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ORIGINAL RESEARCH ARTICLE
Clin Pharmacokinet 2012; 51 (3): 175-186 0312-5963/12/0003-0175/$49.95/0
ª 2012 Adis Data Information BV. All rights reserved.
Population Pharmacokinetic Modelling and Design of a Bayesian Estimator for Therapeutic Drug Monitoring of Tacrolimus in Lung Transplantation Caroline Monchaud,1,2 Brenda C. de Winter,1 Christiane Knoop,3 Marc Estenne,3 Martine Reynaud-Gaubert,4 Christophe Pison,5 Marc Stern,6 Romain Kessler,7 Romain Guillemain,8 Pierre Marquet1,2 and Annick Rousseau1 1 2 3 4 5 6 7 8
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INSERM UMR-S850, CHU Limoges, Universite´ de Limoges, Limoges, France Service de Pharmacologie, Toxicologie et Pharmacovigilance, CHU Limoges, Limoges, France Service de Pneumologie, Hoˆpital Universitaire Erasme, Universite´ Libre de Bruxelles, Bruxelles, Belgium Service de Pneumologie, CHU Nord, Faculte´ de Me´decine, Universite´ de la Me´diterrane´e Aix-Marseille, Marseille, France Clinique de Pneumologie, CHU de Grenoble, Universite´ Joseph Fourier, INSERM 884, Grenoble, France Service de Pneumologie, Hoˆpital Foch, Suresnes, France Service de Pneumologie, Hoˆpitaux Universitaires de Strasbourg, Strasbourg, France Service de Chirurgie Cardiovasculaire, Poˆle Cardio-Thoracique, AP-HP, HEGP, Paris, France
Abstract
Background: Therapeutic drug monitoring of tacrolimus is a major support to patient management and could help improve the outcome of lung transplant recipients, by minimizing the risk of rejections and infections. However, despite the wide use of tacrolimus as part of maintenance immunosuppressive regimens after lung transplantation, little is known about its pharmacokinetics in this population. Better knowledge of the pharmacokinetics of tacrolimus in lung transplant recipients, and the development of tools dedicated to its therapeutic drug monitoring, could thus help improve their outcome. Objectives: The aims of this study were (i) to characterize the population pharmacokinetics of tacrolimus in lung transplant recipients, including the influence of biological and pharmacogenetic covariates; and (ii) to develop a Bayesian estimator of the tacrolimus area under the blood concentration-time curve from time zero to 12 hours (AUC12) for its therapeutic drug monitoring in lung transplant recipients. Methods: A population pharmacokinetic model was developed by nonlinear mixed-effects modelling using NONMEM version VI, from 182 tacrolimus full concentration-time profiles collected in 78 lung transplant recipients within the first year post-transplantation. Patient genotypes for the cytochrome P450 3A5 (CYP3A5) A6986G single nucleotide polymorphism (SNP) were characterized by TaqMan allelic discrimination. Patients were divided into an index dataset (n = 125 profiles) and a validation dataset (n = 57 profiles). A Bayesian estimator was derived from the final model using the index dataset, in order to determine the tacrolimus AUC12 on the basis of a limited number of samples. The predictive performance of the Bayesian estimator was evaluated in the validation dataset by comparing the estimated AUC12 with the trapezoidal AUC12. Results: Tacrolimus pharmacokinetics were described using a two-compartment model with Erlang absorption and first-order elimination. The model included cystic fibrosis (CF) and CYP3A5 polymorphism as covariates. The relative bioavailability in patients with CF was approximately 60% of the relative bioavailability observed in patients without CF, and the transfer rate constant between the transit compartments was 2-fold smaller in patients with CF than in those without CF (3.32 vs 7.06 h-1). The apparent clearance was 40% faster in CYP3A5 expressers than in non-expressers (24.5 vs 17.5 L/h). Good predictive performance was obtained with the Bayesian estimator developed using the final model and concentrations measured at 40 minutes and at 2 and 4 hours post-dose, as shown by the mean bias (1.1%, 95% CI -1.4, 3.7) and imprecision (9.8%) between the estimated and the trapezoidal AUC12. The bias was >20% in 1.8% of patients.
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Conclusion: Population pharmacokinetic analysis showed that lung transplant patients with CF displayed lower bioavailability and a smaller transfer rate constant between transit compartments than those without CF, while the apparent clearance was faster in CYP3A5 expressers than in non-expressers. The Bayesian estimator developed in this study provides an accurate prediction of tacrolimus exposure in lung transplant patients, with and without CF, throughout the first year post-transplantation. This tool may allow routine tacrolimus dose individualization and may be used to conduct clinical trials on therapeutic drug monitoring of tacrolimus after lung transplantation.
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Introduction
Tacrolimus suppresses the T-cell immune response by inhibiting the synthesis of interleukin (IL)-2 through the inhibition of calcineurin. Its use in lung transplantation has progressively increased, and so its use in combination with mycophenolate mofetil now represents the maintenance immunosuppressive regimen in approximately 60% of patients.[1] The pharmacokinetics of tacrolimus have been previously described in healthy volunteers and in other solid organ transplant settings, and are known to be highly variable. However, data in lung transplantation remain relatively scarce. Only one compartmental pharmacokinetic study has been published – by our group[2] – but it focused on stable patients. A recent review reported that lung transplant patients display tacrolimus pharmacokinetic profiles different from those of other transplant groups, justifying the need for specific studies in this population.[3,4] Lung transplantation displays several specificities when compared with the transplantation of other solid organs. First, more sustained immunosuppression is required in lung transplant recipients, because the lung is a highly immunogenic organ. Despite higher levels of immunosuppression, the incidences of acute and chronic rejection and mortality are high.[3,4] Second, the lung is rich in metabolic enzymes that participate in the elimination of certain drugs (fentanyl, sufentanyl[5]) and is characterized by a large contact surface area between the alveolar walls and the blood stream, which favour local metabolism of certain drugs.[3,4] Third, lung transplant patients suffer from diverse co-morbidities, including cystic fibrosis (CF), resulting in a very heterogeneous population. CF patients, who represent 16% of lung transplant recipients,[1] display specific characteristics that can affect the pharmacokinetics of immunosuppressive drugs. Indeed, exocrine pancreatic insufficiency and the resulting fat malabsorption and very frequently observed malnutrition affect drug absorption and distribution. Moreover, the airways and sinuses are colonized with a number of virulent bacteria, which are ª 2012 Adis Data Information BV. All rights reserved.
often resistant to anti-infective drugs and are impossible to eradicate prior to transplantation.[6] Consequently, a close study of the dose-concentration relationships of immunosuppressive drugs in the lung transplant population and the development of robust tools for therapeutic drug monitoring are of major interest. To date, the majority of the pharmacokinetic studies on tacrolimus performed in lung transplantation have been descriptive and have used model-independent pharmacokinetic methods.[3,4] One compartmental pharmacokinetic study of tacrolimus, using the iterative two-stage Bayesian (IT2B) method, has been previously performed by our team in stable lung transplant recipients[2] but, to our knowledge, no population pharmacokinetic study of tacrolimus has ever been performed in lung transplantation. Most results of clinical studies in kidney and liver transplantation suggest that the tacrolimus pre-dose concentration (C0) is predictive of the drug efficacy and toxicity.[7] Therefore, monitoring of the tacrolimus C0 is routinely used for dose individualization in these patients, as well as in lung transplant recipients.[8] However, the most reliable assessment of tacrolimus exposure in its immediate-release formulation is obtained through the measurement of its 12-hour area under the blood concentration-time curve (AUC12). Also, although the relationship between tacrolimus exposure and patient outcome has not been precisely defined, the last consensus report on tacrolimus retained the AUC12 as the best marker of drug exposure in renal transplantation.[3,4,8] This may necessitate 10–12 blood samples over the 12-hour dose interval, which is uncomfortable for the patient and impractical from a logistical standpoint. Moreover, the most relevant tacrolimus exposure indices and dose adjustment tools need to be clearly defined in lung transplantation. Therefore, tools such as Bayesian estimators to estimate the AUC12, using a sparse sampling strategy over a limited time interval, would be of clinical interest in lung transplant recipients. These tools could then be used to define therapeutic ranges for these exposure indices in lung transplantation and to conduct multicentre prospective clinical trials assessing the efficacy of AUC12 monitoring versus C0 monitoring. Clin Pharmacokinet 2012; 51 (3)
Tacrolimus PopPK in Lung Transplantation
Accordingly, the purposes of this study were (i) to describe the population pharmacokinetics of tacrolimus in a cohort of lung transplant recipients (with and without CF) followed up 12 months after transplantation and to investigate the determinants of its variability; and (ii) to develop a Bayesian estimator dedicated to calculation of the AUC12, using a sparse sampling strategy, for optimized therapeutic drug monitoring of tacrolimus in lung transplant recipients during their first year post-transplantation.
177
without CF) aged 40.3 – 14.1 years. All patients received a combination of tacrolimus (Prograf) twice daily, an antimetabolite (either azathioprine or mycophenolate mofetil) and a corticosteroid. Fifteen patients with CF and 13 patients without CF received pancreatic enzymes. Tacrolimus dose adjustment was performed at each centre, in accordance with local practice, typically based on the monitoring of the C0. No standardized C0 target was defined for the purpose of this observational study.
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Methods
Patients and Study Protocol
This pharmacokinetic study was part of a prospective pharmacokinetic trial in lung transplant recipients with and without CF, intended to develop population pharmacokinetic models and Bayesian estimators for optimized dose adjustment of immunosuppressive drugs. The study complied with legal requirements and the Declaration of Helsinki, and was approved by the regional ethics committee and authorized by the French and Belgian National Health Agencies. 121 adult patients, with CF (n = 52) or without CF (n = 69), were recruited in seven transplantation centres in France and Belgium. The patients who were enrolled had benefited from a lung or heartlung transplantation within the previous 3 months and had provided informed consent to participate in the study. In this observational study, the choice of the immunosuppressive strategy was at the discretion of the investigators. The maintenance immunosuppressive regimen typically consisted of the association of a calcineurin inhibitor (ciclosporin or tacrolimus), an antimetabolite (azathioprine or mycophenolate mofetil) and oral corticosteroids. Once recruited, the patients were followed up until the end of the first year post-transplantation. Full pharmacokinetic profiles were collected from each patient during one or more of the following post-transplantation periods: between days 7 and 14 and at month 1, month 3 and month 12. Blood samples were collected at the following timepoints: predose, at 20, 40, 60 and 90 minutes, and at 2, 3, 4, 6, 8, 10 and 12 hours after the morning dose of the immunosuppressive drugs. A standardized schedule was used in the study, with regard to the time of (i) drug intake on the day prior to sampling and on the day of sampling; (ii) meals; and (iii) absorption of pancreatic enzymes in patients with CF. After collection, samples were stored at -20C until the analysis. For this pharmacokinetic study on tacrolimus, 182 profiles were collected from 78 patients (38 patients with and 40 patients ª 2012 Adis Data Information BV. All rights reserved.
Tacrolimus Assay
Whole-blood samples were centralized in the Department of Pharmacology, Toxicology and Pharmacovigilance of Limoges University Hospital (Limoges, France), and tacrolimus was assayed by turbulent-flow chromatography–tandem mass spectrometry after whole-blood precipitation following a previously described and fully validated method.[9] The lower limit of quantification (LLQ) was 1 mg/L and the calibration curves obtained using quadratic regression from the LLQ up to 100 mg/L yielded an r2 value of >0.998. The method was found to be accurate and precise, with a mean inaccuracy of -4.4% to +0.6% and a precision coefficient of variation (CV%) of -3.8% to +6.4% over the linearity range (1–100 mg/L). Genotyping
In each patient, an extra sample was collected for pharmacogenetic analyses. Genomic DNA was isolated then stored at -20C until the analysis.[9] The cytochrome P450 3A5 (CYP3A5) A6986G single nucleotide polymorphism (SNP) [rs776746] was characterized using a validated TaqMan allelic discrimination assay on an ABI PRISM 7000 Sequence Detection System (Applied Biosystems, Courtaboeuf, France) and as a negative control, all runs included duplicates of a null sample. Deviation from the Hardy-Weinberg equilibrium was studied using Fisher’s exact test[10] in R, version 2.10.1 (R Project for Statistical Computing; http://www.r-project.org[11]). Population Pharmacokinetic Modelling
All data were analysed simultaneously using the nonlinear mixed-effects modelling software NONMEM, version VI (GloboMax LLC, Ellicott City, MD, USA),[12] together with Wings for NONMEM, version 614 (developed by N. Holford; available from http://wfn.sourceforge.net/). All population pharmacokinetic analyses were carried out using the first-order conditional estimation (FOCE) method. Clin Pharmacokinet 2012; 51 (3)
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Base Model
In the first step, a compartmental pharmacokinetic model was developed to fit the experimental concentration-time data. The following structural models that were tested were all based on a two-compartment model, as previously described in the literature,[9,13-15] and differed by the absorption process: (i) first-order absorption with lag-time; (ii) Erlang distribution, with and without lag time,[16] a transit compartment absorption model in which the number of transit compartments (added upstream from the central compartment, in order to describe delayed absorption) is the same for all patients; and (iii) the transit compartment model proposed by Savic et al.,[17] which is also a transit compartment model, but where the optimal number of transit compartments is estimated in each patient using the Stirling approximation. In order to discriminate between these three nested absorption models, the coding used for the comparison was based on ADVAN6. The selected model was optimized eventually using another ADVAN (e.g. ADVAN5 for Erlang model or ADVAN4 for first order). The pharmacokinetic parameters that were estimated were the absorption parameters, the apparent central volume of distribution (V1/F), the apparent peripheral volume of distribution (V2/F), the apparent inter-compartmental clearance (Q/F) and the apparent clearance (CL/F) after oral administration. The inter-individual variability (IIV) and inter-occasion variability (IOV) were described using exponential models (equation 1) and tested for each parameter: (Eq: 1Þ CLij ¼ ypop exp Zi þ kj
larger than the critical value from a w2 distribution with degrees of freedom (df) equal to the difference in the number of estimated parameters. For instance, a decrease in the OFV of >10.83 shows a significant improvement in a nested model with 1 df of p < 0.001. In order to be comparable using the OFV, all three absorption processes (first-order, Erlang[16] and Savic[17]) were coded using differential equations (ADVAN6). The discrimination between the tested models was based on the goodness-of-fit plots: model-predicted (PRED) versus observed concentrations (OBS); IPRED versus OBS; and the density distribution of the conditional weighted residuals (CWRES).
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where CLij represents tacrolimus clearance of the ith individual on the jth occasion, ypop is the population value for tacrolimus clearance, Zi is the individual random effect with a mean of 0 and a variance of o2, and kj is the interoccasion random effect with a mean of 0 and a variance of p2. The covariance between values for the IIV was estimated using a variance-covariance matrix. The residual variability was described using a combined (additive and proportional) error model (equation 2): Cobs ¼ e1i þ Cipred ð1 þ e2i Þ
(Eq: 2Þ
where e1 and e2 represent the additive and proportional residual random errors, respectively, each displaying a mean of 0 and a variance of s2, and Cobs and Cipred are the observed and individual-predicted concentrations. The population model was built stepwise. The objective function value (OFV) provided by NONMEM, which is equal to minus twice the log likelihood, was used to compare nested models. Two nested models were considered significantly different from each other when the difference in the OFV was ª 2012 Adis Data Information BV. All rights reserved.
Screening of Covariates and Design of the Final Model
The classical stepwise approach was used as part of the population pharmacokinetic analysis to screen and select significant covariates.[18,19] After computing the base population pharmacokinetic model, we graphically investigated the influence of covariates on the following individual pharmacokinetic parameters, estimated with NONMEM using the post hoc option. Covariates that were suspected to have an essential impact on a pharmacokinetic parameter were considered. The only covariate tested for inclusion on absorption parameters was CF, while the influence of the demographic characteristics (sex, age, bodyweight), time post-transplantation, serum creatinine, haematocrit and the CYP3A5(*1/*3) genetic polymorphism on CL/F and V1/F was studied. The influence of quantitative covariates on pharmacokinetic parameters was tested systematically using a generalized modelling approach according to a power function (equation 3) such as: yðcovÞ (Eq: 3Þ CL ¼ yðCLÞ cov= medcov
where y(CL) is the typical value of clearance for a patient with the median covariate value of the population (medcov), and y(cov) is the estimated influential factor for the covariate (cov). The effect of each binomial covariate was tested using a proportional function, as for the effect of CYP3A5 polymorphism on clearance, described in equation 4: CL ¼ yðCLÞ yðCYPÞCYP
(Eq: 4Þ
where y(CL) is the expected mean value of CL in CYP3A5 non-expressers (CYP3A5*3/*3 carriers, CYP = 0) and y(CYP) is the fractional change in clearance in CYP3A5 expressers (CYP3A5*1/*1 and CYP3A5*1/*3 carriers, CYP = 1). As CF patients are known to display decreased bioavailability,[2,20] the effect of CF on bioavailability (F1) was also tested using a proportional function (equation 5): F1 ¼ 1 yðCFÞCF
(Eq: 5Þ Clin Pharmacokinet 2012; 51 (3)
Tacrolimus PopPK in Lung Transplantation
where y(CF) is the fractional change of the mean bioavailability in patients with CF compared with patients without CF. The inclusion of covariates was performed classically, in a stepwise fashion, with forward inclusion and backward deletion.[21] The statistical significance level was set to p < 0.05 (corresponding to a reduction in the OFV of at least 3.84 for 1 df) in the forward inclusion, and to p < 0.001 (an OFV reduction of at least 10.83 for 1 df) for the backward deletion. The clinical relevance of the covariates was then appraised, taking into account the improvement in parameter estimation precision, the reduction in IIV, IOV, and residual variability, and the changes in parameters at the extremes of the covariate distribution. Finally, the extent of the shrinkage was evaluated in the final model for each parameter.[22]
179
was selected on the basis of a combination of a maximum of two or three sampling times in the first 4 hours post-dose, which seemed to be a good compromise between the precision of parameter estimates and possible implementation in clinical practice, consistent with our experience with other immunosuppressive drugs. The selected strategy was then evaluated as a Bayesian estimator, using the POSTHOC option in NONMEM. The AUC12 values of the patients were estimated using the final population pharmacokinetic model and the estimated pharmacokinetic parameter values of the index dataset. The predictive performance of the selected strategy was finally evaluated by computation of the bias, or mean error (ME, equation 6) and precision or root mean square error (RMSE, equation 7) of Bayesian AUC12 estimates, with respect to the reference values obtained using the linear trapezoidal method applied to the full profiles:[26] PN i ¼ 1 ðPEi Þ ME ¼ (Eq. 6) N
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Model Validation
The accuracy and robustness of the final population model were evaluated using the nonparametric, internal validation bootstrap method, as well as visual predictive checks (VPCs).[23] The bootstrap procedure was performed using Wings for NONMEM, version 614. First, 350 bootstrap datasets of 78 patients were generated from the original population dataset by random sampling with replacement. Second, the median values and 95-percentile range of the pharmacokinetic parameters estimated in each population were compared with the final model.[24] For the VPCs, a total of 1000 replicates were simulated in NONMEM, using the final model to simulate expected concentrations. As the tacrolimus dose (in mg) was different in each patient, and its pharmacokinetics are linear, the simulated and observed concentrations were then dose-normalized and eventually stratified by covariates (e.g. by CYP3A5). The 90% prediction intervals were then generated. Finally, the observed data were overlaid on the prediction intervals and compared visually. Design of a Bayesian Estimator
The patient database was randomly split into an index dataset and a validation dataset (table I). The population parameters of the index dataset were re-estimated, and each covariate was tested again, to validate the Bayesian estimator in the independent validation dataset. The population parameters and variability estimates obtained with the index dataset (concentration-time values from 1325 blood samples) and the whole dataset (concentration-time values from 2113 blood samples) were then compared. The best limited sampling strategy, based on the Doptimality criterion implemented in ADAPT II software,[25] ª 2012 Adis Data Information BV. All rights reserved.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i ¼ 1 ðPEi Þ RMSE ¼ N
(Eq. 7)
where N represents the number of pairs of estimated and reference AUCi values, and prediction error (PEi) is the difference between the estimated and the reference AUC12. The predictive performance of the developed Bayesian estimator was then evaluated in the validation dataset, and the agreement between the estimated and the reference AUC12 values was evaluated using r2. Results
A total of 182 pharmacokinetic profiles collected from 78 lung transplant patients, of which 56 were sampled on more than one occasion, were analysed in this study. The main demographic characteristics of the patients enrolled in the study are reported in table I. The concentration-time curves for tacrolimus (figure 1) exhibited wide IIV, as confirmed by the high-interindividual CV of the dose-normalized AUC12 (96%), C0 (118%), maximum blood concentration (Cmax) [81%] and time to Cmax (tmax) [80%]. A fairly poor correlation was observed between both the dose and AUC12 (r2 = 0.07 in non-CF patients and 0.03 in CF patients) and the C0 and AUC12 (in non-CF patients, r2 = 0.61, p < 0.0001, with a mean prediction error (MPE) of 7.10-17 h mg/L and an RMSE of 7.1%; in CF patients, r2 = 0.33, p < 0.0001, with an MPE of 0.002 h mg/L and an RMSE of 6.5%). In CF patients, r2 = 0.33 suggests that only approximately 33% of the variability
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Table I. Patient characteristics Parameter
Index dataset (n = 51)a
Validation dataset (n = 27)a
p-Valueb
Sex (n; female/male)
25/26
13/14
0.94
Age (y)
41 [20–65]
34 [18–70]
0.12
Primary disease (n; CF/non-CF)
24/27
14/13
0.69
Bodyweight (kg)
51.0 [32.0–84.0]
57.5 [34.0–94.5]
0.16
Serum creatinine (mmol/L)d
80.0 [19.0–283]
88.0 [22.0–543]
0.27
34.0 [19.0–46.0]
33.5 [21.0–43.0]
0.71
44/7
22/5
0.74
c
Haematocrit (%)
e
CYP3A5 (n; GG/AG&AA) Profiles (n) Days 7–14 Month 1 Month 3 Month 12 Dose (mg) Days 7–14 Month 1 Month 3 Month 12
This material is the copyright of the original publisher. Unauthorised copying and distribution is prohibited. 125
57
19
5
29
8
34
18
43
26
2.5 [0.5–11]
2 [1–6.5]
0.86
3 [1–9.5]
3.25 [2–7]
0.50
3.25 [0.5–10]
3.5 [0.5–7]
0.85
4 [1–12]
3.75 [0.5–7.5]
0.64
a Data are presented as median [range] unless specified otherwise.
b Comparisons of continuous variables were performed using the Mann-Whitney test. Comparisons of binomial variables were performed using the w2 test, except for CYP3A5 polymorphism, for which Fisher’s exact test was employed. c Data on weight were available for 136 pharmacokinetic profiles (index, 92; validation, 44).
d Data on serum creatinine were available for 171 pharmacokinetic profiles (index, 110; validation, 61). e Data on the haematocrit were available for 177 pharmacokinetic profiles (index, 113; validation, 64). CF = cystic fibrosis; CYP = cytochrome P450.
60
Blood tacrolimus concentration (µg/L)
in the AUC12 was explained by the C0, while the other 67% was unexplained. In some patients, AUC12 values in a 3-fold range were observed for comparable C0 values (for instance, in the CF group, a C0 of 7.2 mg/L resulted in an AUC12 of 93 mg h/L in one patient and in an AUC12 of 270 mg h/L in another; in the non-CF group, a C0 of 13 mg/L resulted in an AUC12 of 99 mg h/L in one patient and in an AUC12 of 258 mg h/L in another). The mean AUC12 was 153 – 46 mg h/L in CF patients and 153 – 55 mg h/L in non-CF patients (p = 0.97). However, the dose of tacrolimus administered in CF patients versus non-CF patients was significantly different (4.7 – 2.8 vs 3.0 – 1.5 mg twice daily, p < 0.0001).
50
40
30
20
10
Pharmacokinetic Modelling 0
Among the different structural models that were tested, a two-compartment model, with the absorption described as an Erlang model with four transit compartments and no additional lag-time, best described the concentration-time data ª 2012 Adis Data Information BV. All rights reserved.
2
4
6
8
10
12
Time (h)
Fig. 1. Whole-blood tacrolimus concentration-time profiles obtained from 78 lung transplant patients during the first year post-transplantation. The dots represent the observed concentration-timepoints. Clin Pharmacokinet 2012; 51 (3)
Tacrolimus PopPK in Lung Transplantation
Dose
F
181
D
ktr
a2
ktr
a3
ktr
a4
ktr
a5
ktr
Q V1
V2
CL
Fig. 2. Structural population pharmacokinetic model of tacrolimus in lung transplant recipients. a2, a3, a4, a5 = transit compartments; CL = clearance; D = deposit compartment; F = bioavailability; ktr = transfer rate constant; Q = inter-compartmental clearance; V1 = central volume of distribution; V2 = peripheral volume of distribution.
(figure 2). The structural model was then significantly improved by addition of IIV on the transfer rate constant (ktr), V1/F, V2/F, Q/F and CL/F, as well as addition of IOV on the ktr, V1/F and CL/F. Genotyping results were consistent with the HardyWeinberg equilibrium. Among the tested covariates, CF and CYP3A5 genetic polymorphism significantly improved the model. The introduction of these two covariates in the model resulted in a significant decrease in the OFV when compared with the structural model without covariates (DOFV = 76, p < 0.001). The population pharmacokinetic parameters obtained with the final model with covariates are summarized in table II. CF displayed a significant effect on the relative bioavailability (F) and ktr, with on average 40% lower bioavailability and a 2-fold lower ktr in CF versus non-CF patients. The CYP3A5*1/*3 genetic polymorphism displayed a significant effect on CL/F, which was 40% faster in CYP3A5 expressers (CYP3A5*1/*1 and CYP3A5*1/*3 genotypes) than in non-expressers (CYP3A5*3/*3 genotypes). The final model was characterized by a low residual error (1.6 mg/L and 6.9% for the additive and the proportional errors, respectively). It is worth noting that the additive error, which is an expected systematic error, was close to the LLQ of the assay method that was used (1 mg/L). The estimates of shrinkage were 24.4% for the ktr, 12.3% for the V1/F, 36.0% for the V2/F, 8.0% for the Q/F and 7.6% for the CL/F, confirming that the individual estimates of the pharmacokinetics parameters were robust. The scatter plot of PRED and IPRED versus OBS showed no structural bias (figure 3). CWRES did not reflect any systematic deviations, suggesting that the model is unbiased in its predictions. The pharmacokinetic parameter and variability estimates obtained during bootstrap analysis (350 runs) were similar to those obtained with the original dataset, confirming the accuracy of the estimates for the fixed and random effects in the final model, and model stability (table II). As the patients received different doses and the pharmacokinetics of tacrolimus are linear, the VPCs were based on dose-normalized concentrations. They revealed good agreement between the simulated and observed concentrations at all
sampling timepoints, when data were stratified by CF (figure 4a) and by CYP3A5 polymorphism (figure 4b). The variability was reasonably estimated for all the patients. In some subgroups, there was a slightly higher number of observed concentrations under the expected median. However, in all subgroups, around 90% of the observed points fell within the 90% prediction interval.
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ª 2012 Adis Data Information BV. All rights reserved.
Design of a Bayesian Estimator
The patient characteristics in the index and validation datasets were similar (table I). The parameters of the final model re-estimated in the index dataset had similar values (table II). The optimal limited-sampling schedule (selected using the Doptimality criterion) was determined separately for CF and non-CF patients. All attempts resulted in the same optimal sampling schedule for CF and non-CF patients: 20 minutes, 2 hours and 4 hours. This schedule was then tested in the validation dataset. One pharmacokinetic profile in the validation group did not contain enough information to calculate a reliable reference AUC12. The Bayesian estimator based on this limited sampling strategy was characterized by a mean bias between estimated and reference AUC12 values of 1.1%, not significantly different from 0 (95% CI -1.4, +3.7), an RMSE of 9.8% (95% CI +7.5, +11.7) and a determination coefficient r2 value of 0.95. Interestingly, only 1.8% of the deviations (1/56) were outside the –20% interval. No difference in the bias was observed when comparing post-transplantation periods or when comparing patients with versus patients without CF. Discussion For the first time, a population pharmacokinetic model has been developed for tacrolimus in lung transplantation (figure 2), and factors influencing its pharmacokinetics have been identified. A Bayesian estimator able to reliably estimate tacrolimus global exposure, using three blood samples, was built on the basis of this model. Clin Pharmacokinet 2012; 51 (3)
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Concentration-time profiles were described using a population pharmacokinetic model combining an Erlang distribution with four transit compartments for the absorption process and a two-compartment model with first-order elimination. This model was used previously for Prograf in renal transplantation.[9] Erlang absorption is appropriate for drugs with a highly variable absorption time; it describes the sigmoidal increase in drug concentrations in the central com-
partment and it is close to physiological conditions.[16] However, one limitation of our study is evidenced by the scatter VPC plots, which show that the sampling times in the absorption phase did not allow optimal fitting of the absorption profiles in some categories of patients (i.e. CYP3A5 expressers and CF patients). The covariates retained in the final model were CF and CYP3A5 polymorphism, which is in accordance with the lit-
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Table II. Parameter estimates of the pharmacokinetic models Parameter (population mean)
ktr (h-1)a yktr yCF/ktr CF on Fb
Basic model (OFV = 6912)
Final model obtained with the whole dataset (OFV = 6836)
Final model obtained with the index dataset
Bootstrap analysis (n = 350)
Estimate
SE (CV%)
Estimate
SE (CV%)
Estimate
SE (CV%)
Median
95-percentile range
4.92
8
7.06
9
7.84
15
6.98
5.76–9.07
0.47
11
0.42
19
0.47
0.33–0.66
0.63
7
0.55
14
0.63
0.46–0.86
179
16
136
14
117
23
136
107–168
50.3
13
41.1
14
38.1
19
41.3
33.6–50.0
556
27
529
30
581
56
524
277–3021
22.5
12
17.5
11
15.6
15
17.4
14.0–21.5
1.4
8
1.9
41
1.4
0.9–2.0
Additive error (mg/L)
1.7
2
1.6
2
1.6
3
1.5
1.4–1.7
Proportional error (%)
5.4
14
6.9
13
6.8
20
6.9
4.3–9.1
46.4
28.1, 59.3d
42.7
24.0, 55.5d
57.0
15.2, 79.2d
42.0
22.0–62.6
yCF/F V1/F (L) Q/F (L/h) V2/F (L) c
CL/F (L/h) yCL/F
yCYP/(CL/F)
IIV (%) ktr V1/F Q/F
56.0
0, 81.2
41.0
0, 67.0
33.6
0, 77.0
41.4
23.7–59.0
68.2
48.9, 83.1d
71.7
50.5, 87.7d
76.0
35.6, 101d
71.0
48.5–95.9
121
42.9, 166
126
37.6, 174
133
0, 215
122
61.6–190
61.2
38.4, 77.6d
53.7
31.0, 69.3d
57.0
0, 82.5d
53.9
44.0–63.1
45.1
37.3, 51.6d
45.8
38.5, 52.2d
43.2
28.3, 54.2d
45.7
35.4–55.8
V1/F
77.9
d
57.2, 94.2
75.4
d
54.0, 91.9
80.6
39.5, 107
75.9
63.3–89.3
CL/F
47.1
38.7, 54.2d
46.8
38.2, 54.1d
50.4
37.8, 60.4d
46.8
39.9–53.8
V2/F CL/F IOV (%) ktr
CF
d
a ktr ¼ yktr yCF=ktr : CF , where CF = 0 in non-CF patients and 1 in CF patients. b F1 ¼ 1 yCF=F1 CYP , where CYP = 0 in patients with CYP3A5*3/*3 polymorphism and CYP = 1 in patients with CYP3A5 *1/*3 or CYP3A5 *1/*1 c CL = F ¼ yCL yCYP=ðCL = FÞ polymorphism. d 95% CI. CF = cystic fibrosis; CI = confidence interval; CL = clearance; CL/F = clearance after oral administration; CV = coefficient of variation; CYP = cytochrome P450; F1 = oral bioavailability; F = relative bioavailability; IIV = inter-individual variability; IOV = inter-occasion variability; ktr = transfer rate constant; OFV = objective function value; Q = inter-compartment clearance; SE = standard error; V1/F = central volume of distribution after oral administration; V2/F = peripheral volume of distribution after oral administration. ª 2012 Adis Data Information BV. All rights reserved.
Clin Pharmacokinet 2012; 51 (3)
Tacrolimus PopPK in Lung Transplantation
a 70
Individual-predicted blood tacrolimus concentration (µg/L)
erature.[3,4,9] The estimate of the ktr in CF patients (3.32 h-1) was half of the estimate of the ktr in non-CF patients (7.06 h-1), which is consistent with the flatter absorption profiles observed in CF patients. Moreover, the bioavailability of tacrolimus was 40% lower in patients with CF. This was previously reported and attributed to fat malabsorption due to pancreatic insufficiency.[2,20] However, to our knowledge, this difference in bioavailability has never been quantified. This explains the necessity of higher tacrolimus doses in CF patients compared with non-CF patients to reach similar exposure.[2,20,27] CL/F was 40% faster in CYP3A5 expressers (24.5 L/h) than in nonexpressers (17.5 L/h), which is consistent with previous results.[13] The introduction of these two covariates resulted in a decrease in the IIV in CL/F from 61.2% to 53.7%. In contrast to studies in liver transplantation,[28-31] no effect of bodyweight on the CL/F or V1/F was retained here. The model that was developed provided good estimation of all pharmacokinetic parameters, except for the V2/F, which displayed a standard error (SE) of its estimate over 30% and a large bootstrap confidence interval. In the index dataset, an SE of 41% was obtained on the estimate of the fractional change in clearance for CYP3A5*1 carriers; however, the precision of this parameter was good for both the final model obtained using the whole dataset and the bootstrap (SE = 8% and 17%, respectively). Furthermore, to take into account the fractional change in clearance in CYP3A5*1 carriers, the VPCs were studied separately for expressors and non-expressors: acceptable results were obtained. In this study, CL/F was comparable with values reported in heart transplantation (between 0.19 and 0.23 L/h/kg).[14,32] The only compartmental pharmacokinetic study in lung transplantation, previously performed by our team in another cohort of patients, used a one-compartment model and reported mean CL/F values of 68 – 30 L/h in CF and 36 – 19 L/h in nonCF patients,[2] which were higher than the present results but confirm an approximate 2-fold difference between CF and nonCF patients. Previous studies in renal transplantation described a negative correlation between the haematocrit and tacrolimus CL/F in the early period post-transplantation,[9,33] which was not observed in this study. This may be explained by a small variability in the haematocrit in our population (table I). The typical value of the V1/F (218 – 31 L) in our study was higher than reported values in kidney transplant patients (147 – 24 L)[9] and heart transplant patients (1.69 – 0.61 L/kg at day 10 and 1.13 – 0.38 L/kg at month 2 post-transplantation).[14] More research is needed to confirm if this higher V1/F value is specific for lung transplant patients.
183
60 50 40 30 20 10
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ª 2012 Adis Data Information BV. All rights reserved.
r2 = 0.97, p < 0.0001
0
0
10
20
30
40
50
60
70
Observed blood tacrolimus concentration (µg/L)
b
Model-predicted blood tacrolimus concentration (µg/L)
70 60 50 40 30 20 10
r2 = 0.29, p < 0.0001
0
0
10 20 30 40 50 60 Observed blood tacrolimus concentration (µg/L)
70
c
0.6
0.5
Density
0.4
0.3
0.2
0.1
0 −3
−2
−1
0
1
2
3
CWRES
Fig. 3. Goodness-of-fit plots of the final model: plots of (a) individualpredicted blood tacrolimus concentrations vs observed blood tacrolimus concentrations; (b) model-predicted blood tacrolimus concentrations vs observed blood tacrolimus concentrations; and (c) density distribution of the conditional weighted residuals. The solid line in (a) and (b) is the line of identity. CWRES = conditional weighted residuals.
Clin Pharmacokinet 2012; 51 (3)
Monchaud et al.
184
a
Observed concentration 90-Percentile interval of simulated datasets Median of simulated datasets 90-Percentile interval of observed concentrations Median of observed concentrations
b
175
175
150
150
125
125
100
100
75
75
Blood tacrolimus concentration (µg/L)
This material is the copyright of the original publisher. Unauthorised copying and distribution is prohibited. 50
50
25
25
0
0
0
2
4
6
8
10
0
12
c
2
4
6
8
10
12
2
4
6
8
10
12
d
175
175
150
150
125
125
100
100
75
75
50
50
25
25
0
0
0
2
4
6
8
10
12
0
Time post-dose (h)
Fig. 4. Visual predictive check. Comparison of observed blood tacrolimus concentrations with the median and 90-percentile interval of observed blood tacrolimus concentrations and of 1000 simulated datasets. As the visual predictive checks were stratified on cystic fibrosis, the results for (a) cystic fibrosis patients and (b) non-cystic fibrosis patients are presented separately. The mean doses taken into account were 4.7 and 3.0 mg twice daily for cystic fibrosis and non-cystic fibrosis patients, respectively. As the visual predictive checks were also stratified on cytochrome P450 3A5 (CYP3A5) polymorphism, the results for patients with (c) CYP3A5*3/*3 and (d) CYP3A5*1/*3 or *1/*1 are presently separately. The mean doses taken into account were 3.4 mg and 6.2 mg twice daily for patients with CYP3A5*3/*3 and for patients with CYP3A5*1/*3 or *1/*1, respectively.
On the basis of the final model, we developed a Bayesian estimator for accurate estimation of the tacrolimus AUC12, using three concentration-time points: 40 minutes, 2 hours and 4 hours post-dose. The only available sparse sampling strategy in lung and heart-lung transplantation was developed with the IT2B method and proposed two schedules for non-CF and CF patients: 0, 1 and 3 hours, and 0, 1.5 and 4 hours, respectively.[2] IT2B is different from population pharmacokinetics using NONMEM, as it requires a homogeneous population, whereas in NONMEM the population included in the analysis should represent the general population, in order to be able to describe and explain the pharmacokinetic variability. Combining the data gives the analysis more power to estimate the ª 2012 Adis Data Information BV. All rights reserved.
influence of covariates, such as CF or CYP3A5. Furthermore, in a study based on a simulation approach, Lee[34] demonstrated that in a subpopulation, 20 patients were required to identify a 30% difference in the clearance between the typical value and the subpopulation, with an 80% power. Consequently, splitting the data into four groups based on CF (patients with or without CF) and on the CYP3A5 expression profile (expressers or non-expressers) would have resulted in groups that were too small to be able to develop population models. Here, a single Bayesian estimator for both CF and non-CF patients, which is probably easier to handle in routine clinical practice than several sampling strategies, and with an even better predictive performance than the Bayesian estimaClin Pharmacokinet 2012; 51 (3)
Tacrolimus PopPK in Lung Transplantation
tors previously developed using IT2B,[2] was developed. The schedule proposed for optimized therapeutic drug monitoring of tacrolimus, based on the AUC12 – for instance, in cases of discrepancy between C0 values and clinical findings – is compatible with clinical practice. It can also be facilitated by dried blood spot sampling, which can be performed at home by the patients, with the blotted paper posted to the laboratory.[35] In clinical practice, the CYP3A5 genotype is not always available. Consequently, we also evaluated the population pharmacokinetic model without this covariate. This did not modify the estimates significantly, except for an 8% increase in the IIV on CL/F, and the fit remained good, probably due to the rich information provided by the three measured concentrations. However, as this increased the unexplained variability, we consider that CYP3A5 polymorphism should be included if this information is available. The Bayesian estimator developed in this study should be useful in clinical practice, particularly in situations where patients display signs of inefficacy or toxicity, despite appropriate tacrolimus C0 values. In fact, because of highly variable pharmacokinetic profiles, the correlation between the C0 and AUC12 is lower in lung transplant patients than in other solid organ transplant patients; in this study, AUC12 values in a 3-fold range were observed for comparable C0 values, raising doubts about the accuracy of therapeutic drug monitoring based on the C0. More research is needed to define the best AUC12 target in lung transplantation.
185
determine the most relevant tacrolimus exposure indices (for example, in clinical trials investigating the value of AUC12 over C0 monitoring in this population), or to define the AUC12 target in this population, in studies designed to investigate the relationship between exposure and effect (efficacy or toxicity). Acknowledgements The Stimmugrep trial was sponsored by the Direction de la Recherche Clinique et de l’Innovation, Limoges University Hospital, and co-funded by PHRC Re´gional, Vaincre la Mucoviscidose and Agence de la Biome´decine, France. Pierre Marquet is a consultant for Roche Pharma France and has received honoraria and research grants from Roche Pharma and Novartis. The other authors have no conflicts of interest that are directly relevant to the content of this study. The authors gratefully thank He´le`ne Roussel, Fabrice Be´avogui, Franc¸ois-Ludovic Sauvage and Je´rome Lacouture for their excellent technical assistance.
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Conclusion
This study was the first population pharmacokinetic analysis of tacrolimus in a population of lung transplant recipients with and without CF. A two-compartment model, with Erlang absorption and first-order elimination, accurately fitted the profiles. The CYP3A5*3 polymorphism significantly influenced tacrolimus oral clearance. CF patients were characterized by slower absorption and lower bioavailability, justifying higher tacrolimus doses in this group. Finally, a Bayesian estimator was developed to predict AUC12 values using tacrolimus concentrations at 40 minutes, 2 hours and 4 hours post-dose, preferably together with, but possibly without, the CYP3A5 genotype. Therefore, this study provides a convenient tool that can be used routinely to individualize the tacrolimus dose in the lung transplant population, which is known to be at high risk of rejection and adverse events. Moreover, this tool is of major interest in patients with co-morbidities like CF, in whom the immunosuppressive therapy is particularly difficult to optimize. Furthermore, this tool can be used in clinical trials to ª 2012 Adis Data Information BV. All rights reserved.
References
1. Christie JD, Edwards LB, Kucheryavaya AY, et al. The registry of the International Society for Heart and Lung Transplantation: twenty-seventh official adult lung and heart-lung transplant report – 2010. J Heart Lung Transplant 2010 Oct; 29 (10): 1104-18 2. Saint-Marcoux F, Knoop C, Debord J, et al. Pharmacokinetic study of tacrolimus in cystic fibrosis and non-cystic fibrosis lung transplant patients and design of Bayesian estimators using limited sampling strategies. Clin Pharmacokinet 2005; 44 (12): 1317-28 3. Monchaud C, Marquet P. Pharmacokinetic optimization of immunosuppressive therapy in thoracic transplantation: part I. Clin Pharmacokinet 2009; 48 (7): 419-62 4. Monchaud C, Marquet P. Pharmacokinetic optimization of immunosuppressive therapy in thoracic transplantation: part II. Clin Pharmacokinet 2009; 48 (8): 489-516 5. Boer F. Drug handling by the lungs. Br J Anaesth 2003 Jul; 91 (1): 50-60 6. Egan TM, Detterbeck FC, Mill MR, et al. Long term results of lung transplantation for cystic fibrosis. Eur J Cardiothorac Surg 2002 Oct; 22 (4): 602-9 7. Kahan BD, Keown P, Levy GA, et al. Therapeutic drug monitoring of immunosuppressant drugs in clinical practice. Clin Ther 2002 Mar; 24 (3): 330-50 8. Wallemacq P, Armstrong VW, Brunet M, et al. Opportunities to optimize tacrolimus therapy in solid organ transplantation: report of the European consensus conference. Ther Drug Monit 2009 Apr; 31 (2): 139-52 9. Benkali K, Premaud A, Picard N, et al. Tacrolimus population pharmacokinetic-pharmacogenetic analysis and Bayesian estimation in renal transplant recipients. Clin Pharmacokinet 2009; 48 (12): 805-16
10. Nei M. Analysis of gene diversity in subdivided populations. Proc Natl Acad Sci U S A 1973 Dec; 70 (12): 3321-3 11. R Development Core Team. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2011 12. Boeckmann AJ, Sheiner LB, Beal SL. NONMEM user’s guide: part V. Introductory guide. San Francisco (CA): NONMEM Project Group, University of California, 1992 13. Musuamba FT, Mourad M, Haufroid V, et al. Time of drug administration, CYP3A5 and ABCB1 genotypes, and analytical method influence tacrolimus pharmacokinetics: a population pharmacokinetic study. Ther Drug Monit 2009 Dec; 31 (6): 734-42 Clin Pharmacokinet 2012; 51 (3)
Monchaud et al.
186
14. Molinaro M, Regazzi MB, Pasquino S, et al. Pharmacokinetics of tacrolimus during the early phase after heart transplantation. Transplant Proc 2001 May; 33 (3): 2386-9 15. Press RR, Ploeger BA, den HJ, et al. Explaining variability in tacrolimus pharmacokinetics to optimize early exposure in adult kidney transplant recipients. Ther Drug Monit 2009 Apr; 31 (2): 187-97 16. Rousseau A, Leger F, Le Meur Y, et al. Population pharmacokinetic modeling of oral cyclosporin using NONMEM: comparison of absorption pharmacokinetic models and design of a Bayesian estimator. Ther Drug Monit 2004 Feb; 26 (1): 23-30 17. Savic RM, Jonker DM, Kerbusch T, et al. Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. J Pharmacokinet Pharmacodyn 2007 Oct; 34 (5): 711-26
26. Sheiner LB, Beal SL. Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm 1981 Aug; 9 (4): 503-12 27. Walker S, Habib S, Rose M, et al. Clinical use and bioavailability of tacrolimus in heart-lung and double lung transplant recipients with cystic fibrosis. Transplant Proc 1998 Jun; 30 (4): 1519-20 28. Sam WJ, Tham LS, Holmes MJ, et al. Population pharmacokinetics of tacrolimus in whole blood and plasma in Asian liver transplant patients. Clin Pharmacokinet 2006; 45 (1): 59-75 29. Sam WJ, Aw M, Quak SH, et al. Population pharmacokinetics of tacrolimus in Asian paediatric liver transplant patients. Br J Clin Pharmacol 2000 Dec; 50 (6): 531-41 30. Staatz CE, Willis C, Taylor PJ, et al. Toward better outcomes with tacrolimus therapy: population pharmacokinetics and individualized dosage prediction in adult liver transplantation. Liver Transpl 2003 Feb; 9 (2): 130-7
This material is the copyright of the original publisher. Unauthorised copying and distribution is prohibited.
18. Etienne MC, Chatelut E, Pivot X, et al. Co-variables influencing 5-fluorouracil clearance during continuous venous infusion: a NONMEM analysis. Eur J Cancer 1998 Jan; 34 (1): 92-7 19. Mandema JW, Verotta D, Sheiner LB. Building population pharmacokineticpharmacodynamic models: I. Models for covariate effects. J Pharmacokinet Biopharm 1992 Oct; 20 (5): 511-28 20. Knoop C, Thiry P, Saint-Marcoux F, et al. Tacrolimus pharmacokinetics and dose monitoring after lung transplantation for cystic fibrosis and other conditions. Am J Transplant 2005 Jun; 5 (6): 1477-82
21. Lindbom L, Pihlgren P, Jonsson EN. PsN-Toolkit: a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Comput Methods Programs Biomed 2005 Sep; 79 (3): 241-57 22. Savic RM, Karlsson MO. Importance of shrinkage in empirical Bayes estimates for diagnostics: problems and solutions. Am Assoc Pharm Sci J 2009 Sep; 11 (3): 558-69 23. Jadhav PR, Gobburu JV. A new equivalence based metric for predictive check to qualify mixed-effects models. Am Assoc Pharm Sci J 2005; 7 (3): E523-31
24. Parke J, Holford NH, Charles BG. A procedure for generating bootstrap samples for the validation of nonlinear mixed-effects population models. Comput Methods Programs Biomed 1999 Apr; 59 (1): 19-29
25. D’Argenio DZ, Schumitzki A. ADAPT II user’s guide: pharmacokinetic/ pharmacodynamic systems analysis software. Los Angeles (CA): Biomedical Simulations Resource, 1997
ª 2012 Adis Data Information BV. All rights reserved.
31. Garcia Sanchez MJ, Manzanares C, Santos-Buelga D, et al. Covariate effects on the apparent clearance of tacrolimus in paediatric liver transplant patients undergoing conversion therapy. Clin Pharmacokinet 2001 Jan; 40 (1): 63-71 32. Regazzi M, Rinaldi M, Molinaro M, et al. Clinical pharmacokinetics of tacrolimus in heart transplant recipients. Ther Drug Monit 1999; 21 (1): 2-7 33. Staatz CE, Willis C, Taylor PJ, et al. Population pharmacokinetics of tacrolimus in adult kidney transplant recipients. Clin Pharmacol Ther 2002 Dec; 72 (6): 660-9 34. Lee PI. Design and power of a population pharmacokinetic study. Pharm Res 2001 Jan; 18 (1): 75-82 35. Hoogtanders K, van der Heijden J, Christiaans M, et al. Dried blood spot measurement of tacrolimus is promising for patient monitoring. Transplantation 2007 Jan 27; 83 (2): 237-8
Correspondence: Prof. Annick Rousseau, INSERM UMR-S850, Faculty of Medicine, University of Limoges, 2 rue du Dr Marcland, 87025, Limoges CEDEX, France. E-mail:
[email protected]
Clin Pharmacokinet 2012; 51 (3)
