Objectives: The aim of this study was to develop a pharmacokinetics model allowing the description of the evolution of tacrolimus exposure in kidney transplant patients over the first months after transplant, using trough concentrations of routinely collected blood.
Materials and Methods: The authors performed a retrospective analysis of trough concentration data collected from adult kidney transplant recipients (from 2008 to 2013). The total data set was divided into a building data set, used to build the structural model, and a validation data set, used to validate the structural model. (C0 = 133; 26 patients). A pharmacokinetics analysis was carried out by applying a nonparametric adaptive grid approach. The structural model parameters were tacrolimus clearance and volume of distribution.
Results: In patients in the building set group, estimated clearance was 3.6 ± 0.57 L/h and estimated volume of distribution was 9.9 ± 1.14 L. No covariate was significantly associated with tacrolimus clearance or volume of distribution. The model adequately described tacrolimus dose-normalized trough concentration evolution after transplant (the plot of individual model predicted versus observed concentrations resulted in r = 0.84). The prediction performance in the validation group yielded 2.3% mean prediction error and 21.4% root mean squared error.
Conclusions: This model could be highly useful in the optimization of tacrolimus prescription at any posttransplant time in kidney transplant patients.
Key words : Population pharmacokinetics, Posttransplant period
Tacrolimus is a calcineurin inhibitor widely used for the prevention of allograft rejection in solid-organ transplant.1,2 This immunosuppressant is characterized by a narrow therapeutic window and a rather large within-patient and between-patient variability in both pharmacokinetics and pharmacodynamics.3,4 Therefore, tacrolimus therapeutic drug monitoring is highly recommended in clinical practice to evaluate individual drug exposure and adjust tacrolimus dose accordingly.
In this respect, population pharmacokinetics analysis has emerged as a key approach in therapeutic drug monitoring optimization of tacrolimus because it allows the use of therapeutic drug monitoring data for the calculation of individual pharmacokinetics parameters and for subsequent individualization of the dosing regimen using pharmacokinetics models.5-9 Therapeutic drug monitoring of tacrolimus is routinely performed using trough blood concentrations (C0). In fact, it has been shown that tacrolimus C0 results are significantly related to clinical endpoints; that is, there is a significant correlation between increased C0 and decreased risk of acute rejection.10,11 Moreover, it has been shown that tacrolimus C0 of less than 15 ng/mL is associated with a lower occurrence of nephrotoxicity.12
Previous pharmacokinetics studies performed on adult renal transplant patients reported an increase in tacrolimus exposure during the first year after transplant.13 Similarly, other studies showed a decrease in tacrolimus dose requirements to maintain similar trough concentrations with increasing time after transplant.14,15
Several pharmacokinetics or population pharmacokinetics models have been published for tacrolimus, generally using intensive sampling strategies.6-9 However, only 1 study modeled tacrolimus exposure using only tacrolimus C0 in the first 2 months after transplant,16 and no studies have been published regarding the third month in kidney graft recipients.
In this study, our aim was to develop a population pharmacokinetics model that could describe the evolution of tacrolimus dose-normalized trough concentration(C0/D) according to the time elapsed since transplant, using routine drug monitoring data (C0) in kidney transplant recipients.
Materials and Methods
Patients and data collection
We performed a retrospective analyses of data collected from Tunisian adult kidney transplant recipients from March 2008 to December 2013. The patients had received tacrolimus as primary immunosuppressant therapy started on the day of renal transplant. The initial tacrolimus dose (Prograf; Hikma Pharmaceuticals, London, UK) was 0.15 mg/kg/d administered in 2 divided doses. The concomitant immunosuppressive drugs administered to all patients were 2000 mg/d mycophenolate mofetil and 500 mg/d methylprednisolone. The corticosteroid dose was progressively reduced to 20 mg/d prednisone on day 7, to reach a long-term maintenance dose of 10 mg/d at the end of week 2 posttransplant.
Blood samples for the determination of tacrolimus C0 were those taken immediately before the morning dose. Tacrolimus dose was adjusted according to the C0 target range proposed by the European consensus conference on tacrolimus optimization.17 The samples were subdivided according to the posttransplant period into 3 groups, as proposed by the European consensus conference. We compared blood samples collected from the 3 posttransplant groups: patients who were less than 3 months posttransplant (period 1), at 3 to 12 months posttransplant (period 2), and at more than 12months posttransplant (period 3).
For each patient, the following covariates were recorded: age, sex, weight, mycophenolate mofetil dose, and corticosteroid dose. Tacrolimus blood concentrations were determined by an enzyme multiplied immunoassay technique (V-Twin System, Siemens Healthcare Diagnostics, Deerfield, IL, USA). According to the manufacturer’s information, the lowest limit of quantification of the assay is 2 ng/mL and the assay is linear over a range of 2 to 30 ng/mL. Blood samples exceeding the upper limit of the calibration range (30 ng/mL) were diluted according to the manufacturer’s protocol.
A pharmacokinetics analysis was carried out by applying a nonparametric adaptive grid approach, using Pmetrics software for R package (version 2.15.2).18 The total data set was divided into a building data set (C0 = 306; 50 patients) and a validation data set (C0 = 133; 26 patients).
We started with the classical equation giving the residual C0 for a single linear compartment receiving the drug at a constant dose (D) and a constant dosing interval (τ)19:
C0= D / Vd * E / 1-E (1-e-nkτ)
where Vd denotes the volume of distribution, k the elimination rate constant, n the number of administrations, and the constant E = e−kτ. In our conditions, if we express the time in units of days, τ = 0.5, E = e−0.5k, and n=T/τ, if T denotes the number of days since the first administration. Therefore, the previous equation becomes:
C0= D / Vd * E / 1-E (1-e-kτ)
The parameters of the structural model were log-transformed. The mean, median, and standard deviations of the population parameters (Vd, clearance) were estimated using the above equation. In a second step, the influence of different covariates on tacrolimus clearance and Vd were plotted and tested using the Mann-Whitney test for binary covariates (sex) and the Pearson correlation for continuous covariates (body weight, age, corticosteroid dose, and mycophenolate mofetil dose).
The accuracy of the final building model was evaluated by goodness-of-fit plots (observed C0/D vs predicted C0/D and weighted residual error as a function of concentration and time). An internal validation was performed using visual predictive check.
We then performed an external validation of this pharmacokinetics model in the validation dataset. The predictive performance of the model developed in the validation data set was evaluated by goodness-of-fit plots, mean prediction error, and root mean squared error.20
We had 439 whole blood tacrolimus C0 results from kidney transplant patients available for population modeling. The mean number of sampling points per patient was 3.25 (range, 2-14) regardless of posttransplant time, of which 3.16 (range, 2-11) were available during the first year posttransplant. Patient characteristics for both groups are shown in Table 1.
The estimated values for clearance and Vd in the building set group were 3.6 ± 0.57 L/h and 9.9 ± 1.14 L (Figure 1). No covariate (age, sex, weight, mycophenolate mofetil dose, or corticosteroid dose) was significantly associated with tacrolimus clearance or Vd data.
The model adequately described C0/D evolution over time after transplant. The plot of individual model-predicted versus observed concentrations showed no structural bias, with a correlation coefficient of r = 0.84 (Figure 2). Moreover, the weighted residuals were homogeneously distributed as a function of the posttransplant time and concentration level (Figure 3). The final model was also evaluated using the visual predictive check to assess its accuracy and robustness: 1000 replicates of the original data set were simulated using the final model. The visual predictive check showed that approximately 90% of the data fitted well within the 5th to 95th percentiles (Figure 4).
The present study showed that there is a significant increase in tacrolimus dose-standardized C0 during the first year after kidney transplant, while no evolution was noted after 1 year, as shown by the evolution of observed C0/D with posttransplant time (Figure 5; Scheffé analysis of variance post hoc test period 2 vs period 1, P < .001, and period 3 vs period 2, P = .98). The population pharmacokinetics parameters obtained from the building dataset were used for the validation of the model, conducted using data from 25 renal transplant patients (validation group) (Figure 6). Posterior estimates of C0/D values in the validation group yielded an acceptable prediction: plot of individual model-predicted versus observed concentrations having r = 0.80 (Figure 7). The model performance was also assessed by low mean prediction error value of 2.3% and moderate root mean squared error value of 21.4% (95% confidence interval, -0.02% to 0.06%).
In the present study, we developed a population pharmacokinetics model able to describe C0/Devolution according to posttransplant time in adult kidney transplant recipients. The predictive performance of our population model was successfully demonstrated through both internal and external validation.
Several population pharmacokinetics models for tacrolimus have been reported previously, in renal7,8 and in lung transplant patients.6-9 These models were developed from patients with complete pharmacokinetics profiles, including multiple blood samples, and most models were based on fixed days and/or months after transplant. However, the time evolution of dose-standardized exposure of tacrolimus in kidney transplant recipients has been rarely modeled previously. Saint-Marcoux and associates developed a pharmacokinetics model using a logistic function to describe area under the curve normalized per dose (ie, tacrolimus apparent clearance) evolution according to posttransplant time using blood sample results obtained from routine examinations. This model confirmed a significant increase in tacrolimus dose-standardized exposure during the first year after transplant.13 Although area under the curve is generally considered as the best marker of drug exposure, the present study analyzed routine tacrolimus C0, which is the marker used in our center to adjust tacrolimus dose. In fact, the absence of consensually recommended area under the curve target ranges is considered a limitation in area under the curve-guided tacrolimus therapeutic drug monitoring. Moreover, many studies have demonstrated that tacrolimus C0 could be a good surrogate of tacrolimus exposure in kidney renal transplant recipients. On the one hand, it has been demonstrated that tacrolimus C0 are well correlated with the area under the time-concentration curves from time 0 to 12 hours and could subsequently be considered as a good index of patient exposure to tacrolimus.21 On the other hand, both prospective and retrospective clinical studies showed that there was a good relationship between tacrolimus C0 and clinical outcomes.10,11 In fact, a significant correlation between high trough levels and toxicity was found in both kidney and liver transplant patients. Likewise, a low tacrolimus C0 level was significantly associated with rejection in kidney transplant patients.12 Furthermore, different tacrolimus C0 target ranges have been proposed in several retrospective clinical studies, which were updated at the European Consensus Conference held in Brussels in 2007, with C0 target ranges divided according to 3 posttransplant periods.17
Modeling tacrolimus exposure using only trough concentration data has been performed in only 1 previous study, in which the author designed a pharmacokinetics model using C0 data obtained from 83 adult kidney transplant recipients and a 1-compartment open model with first-order absorption.12 Unlike our study, Antignac and associates explored the C0 level collected during the first 2 months after transplant; therefore, this model did not really allow the investigation of tacrolimus exposure over the early posttransplant period (nor was it apparently the intention of the authors). Moreover, our analysis was performed using a population nonparametric approach, which is known to have theoretical superiority over parametric methods18 because it may better detect outliers and subpopulations.
The present study is the first to investigate pharmacokinetics parameters of tacrolimus in a Tunisian kidney transplant population. The results are in accordance with previously published data obtained from pharmacokinetics studies performed in other kidney transplant recipients. Gruber and associates22 have shown a clearance value of 2.4 L/h after oral administration of tacrolimus. Similarly, Velickovic and associates,23 who performed a population pharmacokinetics study on 63 Serbian adult kidney transplant patients, found a typical mean value of tacrolimus clearance of 1.03 L/h.
Our analyses showed that age, sex, and weight had no significant effect on either clearance or Vd. These results are in accordance with other previous studies that did not find any effect of demographic factors on clearance and/or Vd.24,25 However, it has been demonstrated previously that other covariates such as steroid dose had a significant influence on tacrolimus clearance. In a study of 83 renal transplant recipients, it was shown that the higher the steroid dose, the higher the dose of tacrolimus needed to achieve target C0.26 Similarly, Undre and associates reported a significant correlation between apparent clearance and mean oral corticosteroid dosage (r = 0.94) between month 2 and month 12 after transplant in 303 kidney transplant recipients.15 Recently, Press and associates have shown that a concomitant prednisolone dose of more than 10 mg/d increased the tacrolimus apparent clearance by 15%,27 which could be explained by the fact that corticosteroids increased tacrolimus metabolism, since they are known to be inducers of CYP3A, the enzymes involved in tacrolimus metabolism. Our analyses failed to demonstrate any significant effect of corticosteroids on pharmacokinetics parameters, but this may be due to the imprecise pharmacokinetics information brought by C0 values only in our model.
Some biologic parameters, such as hematocrit and albumin concentrations, were also reported as significant covariates.28,29 Also, it has been reported that concomitant drug administration, for example with voriconazole, could affect tacrolimus pharmacokinetics.30
In the present study, some of the laboratory parameters and associated drugs were not available for all patients in their medical records and subsequently were not included in this analysis; thus, the pharmacokinetics model developed here does take into account only the analytic errors. The inclusion of other covariates explaining part of the within-patient variability, such as CYP3A genotype and/or hematologic parameters, could have improved the prediction performance of our model.
Our analyses showed that there is a continuous increase in tacrolimus dose-standardized exposure during the first year after kidney transplant, since predicted C0/D values increased from period 1 to period 3. This increase was significant between period 1 and period 2 and not significant between period 2 and period 3. Some previous studies in adult renal transplant patients reported that the tacrolimus dose required to maintain a predefined “therapeutic level” should be lowered along posttransplant time. In a population of 303 adult renal transplant patients, Undre and associates reported a decrease in tacrolimus clearance throughout the first year after transplant.15 We have also shown in a previous study performed on 110 renal transplant recipients that a reduction by 36% and 65% of tacrolimus initial dose during period 2 and period 3 after transplant was necessary to maintain tacrolimus concentration within a therapeutic range.9 This supposes that tacrolimus blood levels must be monitored regularly during the first year. However, tacrolimus therapeutic drug monitoring does not require frequent administration beyond the first year after transplant. According to the last consensus conference on tacrolimus optimization,11 target C0 must also be decreased with posttransplant time. Tacrolimus C0 should range from 10 to 15 ng/mL during the first 3 months after transplant and then from 8 to 12 ng/mL during the second period after transplant (3 to 12 mo) and from 5 to 10 ng/mL thereafter.
Our model allowed the establishment of an individualized tacrolimus dose in kidney transplant recipients at any posttransplant time. Knowing the tacrolimus concentration target level as a function of posttransplant time, as defined by the European consensus conference, the proposed individual dose is calculated as follows:
D= Vd * (1-E)/ E * 1/(1-e-kτ) * target connecntration
where E = e−k·0.5, k = (clearance/Vd) × 24, T = posttransplant day, and target concentration = target C0 according to posttransplant delay.
In the present study, we developed a pharmacokinetics model able to accurately describe the evolution of tacrolimus dose-standardized exposure over the first year after transplant in kidney transplant recipients. This model is based on routine tacrolimus C0 and has been validated using external data. It should be a powerful tool to help clinicians to optimize tacrolimus dose in kidney transplant population at any posttransplant time.
Volume : 14
Issue : 4
Pages : 394 - 400
DOI : 10.6002/ect.2015.0273
From the 1Service de Pharmacologie, Faculté de Médecine, Monastir,
Tunisia; and the 2INSERM U850, Le centre hospitalier et universitaire
de Limoges, Limoges, France
Acknowledgements: The authors have no conflicts of interest to declare and no outside funds supported this study. The authors are greatly indebted to Professor Adel Rdissi for his help with improving the language used in this article.
Corresponding author: Nadia Ben Fredj, Laboratoire de Pharmacologie, Faculté de Médecine de Monastir, Rue Avicenne, 5019 Monastir, Tunisia
Phone: +21 622 657 808
Figure 1. Distribution of Pharmacokinetics Parameters in Building Set Population
Figure 2. Plot of Observed Tacrolimus Dose-Normalized Trough Concentration Versus Individual Predicted Tacrolimus Dose-Normalized Trough Concentration
Figure 3. Weighted Residual Error of Predicted Tacrolimus Dose-Normalized Trough Concentration as Function of Posttransplant Time and Observed Tacrolimus Dose-Normalized Trough Concentration
Figure 4. Visual Predictive Check Obtained From 1000 Simulations
Figure 5. Evolution of Observed C0/D
Figure 6. Examples of 3 Different Modeled Patients
Figure 7. Plot of Observed C0/D Versus Individual Predicted C0/D in Validation Group
Table 1. Patient Characteristics