6], weight, post-transplantation time or hepatic impairment [7]. In addition, unexplained pharmacokinetic variability remains high and justifies therapeutic drug monitoring (TDM) to optimize the dose individually [8, 9].

Several authors have shown that occurrence of acute rejection and graft survival were better related to the area under the concentration-time curve (AUC) than to the trough concentration (C_trough) of CsA [10, 11]. Therefore, AUC-based monitoring of CsA could be useful to optimize the dose when C_trough does not seem reliable [1, 12–14]. However, obtaining multiple samples from a patient has obvious limitations, and thus AUC estimation procedures using a limited number of measurements are needed. The so-called ‘limited sampling strategy’ involves multilinear regression models, many of which have been proposed for CsA, using 1–4 concentrations [13–18]. This approach is limited by the use of fixed sampling times, not very suitable for routine use where flexibility in sampling is necessary. Moreover, this method does not take account of individual factors that influence CsA pharmacokinetics [19, 20].

Bayesian estimation of individual parameters using a population pharmacokinetic model has been proposed for the estimation of exposure to CsA. However, most of these studies were conducted with Sandimmun® and none of them allowed a reliable estimation of CsA concentrations [21–25]. Recently, satisfactory descriptions of CsA pharmacokinetics in patients with the microemulsion formulation were obtained using a computer program developed by the authors [26–28]. The lower pharmacokinetic variability of the new formulation may allow the construction of a model taking account of factors known to affect CsA pharmacokinetics.

The aim of our study was to develop a population pharmacokinetic model for the microemulsion formulation of CsA using an approach that allows the identification of covariates. We also evaluated a Bayesian approach aimed at estimating individuals' pharmacokinetic parameters from only a few samples.

Methods

Patients

Eighty-four kidney transplant patients were enrolled in this study. All had been receiving Neoral® every 12 h for at least 3 months. All patients had received induction therapy with antithymocyte globulin and were being treated by mycophenolate mofetil with or without corticosteroids. A detailed history of CsA dosing and other factors that could affect CsA pharmacokinetics, and therefore be included as covariates in the model were recorded. Some of the patients had been recruited for a bicentric prospective study [28], the others being outpatients for whom a full CsA AUC had been obtained for routine TDM purposes. The bicentric study was approved by the ethics committee of the University Hospital of Limoges and written informed consent was obtained from all patients.

An additional study was performed in eight other patients who had undergone routine TDM. These patients had unusual pharmacokinetic profiles observed in the context of clinical events (rejection, renal toxicity). Informed consent and ethics committee approval were not required for these eight subjects since AUC estimation was part of their routine medical care.

Characteristics of patients from the bicentric prospective study In this group (n = 44), patients were from 18 to 65 years old, transplanted for more than 3 months and had stable CsA doses for more than 1 month. The other inclusion criteria were a lack of clinical or histological evidence of acute rejection, a lack of recurrence of the initial nephropathology or of any other renal progressive disease, stable renal function for at least 1 month before the study, and a lack of significant hepatic cytolysis. Cotreatment with drugs that may interact with CsA pharmacokinetics (rifampicin, carbamazepine, phenobarbital, phenytoin, valproic acid, primidone, griseofulvin, azole antifungals, macrolides, nicardipine, diltiazem, verapamil, oral contraceptives and androgenic steroids, methylprednisolone, cimetidine, cholestyramine, antacids containing magnesium or aluminium hydroxide, alcohol or grapefruit juice) within a week preceding the study was also an exclusion criterion.

Full CsA pharmacokinetic profiles (full-PK) were obtained from 20 patients, from samples drawn immediately before (0) and at 20 min, 40 min, 1 h, 1.5 h, 2 h, 3 h, 4 h, 6 h and 9 h after dosing.

Sparse CsA pharmacokinetic profiles (sparse-PK) were obtained from the other 24 patients, from samples drawn at 0, 2 h, and at two other times selected randomly.

Characteristics of patients from the routine TDM group

CsA pharmacokinetic profiles (TDM-PK) were available in 40 patients. The number of samples ranged from 6 to 8 and always included those at 0, 1, 2 and 4 h post dose. Information on comedication was not available for the patients in the TDM group.

CsA analysis

CsA blood concentrations were measured using a specific Enzyme Multiplied Immunoassay Technique (Cobas Mira – Dade Behring) [29]. Intraday variability was 6.0–11.8% and 3.8–6.1% and interassay variability was 10.4–19.1% and 6.3–8.5% at concentrations of 72 and 414 ng ml⁻¹, respectively. The assay allows quantification of CsA over 40–500 ng ml⁻¹. When necessary, dilution was made using blood from transplant patients not receiving CsA.

Data analysis

Model building The data were analyzed by nonlinear mixed effects modelling using NONMEM Version V [30]. The First Order approximation (FO) was used during the model building process, and this model was subsequently tested using the first-order conditional estimation (FOCE) method to try to improve the final model [31, 32]. Assuming that the parameters had no covariances, a diagonal covariance matrix was applied. Descriptive statistics and comparative analyses were performed using Statistica® 5.5 A (Statsoft, France).

The selection of the structural model was based on the 20 full profiles of the patients included in the bicentric study. One and two-compartments models with first or zero–order absorption were fitted to the data. Between-subject variability was modelled using additive, proportional or exponential error models. Residual error was modelled using additive, proportional or combined error models [32]. Goodness-of-fit was evaluated by plots of predicted vs observed concentrations and absolute and weighted residuals vs time [33–36].

The selected structural model was then applied to the entire data set (n = 84). Graphical analyses were performed to screen for relationships between each pharmacokinetic parameter and the covariates. The individual influence of age, weight, height, body surface area (BSA) (0.20247 × Height(m)^0.725 × Weight(kg)^0.425), ideal body weight (IBW) (weight/height²), serum creatinine, creatinine clearance calculated with the Cockroft & Gault formula, ALAT, ASAT, bilirubin and post-transplantation delay was tested. Age, weight, height, BSA, IBW, ALAT, ASAT, bilirubin, serum creatinine, creatinine clearance were explored as continuous variables and post-transplantation delay as a categorical variable. Serum creatinine and bilirubin data were not available in 13 of the 84 patients studied. In order to avoid bias, we used the mean population value of the covariate for each subject with missing data. Drugs known to interact with CsA were an exclusion criteria so the influence of comedication was not studied. Linear and exponential relationships were evaluated using Statistica®. Covariates for which a significant relationship was found were introduced sequentially into the population models, which were compared using the likelihood ratio test. The final inclusion of a covariate was considered if it decreased the objective function by at least 5 units.

Bayesian estimation The above population pharmacokinetic model was used to obtain Bayesian estimates from three samples per patient. A cross-validation approach was selected to assess the predictive value of the Bayesian procedure [37, 38].

Assignment of patients to index and validation groups An index group was built by random selection of 75% of the patients. This group included 15 full-PK, 18 sparse-PK and 30 TDM-PK patients. The validation group consisted of the remaining 25% of the patients and included 5 full-PK, 6 sparse-PK and 10 TDM-PK patients. The model was fitted to the data from the index group, and then Bayesian estimates of the individual parameters were obtained in the validation group. Bayesian estimates of AUC were also derived.

Then, 25% of the subjects from this first index group were exchanged to create second index and validation groups. The model was fitted again to the data of the new index group and evaluated in the new validation group. This procedure was repeated twice more, so that predictions could be generated for all 84 patients.

Bayesian procedure Bayesian estimation was performed using samples drawn at 0, 1 h (or as close as possible to) and 2 h. These sampling times were arbitrarily selected based on practicality. Individual pharmacokinetic parameters were obtained using the ‘posthoc’ subroutine of NONMEM without the estimation step (MAXEVAL = 0), setting mean parameters values, variances of interindividual variability and of error to population values obtained previously in the corresponding index set. Simulation of predicted concentrations at the other available times was performed using these individual parameters.

Evaluation of predictive performance

Predictive performance of the Bayesian method was evaluated by comparing predicted and observed concentrations in all the patients. In those with more than six samples, predicted AUCs were compared with individual AUCs calculated by the linear trapezoidal method.

Bias was estimated by mean error (me), which assesses the accuracy of estimation [39]:

where n is the number of observations, and pe_i is the relative prediction error:

The precision of the predictions was estimated by the root mean squared error (rmse):

Evaluation in patients with unusual pharmacokinetics

This method was subsequently applied to eight independent outpatients exhibiting unusual pharmacokinetic profiles in order to assess its usefulness in routine AUC-based TDM. CsA pharmacokinetic profiles from 7–8 samples taken 0 to 9 h post dose were available in these patients and reference AUCs were calculated by the linear trapezoidal method. These values were compared with Bayesian-estimated AUC, obtained as described previously.

Results

Description of the data

Five hundred and fifty-four concentrations were available from the 84 subjects included in this study. A description of patient characteristics is given in Table 1. Four of the 84 transplanted patients had diabetic nephropathy and may have had more variable CsA pharmacokinetics due to gastrointestinal dysfunction. The others were transplanted for interstitial nephritis, chronic glomerulonephritis, renal polycystic disease or for other nephropathy. The number of patients with diabetes was too small to allow a comparison with the patients transplanted for others reasons. The eight additional patients were studied either because they exhibited unusual pharmacokinetic profiles with poor absorption, or because of renal biopsy proven toxicity or substantial deterioration of their renal function. Six of these eight patients were transplanted for less than 6 months (mean = 66 days post-transplantation). Plots of dose normalized concentrations vs time confirmed the wide interindividual variability of CsA pharmacokinetics (Figure 1).

Table 1

Demographic characteristics of the patients in this study

Figure 1

Dose-normalized cyclosporin concentrations vs time in the 84 patients studied

Population pharmacokinetic modelling

A two-compartment model with zero order absorption (ADVAN 3) and a lag-time provided the best fit to the data (Figure 2). CsA clearance (CL/F), volume of the central compartment (V₁/F), volume of the peripheral compartment (V₂/F), intercompartmental clearance and lag time were obtained using TRANS 4. Proportional error models were selected to describe interindividual and residual variabilities. However, whatever the error model chosen, the value of V₂/F did not vary between subjects and no eta was allocated to this parameter. No significant relationships were found between the pharmacokinetic parameters and the following characteristics: weight, age, creatinine clearance, liver enzymes and post-transplantation time. Table 2 presents the mean pharmacokinetic parameters of the population model and their interindividual variability. Residual variability was 13.7% Since FOCE did not improve the fit of the population model, we used FO for the final model.

Figure 2

Predicted vs observed concentrations (A); Weighted residuals vs time (B). Line of identity (—)

Table 2

Population pharmacokinetic parameters estimated using a two-compartments model with zero-order absorption and a lag time

Bayesian estimation

Examples of concentration-time curves obtained by Bayesian estimation using three time-points are displayed in Figure 3 for three patients. The mean AUC estimated by the Bayesian procedure was 4609 (range: 2757–7075) ng ml⁻¹ h. A good correlation was obtained between Bayesian-estimated and reference AUCs (r² = 0.83, P < 0.001) (Figure 4), with a mean prediction error of 2.8% (95% CI [−0.6, 6.2]) and an accuracy of 13.1% (95% CI [7.5, 17.2]).

Figure 3

Bayesian estimation of CsA concentrations in three representative subjects. Predicted concentrations (—), used concentrations (•), observed concentrations ( [open circle]

)

Figure 4

Relationship between estimated and reference AUCs in the validation group. Line of identity (—)

A high correlation was also obtained in the eight patients with unusual pharmacokinetic profiles (r² = 0.97, P < 0.01), with a mean prediction error of 3.4% (95% CI [−8.2, 14.9]) and an accuracy of 15% (95% CI [−13.5, 24.6]). The patient with the worst fit had an estimated AUC of 2700 ng ml⁻¹ h and a corresponding reference AUC of 1950 ng ml⁻¹ h. Excluding this patient, the mean predictive error would be −1.1% with 95% CI −6.9, 4.6 and the accuracy would be 6.8% with 95% CI −3.2, 9.5.

Representative concentration profiles are shown in Figure 5. In the case of Figure 5A, the post-transplant time was 45 days, the clinical event was renal toxicity with C_trough = 457 ng ml⁻¹ and C2 = 1700 ng ml⁻¹; Bayesian estimated AUC was 11300 ng ml⁻¹ h. In the case of Figure 5B, the post-transplant time was 30 days, the clinical event was an acute rejection with C_trough = 99 ng ml⁻¹ and C2 = 370 ng ml⁻¹; AUC_est was 2700 ng ml⁻¹ h.

Figure 5

Application of the Bayesian estimation in routine TDM of CsA: two representative profiles in patients with unusual pharmacokinetics. See text for more details. Predicted concentrations (—), concentrations used for the Bayesian estimation ( [filled square]

), (more ...)

Discussion

In agreement with previous studies, we observed a high interindividual pharmacokinetic variability for CsA [2, 9]. CsA pharmacokinetics during treatment with the microemulsion formulation were best described by a two-compartment model with a zero-order absorption and a lag time. Previous population studies of CsA microemulsion pharmacokinetics used either a two-compartment model with first-order absorption and a lag time [7] or a model where absorption kinetics were described by a gamma distribution [26–28].

The pharmacokinetic parameters obtained in our study are similar to those of Schädeli et al[7]. Surprisingly, CL/F obtained by Leger et al. (59 l h⁻¹) [28] was twice as high as that estimated in our study. Our absorption models allowed a very satisfactory description of the data without the need for a more complex model. The precision of estimation of CL/F in our study (4.6%) was also high, suggesting a good degree of confidence. We also observed large interindividual variability in the lag time (86%). This could be due to the small number of data points during the early absorption phase.

Previous reports in patients similar to those of our study, showed that an Erlang distribution, or a gamma model for absorption gave a better fit to the data [40, 41]. However, the difference between these models and a zero-order absorption model with a lag time is not large enough to justify the use of complex models for routine TDM. The adequacy of our model is confirmed by the low residual variability obtained (13.7%).

Correlation analyses between pharmacokinetic parameters and individual factors did not show evidence of any association between covariates and CsA pharmacokinetics. In a previous study in 20 stable renal transplant patients, Leger et al[28] did not find an influence of individual factors on CsA pharmacokinetics but the small number of subjects may have hindered proper statistical evaluation. Kyhl et al[42] have studied a much larger population (n = 700) and found no effect of age, gender, dose, height, days since transplantation or weight on cyclosporin pharmacokinetics. These findings suggest that other factors contribute to variability in CsA pharmacokinetics. Genetic factors influencing either CsA absorption (the MDR1 gene encoding P-glycoprotein) or clearance (the CYP3A4 gene) have recently been investigated, but no clear association between known polymorphism of these genes and CsA pharmacokinetics has been demonstrated [43–49].

Validation of a Bayesian method can be performed in different ways [50–53] depending on the future use of the model. We chose a cross-validation approach to evaluate its application to patients with stable CsA pharmacokinetics and to patients whose pharmacokinetics were sub-optimal. A Bayesian method should also demonstrate good predictive performance and be capable of being applied to routine clinical care. Our Bayesian method using three blood samples gave a good prediction of CsA pharmacokinetics and allowed an accurate estimation of individual AUC in patients with different characteristics, thus providing a potentially useful tool for routine AUC-based TDM of CsA.

The sampling times 0, 1 h and 2 h were selected for Bayesian estimation. 0 and 2 h were previously shown to be related to CsA exposure [54–56] and are frequently used for CsA TDM. 1 h was selected because of its potential advantage in describing the absorption phase, which can be difficult to characterize.

A non-significant bias [−0.6 – 6.2% (P = 0.05)] was observed for AUC with an accuracy of 13.1%. This prediction error should not have important clinical consequences, with respect to the proposed therapeutic range for CsA. Recommended AUC targets may differ, depending on transplant type or time to transplantation [54–58]. According to different authors, the target AUC(0,-4 h) in kidney transplant patients is 4400–5500 ng ml⁻¹ h or 5400–6500 ng ml⁻¹ h during the first 6 post-transplant months [57, 59, 60]. In most prospective studies, relating CsA exposure to efficacy, was done at only one time point. The predefined target ranges not only depend on the transplant type and the time to transplant, but also on any comedication. Thus, target ranges are lower for the first 3 months post-transplant if an induction therapy is associated [61].

In summary, Bayesian estimation using a conventional pharmacokinetic model enables a good estimation of exposure to CsA formulated as a microemulsion even in unselected patients. Our Bayesian model may be applied to the AUC-based TDM of CsA in renal transplant patients including those with unusual pharmacokinetic profiles. This approach may have advantages over monitoring at 2 h after the dose, which does not allow the prediction of AUC(0,-4 h) when pharmacokinetics are unusual. However, the present results must be confirmed and tested in a larger population.

In conclusion, Bayesian estimation may be a more precise tool than other methods to evaluate exposure to CsA in renal graft recipients. However, the ‘rich sampling’ AUC will remain the reference.

Acknowledgments

We gratefully acknowledge the financial support of Limoges University Hospital and Dade-Behring, Paris La Défense, France.

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