Pharmacokinetic tools for the dose adjustment of ciclosporin in haematopoietic stem cell transplant patients

Abstract

Aims

Ciclosporin A (CsA) is used in the prophylaxis and treatment of acute and chronic graft vs. host disease after haematopoietic stem cell (HSCT) transplantation. Our objective was to build and compare three independent Bayesian estimators of CsA area under the curve (AUC) using a limited sampling strategy (LSS), to assist in dose adjustment.

Methods

The Bayesian estimators were developed using in parallel: two independent parametric modelling approaches (nonmem® and iterative two stage (ITS) Bayesian modelling) and the non-parametric adaptive grid method (Pmetrics®). Seventy-two full pharmacokinetic profiles (at pre-dose and 0.33, 0.66, 1, 2, 3, 4, 6, 8 and 12h after dosing) collected from 40 HSCT patients given CsA were used to build the pharmacokinetic models, while 15 other profiles (n = 7) were kept for validation. For each Bayesian estimator, AUCs estimated using the full profiles were compared with AUCs estimated using three samples.

Results

The pharmacokinetic profiles were well fitted using a two compartment model with first order elimination, combined with a gamma function for the absorption phase with ITS and Pmetrics or an Erlang distribution with nonmem. The derived Bayesian estimators based on a C0-C1 h-C4 h sampling schedule (best LSS) accurately estimated CsA AUC(0,12 h) in the validation group (n = 15; nonmem: bias (mean ± SD)/RMSE 2.05% ± 13.31%/13.02%; ITS: 4.61% ± 10.56%/11.20%; Pmetrics: 0.30% ± 10.12%/10.47%). The dose chosen confronting the three results led to a pertinent dose proposal.

Conclusions

The developed Bayesian estimators were all able to predict ciclosporin AUC(0,12 h) in HSCT patients using only three blood with minimal bias and may be combined to increase the reliability of CsA dose adjustment in routine.

What is Already Known about this Subject

• Ciclosporin A (CsA) is used in the prophylaxis and treatment of acute and chronic graft vs. host disease after haematopoietic stem cell transplantation.

• Few pharmacokinetics studies of CsA in bone marrow transplant patients have been performed.

• No study have compared and combined the results obtained using three independent modelling approaches

What this Study Adds

• Three Bayesian estimators were developed using independent population modelling approaches (two parametrics, one non-parametric)

• All were able to predict ciclosporin AUC(0,12 h) using only three blood samples in the first 4 h post-dose.

• These Bayesian estimators may be combined to increase the reliability of CsA individual dose adjustment.

Introduction

Ciclosporin A (CsA) is an immunosuppressive drug largely used to prevent acute rejection following solid organ transplantation. It is also used in the prophylaxis and treatment of acute and chronic graft vs. host disease (GVHD) after haematopoietic stem cell transplantation (HSCT), or to improve the engraftment in non-myeloablative and reduced-intensity conditioning HSCT.

Therapeutic drug monitoring (TDM) of CsA has been mandatory for years in solid organ transplantation, due to the high inter-patient pharmacokinetic variability and narrow therapeutic window of the drug. In this context, dose adjustment based on the measurement of trough concentrations (C0) and then using 2 h post-dose concentrations (C2) has been historically and widely performed. However, over the years the inter-dose area under the plasma concentration–time curve (AUC) has often been described as the best marker of exposure to CsA and proposed to monitor the patients [1]. Nevertheless, the first argument frequently put forward against CsA monitoring based on AUC is that it is not practical, due to the multiple samples needed to estimate this parameter. Estimation of the AUC based on a limited number of blood samples using pharmacokinetic models and Bayesian estimators has been proposed as a solution [2,3]. Such tools can provide accurate AUC estimations while reducing clinical constraints, although the AUC targets to be reached have still not been the object of a consensus.

On the other hand, only a few studies have evaluated the pharmacokinetics of CsA and the relationships between CsA blood concentrations and GVHD or toxicity in HSCT patients. Most have concluded that (i) the inter-patient pharmacokinetic variability is high and multifactorial, (ii) low CsA concentrations are linked with an increased risk of GVHD and (iii) elevated concentrations are closely associated with toxicity [4–6].

In this context, a first step to improve the management of HSCT patients would be to develop dedicated, robust and routinely usable PK tools for CsA dose adjustment. Several methods of population modelling can be considered. Briefly, population modelling can employ either parametric or non-parametric methods. Parametric methods work under the assumption that each population PK parameter follows a normal or log normal interindividual distribution. Non-parametric methods do not need to make such an assumption.

The main objective of the present study was to develop pharmacokinetic tools allowing the estimation of CsA PK parameters and AUC(0,12 h) in HSCT patients, on the basis of a limited blood sampling strategy. We compared three commonly used, independent approaches: iterative two-stage Bayesian modelling (IT2S, IT2B), non-linear mixed effect modelling (nonmem) and non-parametric expectation maximization (NPEM). These methods were previously described in detail elsewhere [7] and a brief description is available in Appendix S1.

Methods

Context of the study

In this single centre, non-interventional, prospective study routine clinical, laboratory and pharmacokinetic information was obtained from HSCT patients treated with CsA. At Limoges University Hospital, the attending physicians routinely request PK profiles (10 samples over 12h) to calculate CsA AUC(0,12 h) and MMF AUC(0,8 h) (see below) using the classical trapezoidal rule, to rule out under- or over-exposure to these drugs. For each patient, samplings were performed at several post-stem cell transplantation periods, from day 0 to day 100 after grafting. The development of PK models and Bayesian estimators then became possible when enough data were available.

Patients

Forty-five patients prescribed CsA for graft vs. host prophylaxis gave their written informed consent to participate in this study, according to the legal requirements and the last amendment to the declaration of Helsinki. Their primary disease and conditioning regimen are described in Table 1.

Table 1.

Characteristic of the patients in the development and validation datasets

Variables	Model development group		Validation group
	Value	n	Value	n†
Age (years)	59 (24–67)	40	63 (48–70)	7
Gender M/F	25/15	40	4/3	7
ALAT (IU)	35 (8–195)	72	31 (15–106)	15
ASAT (IU)	27 (10–146)	72	25 (13–52)	15
Total bilirubine (μmol l−1)	11 (4–74)	72	13 (6–20)	15
Creatinine (μmol l−1)	77 (34–198)	72	91 (52–128)	15
Albumin (g l−1)	31.4 (18.8–55.1)	62	31.1 (17.0–39.9)	15
Haemoglobin (g/dl)	10.0 (8.2–14.8)	72	10.6 (8.4–13.2)	15
Haematocrit (%)	29 (23–43)	72	31 (25–41)	15
Weights (Kg)	71 (47–101)	71	72 (66–100)	15
Sampling time (post-transplantation days)	4 (0–99)	72	14 (0–83)	15
HLA sibling donor/Matched unrelated donor	15/25		2/5
Conditioning regimen	Fludarabine + busulfan + ATG	34	Fludarabine + busulfan + ATG	7
	Rituximab + ibritumomab tiuxetan + busulfan + fludarabine + ATG	1
	Umbilical cord blood stem cells, fludarabine, cyclophosphamide, TBI	2
	Fludarabine + melphalan	3
Initial disease	Myeloid acute leukemia	18	Myeloid acute leukemia	6
	Chronic lymphoid leukemia	6
	Non-Hodgkin's lymphoma	3
	Hodgkin's lymphoma	1	Non-Hodgkin's lymphoma	1
	Myelodysplastic syndrome	6
	Acute lymphoblastic leukemia	3
	Myelofibrosis	3

Age and gender are non-time-dependent covariates; continuous values are expressed as median and range and categorical values as numbers; ATG, anti-T lymphocyte globulin; TBI, total body irradiation;

^†5 new patients + 2 already used in the validation dataset (however, PK profiles used at this step were not used for model development).

All patients received a reduced intensity conditioning regimen prior to HSCT. The graft source was peripheral blood stem cells for 43 patients (96%) and cord blood for the other two (4%). T-cell depletion with anti-T lymphocyte globulin (ATG) was used in 40 patients (89%). Patients received CsA alone in the case of a HLA-sibling donor (n = 11) or CsA combined with mycophenolate mofetil in the case of a matched, unrelated donor (n = 29) or a HLA-sibling donor but no ATG administration (n = 5). CsA was administered orally at a dose of 3 mg kg⁻¹ twice daily starting 3 days before engraftment (day −3) and blood trough concentrations were monitored twice a week. MMF was given orally at an initial dose of 1 g three times daily, further adjusted to achieve a trapezoidal MMF AUC(0,8 h) of 30 mg l⁻¹ h (derived from the target used in renal transplantation). Accordingly, for CsA, a target of AUC(0,12 h) of 4.3 mg l⁻¹ h that was previously proposed in renal transplant patients was applied [3]. If no GVHD was noted, MMF and CsA were tapered progressively over 4 weeks, starting from day 60 for MMF and day 100 for CsA.

Blood collection

Blood samples were collected in EDTA tubes. One patient had four sampling periods, eight patients had three, 21 had two and 17 had one. At each sampling period, 10 samples were collected at pre-dose and 0.33, 0.66, 1, 2, 3, 4, 6, 8 and 12 h after CSA dosing. Blood samples were stored at −20°C until analysis.

Ciclosporin assay

CsA blood concentrations were measured using a validated turbulent-flow chromatography-tandem mass spectrometry technique [8]. Briefly, online extraction was performed at 1.25 ml min⁻¹ on a Cyclone P®, 50 μm particle size (50 × 0.5 mm, i.d.) column (Thermo Fisher, Les Ulis, France) in alkaline conditions. Chromatographic separation was performed in acidic conditions (phase A 0.1% formic acid in water and phase B 0.1% formic acid in methanol) using a Propel MS C₁₈, 5 μm (50 × 3.0 mm, i.d.) column (Thermo Fisher, Les Ulis, France) kept at 60°C with a constant flow rate of 300 μl min⁻¹. Detection was performed using a TSQ Quantum Discovery tandem mass spectrometer equipped with an orthogonal electrospray ionization source and controlled by the XCalibur software (Thermo Fisher, Les Ulis, France). Tandem mass spectrometry detection was performed in the positive ion, multiple reaction monitoring (MRM) mode following three transitions for ciclosporin (m/z 1220.0→1203.0 for quantification and m/z 1220.0→1185.0 and m/z 1220.0→425.0 for confirmation) and two transitions (m/z 1234.0→1217.0 for quantification and m/z 1234.0→119.0 for confirmation) for its analogue ciclosporin D, used as internal standard (IS). To 100 μl of whole blood were added 200 μl of a methanol/aqueous zinc sulfate (70:30 v/v) containing the internal standard at 25 μg l⁻¹. The mixture was vortex mixed for 30 s, centrifuged at 13000 rev min^–1 and the supernatant was introduced into a 200 μl vial for injection. Calibration standards at 0, 10, 20, 50, 100, 200, 500, 1000 and 2000 μg l⁻¹ were prepared by spiking blank whole blood with CsA. The limits of detection (LOD) and quantification (LOQ) were 10 μg l⁻¹ and 20 μg l⁻¹ and calibration curves obtained using quadratic regression from the LOQ to 2000 μg l⁻¹ yielded r² > 0.998. Inter-assay precision and accuracy were assessed by analyzing the MassCheck® Immunosuppressants Whole Blood Controls (Chromsystems Instruments & Chemicals GmBH, München, Germany) at four levels on 5 independent days, intra-assay precision and accuracy by analyzing five replicates of the four levels on the same day. The method showed good inter-assay precision and accuracy with relative standard deviation (RSD) between −3.1 and 11.8% and mean relative error (MRE) between 4.0 and 11.7%, as well as good intra-assay precision and accuracy with RSD between −1.1 and 9.1% and MRE between 1.8 and 6.4%.

Pharmacokinetic modelling

Global strategy

All the PK profiles obtained from the 45 HSCT patients were studied using three techniques in parallel, each involving pharmacokinetic modelling and Bayesian estimation of CsA AUC(0,12 h) using a limited blood sampling strategy. With the aim of validating the PK models and Bayesian estimators, the population was randomly divided into a model building subset of 72 PK profiles obtained from 40 patients and a model validation subset of 15 other PK profiles, obtained from two patients used in the development dataset and five other patients. In fact, the number of occasions was not similar among the patients. Consequently, intra-individual variability was not explored and the randomization between model building and validation dataset was based on the available occasions, not on the patients.

Non-linear mixed effects modelling (nonmem)

The distribution of population parameters was studied with nonmem® version VI (GloboMax® LLC) using Wings for nonmem® version 614 (developed by N. Holford, available from http://wfn.sourceforge.net) [9]. Population pharmacokinetic analyses were performed using the first order conditional estimation (FOCE) method with INTER to improve the estimation of pharmacokinetic parameters and their variability. According to our previous work [2], we used a two compartment model with first order elimination and an Erlang distribution to describe the absorption process. A combined (i.e. additive and proportional) error model dependent on the concentration was used to describe the residual variability. The codes and data file structures for this model were previously published [2].

Iterative two stage modelling (ITS)

A previously published two compartment, open model with one gamma law to describe the absorption phase was used [10,11]. The population pharmacokinetic parameters were determined by an iterative two stage (ITS) method, using our own program following a previously published procedure [12,13]. A logistic error model dependent on the concentration was used to describe the residual variability.

Non-parametric modelling

Unlike parametric methods, which make the assumption of a normal or log normal distribution of the pharmacokinetics parameters, non-parametric methods can cope with any type of distribution. We used the same model as for the iterative two stage approach. This model was implemented in a recently released R-package called Pmetrics [14] using the non-parametric NPAG algorithm. A second degree polynomial error model dependent on the concentration was used to describe the residual variability.

Covariate analysis

The screening and selection of covariates was performed using a classical procedure [15]. Briefly, first, using the post hoc parameters from nonmem, Pmetrics and ITS, Spearman correlation tests were performed to explore potential relationships between individual parameters and individual covariates. The following covariates were tested: haemoglobin, haematocrit, total bilirubin, creatinine, albumin, ALAT, ASAT and bodyweight. Secondly, if a relationship was detected, the covariate was introduced into the model and its actual influence on the targeted PK parameter was evaluated based on the objective function value (OFV) for nonmem (P < 0.001, 1 d.f.; i.e. a decrease of 10.83 in OFV), or based on the AIC criteria for Pmetrics and ITS (decrease of 10.83 in nested models). The clinical relevance of the covariates was also appraised by evaluating the decrease in unexplained inter-patient variability.

Statistical analyses were all performed using R software version 2.15.1 (R foundation for statistical computing, http://www.r-project.org).

Evaluation of the models

Evaluation of the models was based on visual inspection of observed vs. predicted (population and individual) concentration plots, weighted residuals vs. concentrations and conditional weighted residuals vs. concentration for nonmem as recommended by Hooker et al. for FOCE methods [16] (error model depending on the concentration). Then visual predictive checks (VPC) were used to evaluate the accuracy and robustness of the model. A total of 1000 replicates of the original dataset were simulated using the final model to generate expected concentrations and their 90% prediction intervals. The observed data were overlaid on the prediction intervals and compared visually. The VPC was based on median, dose-normalized concentrations. Furthermore, these data were used to develop a Bayesian estimator in an independent data set of profiles.

Building of Bayesian estimators

Using each final population pharmacokinetic model and data of the building group, the best limited sampling strategy (LSS) among the combinations of a maximum of three sampling times among those within the first 4 h after drug intake was determined using the d-optimality criterion [17]. Then, the predictive performance of the Bayesian estimators developed using the best LSS was evaluated in the validation group of 15 pharmacokinetic profiles. For this analysis, the Bayesian estimates of the inter-dose AUC (i.e. AUC(0,12 h)) obtained with the three approaches were compared with the reference AUC obtained using the linear trapezoidal rule (AUCtrap) applied to the full profiles, and the bias (mean prediction error, MPE) and precision (root mean squared prediction error, RMSE) were calculated as recommended by Sheiner & Beal [18]. Of note, for 42 pharmacokinetic profiles, C12h was missing. To calculate AUCtrap, this value was replaced by the lower of C0 or the concentration at the 8th hour, assuming that steady-state was reached.

Reliability of dose adjustment when combining the three Bayesian estimators

First, the AUC Bayesian estimates obtained using the three approaches were compared using Bland–Altman graphs and a Kruskal–Wallis test.

Second, for each profile, we determined the theoretical dose to reach an AUC target of 4.3 mg l⁻¹ h [3] using each of the Bayesian estimates as well as the AUCtrap, based on the proportionality rule: dose to reach the 4.3 mg l⁻¹ h target = (4.3*current CSA dose)/estimated AUC.

The dose-predictive performance of each Bayesian estimate was estimated by calculating the bias with respect to the dose proposed based on the AUCtrap.

Third, we explored different strategies that could be routinely employed to perform dose adjustments using AUC estimates from the three PK approaches: (i) mean of the three dose proposals, (ii) exclusion of one of the three values if too different from the two others (difference > 15%) and the arithmetic mean of the remaining values. For each strategy, the bias between the doses proposed using this combined information and those proposed based on AUCtrap was calculated.

Results

Patient characteristics

The characteristics of the patients and the time-dependent covariates of the pharmacokinetic profiles used for model development and validation are presented in Table 1.

Pharmacokinetic models

The results obtained with non-linear mixed effect modelling using nonmem, based on a structural model with two compartments, first order elimination and Erlang distribution with five sequential delay compartments are presented in Table 2. This model included inter-patient variability on the absorption rate (K_tr), CL/F, apparent inter-compartmental clearance (Q/F) and apparent central volume of distribution (V_c/F). The apparent peripheral volume of distribution was arbitrarily fixed to 500 l. Estimation imprecision for all the other parameters was less than 13.1%.

Table 2.

Parameters of the pharmacokinetic model developed using nonmem

Parameter	Population mean estimate	SE	Inter-patient variability estimate (%)	95% CI
Ktr (h−1)	5.72	0.42	50	30–70
Q/F (l h−1)	33.7	4.4	72	31–113
Vc/F (l)	222	24	57	32–82
Vp/F (l)	500	NA	NA	NA
CL/F (l h−1)	41.2	2.97	40	18–64

Proportional error = 12.53% and additive error = 0.023 mg ml⁻¹; CI, confidence interval; CL, clearance; F, oral bioavailability; K_tr, absorption rate; Q, inter-compartmental clearance; SE, standard error; V_c, central volume of distribution; V_p, peripheral volume of distribution.

The estimates of parameters and inter-patient variability obtained with ITS and Pmetrics based on a two compartment model with first order elimination and one gamma law to describe the absorption phase are presented in Table 3. This model included seven parameters: the modelled trough concentration (C₀), the shape (A) and scale (B) of the gamma law, the disposition coefficients following an intravenous bolus administration of a unit dose (FAIV and FBIV) and the disposition rate constants of the two compartments (alpha and beta). Except for C₀, all the parameter estimates were different between the two program, and the inter-patient variability was larger with Pmetrics.

Table 3.

Parameters of the pharmacokinetic model developed using ITS and Pmetrics

ITS			Pmetrics
Parameters	Mean	CV	Parameters	Mean	CV
C0	0.11	54.5%	C0	0.11	54.5%
A	5.22	50.2%	A	9.31	104.9%
B	4.06	51.5%	B	6.95	105.3%
FAIV	0.49	73.5%	FAIV	1.03	102.9%
Alpha	1.31	70.2%	Alpha	5.68	70.1%
FBIV	0.24	54.2%	FBIV	0.77	70.1%
Beta	0.29	41.4%	Beta	0.63	120.6%

CV is the inter-patient coefficient of variation; C0 (mg/L) is the modelled trough concentration standardised to a 100 mg dose; A (dimensionless) is shape and B (h⁻¹) is scale of the gamma law; FAIV and FBIV (mg/L) are the disposition coefficients following an intravenous bolus administration of a unit dose; alpha and beta (h⁻¹) are the disposition rate constants of the two compartments.

Covariate analysis

Using the nonmem approach, haematocrit was significantly associated with ciclosporin apparent clearance (OFV decreased by 17 points). However, as the addition of this covariate decreased the precision of IPV estimation, it was not retained in the final model. With the ITS and Pmetrics approaches, none of the tested covariates was retained.

Internal validation

The scatter plots of individually predicted vs. observed concentrations and population predicted vs. observed concentrations showed no major bias, whatever the PK approach (Figure 1). Weighted residuals were homogeneously distributed over the concentration range and showed a normal distribution (Figure 2).

Figure 1.

Scatter plots of individual model-predicted concentrations and population model-predicted concentrations vs. observed concentrations for the three modelling approaches

Figure 2.

Weighted residuals (WRES) and conditional weighted residuals (CWRES) vs. individual predicted concentrations and histogram of weighted residuals for the three modelling approaches

The final models obtained using the three approaches were evaluated using the VPC normalized for a median dose of 190 mg of CsA (Figure 3), showing that the average prediction of the simulated data matched the observed concentration–time profiles and that the variability was reasonably estimated whatever the approach, with a wider dispersion of quartiles for Pmetrics compared with parametric methods.

Figure 3.

Dose-normalized visual predictive check obtained for final models derived from 1000 simulations and standardized to a 190 mg dose for the three modelling approaches. Shown are comparisons between the observed ciclosporin concentrations (circles) and the 5th (bottom dashed line), 50th (solid line) and 95th (top dashed line) percentiles of the simulated data

External validation

Population parameters obtained with the three approaches were used independently as priors for Bayesian estimation using a limited sampling strategy for inter-dose AUC(0,12 h) estimation in the independent validation dataset. Different sampling times were evaluated and the 0, 1 h and 4 h schedule was selected as it was associated with the lowest d-optimal criterion value. Bayesian estimation using this limited sampling strategy was characterized by accurate estimation of AUC(0,12 h): nonmem mean bias = 2.05%, RMSE = 13.02%; ITS mean bias = 4.61%, RMSE = 11.20%; Pmetrics mean bias = 0.30%, RMSE = 10.47%. Only two, one and one out of the 15 estimated AUCs showed a difference with respect to the trapezoidal AUC outside the ± 20% interval, for nonmem, ITS and Pmetrics, respectively (Table 4).

Table 4.

Relative bias and precision for the 0, 1, 4 h sampling schedule with the three modelling approaches with respect to the reference AUC(0,12 h)

Software	Mean bias (%)	Bias SE (%)	Median bias (%)	Range (%)	RMSE (%)	Number outside ± 20%
nonmem	2.05	13.31	−1.83	−17.51 to 38.00	13.02	2
ITS	4.61	10.56	2.07	−14.77 to 24.99	11.20	1
Pmetrics	0.30	10.47	−0.58	−12.01 to 21.91	10.47	1

SE is standard error; RMSE is root mean squared prediction error.

Model comparison

Bland–Altman analysis (Figure 4) showed that the ITS approach had the lowest relative bias with respect to the reference, trapezoidal AUC. However, no statistical difference in AUC was found between the three approaches or with the reference AUC (Kruskal–Wallis test P = 0.9063).

Figure 4.

Bland–Altman plot showing the relative bias between estimated and reference AUC(0,12 h) vs. the reference AUC(0,12 h) (calculated using the trapezoidal method) for the three modelling approaches

Reliability of dose adjustment when combining the three Bayesian estimators

The results of dose estimation using the three Bayesian estimators compared with the reference AUC are presented in Table 5. Although the second strategy for combining the results of the three approaches allowed lower bias in dose proposal compared with the reference AUC, the difference between the two strategies was not statistically significant.

Table 5.

Comparison of the doses proposed to achieve a 4.3 mg l⁻¹ h AUC(0,12 h) by the three Bayesian estimators and two combination strategies, with those derived from the reference AUC(0,12 h)

Patient	Proposed dose						Bias proposed/reference
	Trapezoidal (reference) method†	Pmetrics	ITS	nonmem	Combined information Method 1	Combined information Method 2	Combined information Method 1	Combined information Method 2
1‡	180	140	170	180	160	180	−11.11%	0.00%
2‡	120	110	120	120	120	120	0.00%	0.00%
3‡	110	140	130	130	130	130	18.18%	18.18%
4	220	260	220	230	240	240	9.09%	9.09%
5	230	190	200	210	200	200	−13.04%	−13.04%
6	440	390	350	320	350	350	−20.45%	−20.45%
7	90	100	90	100	100	100	11.11%	11.11%
8	200	170	170	170	170	170	−15.00%	−15.00%
9	150	120	130	140	130	130	−13.33%	−13.33%
10	120	140	120	120	130	130	8.33%	8.33%
11	170	200	150	170	170	170	0.00%	0.00%
12	60	90	60	60	70	60	16.67%	0.00%
13	180	190	160	170	170	170	−5.56%	−5.56%
14	70	80	80	80	80	80	14.29%	14.29%
15	200	190	200	200	200	200	0.00%	0.00%
Mean ± SD relative bias	Reference	0.04 ± 0.20	−0.04 ± 0.11	−0.01 ± 0.11	−0.0005 ± 0.13	−0.004 ± 0.11

^†Trapezoidal method: proposed dose derived from the trapezoidal AUC(0,12 h). Combined information, method 1: the dose proposed corresponds to the arithmetic mean of the doses proposed using the three BE. Combined information, method 2: exclusion of one of the three values if too different from the two others (difference > 15%) and arithmetic mean of the remaining doses in all cases.

^‡Corresponds to the two patients already represented in the development dataset, but the PK profiles used at this step were not used for model development.

Discussion

In the present study in 45 bone marrow transplant patients, we employed three different approaches to develop efficient pharmacokinetic models of ciclosporin in this population, and Bayesian estimators able to predict accurately patient exposure using limited sampling strategies.

Our objective was not the strict comparison of three PK approaches in terms of parameter values and their precision of estimation, nor was it to rank the three approaches. Rather, we compared the abilities of three independent Bayesian approaches to estimate efficiently individual CsA AUC(0,12 h) and subsequent dose adjustments to achieve a target AUC in bone marrow transplant recipients, using fewer samples than have traditionally been used. We evaluated the concordance of the dose recommendations and whether combining dose recommendations could improve the agreement with those made from full PK profiles. Parametric (ITS and nonmem) and non-parametric (Pmetrics) methods, although yielding very different PK parameter estimates, gave similar results in terms of AUC(0,12 h) bias, RMSE and % of estimates outside the clinically acceptable ±20% interval. Moreover, the simultaneous use of the three tools brings an additional benefit. The estimated AUCs outside the ±20% interval in the validation dataset are not the same with the three methods. We compared here two strategies for combining the dose recommendations provided by the three Bayesian estimators: (i) the arithmetic mean of all three proposed doses; and (ii) exclusion of one of the three values if too different from the two others (difference > 15%) and arithmetic mean of the remaining doses. For each method we compared the dose finally recommended with that derived from the reference (full profile, trapezoidal) AUC. Although the second strategy was marginally better, overall both strategies were similar.

Few PK studies of CsA in bone marrow transplant patients have been published. Hadjibabaie et al. employed multiple regression analysis (MRA) in 35 patients to estimate CsA AUC using a limited number of samples drawn within the dosing interval [19]. However, limited information about the fit quality was provided and the data given do not show an accurate estimation of the AUC. Moreover, no internal or external validation was performed. MRA approaches in general have major drawbacks. They can only be applied in an exact copy of the sampling schedule used to develop the regression equation, errors in timing lead to errors in estimation and attempts of extrapolation to other populations generally fail [20]. Even if sometimes helpful when rigorously validated and appropriately used, multiple linear regression equations are not pharmacokinetic tools as they do not refer to any kind of pharmacokinetic model or parameters. Using data collected from 18 HSCT recipients given oral CsA, Wilhelm et al. developed a PK model using nonmem [6]. In a second step, the authors employed a Bayesian fitting procedure using the MW/PHARM program and determined that a C0-C2-C3 sampling schedule allowed AUC estimation with a reasonable bias. Additionally, they proposed a multilinear regression equation to apply this LSS in the routine. The authors used a jacknife method to validate this tool, as no independent validation group was available. Recently, Eljebari et al. used nonmem to develop a PK model in 30 Tunisian HSCT patients. They found that the C0.5, C2 and C4 sampling schedule was associated with a good bias (AUC bias of −1.03%) and precision (RMSE of 12.07%) in a validation dataset of 30 patients [5]. Zhou et al. developed a popPK model with nonmem in Chinese allogeneic stem cell transplants using only CsA trough concentrations and proposed a multiple linear regression for AUC prediction [21]. The same team later developed a similar model using C0 and C2 concentrations [22]. The authors used a one compartment model to estimate K_a, V and CL. However, the availability of C0 does not provide very much information on elimination and none at all on K_a. Indeed, the inter-patient variability estimated for all parameters was narrow compared with our results in the present study. Moreover, the authors only performed an internal validation with bootstrap and no validation in an external group of patients was performed. The half-life of CsA in these studies was about 10-fold higher than the one estimated in the present study whatever the method used.

Similarly to Wilhelm et al. [6] and Eljebari et al. [5], no covariate was included in our three final models, although for nonmem a significant decrease of the OFV was found when introducing the haematocrit on apparent clearance. Haematocrit is a clinically relevant covariate due to the fixation of CsA on red blood cells, but its introduction in the model was associated with a worse estimation of IPV. The influence of the post-transplantation sampling time could not be investigated because only samples at early periods were available.

A wider dispersion of PK parameters was found with Pmetrics, probably because in non-parametric methods, parameter distribution is not constrained to normality, which can also explain the larger quartile distribution noted with VPC analysis. The non-parametric methods may better detect outliers and sub-populations [14], hence increasing the variance of parameter values in the sample population.

In conclusion, three independent modelling methods were used to develop PK models of CsA after HSCT. Limited sampling, Bayesian estimation strategies showed that each model was able to predict inter-dose CsA AUC with minimal bias relative to more intensive sampling. These three Bayesian estimators may be useful to users of any one of the three methods, or may be combined to increase users' confidence in dose calculations performed in routine clinical settings. They are now implemented and combined in our ISBA website to provide the most accurate results to the HST community.

Competing Interests

All authors have completed the Unified Competing Interest form and declare no support from any organization for the submitted work, no financial relationships with any organizations that might have an interest in the submitted work in the previous 3 years and no other relationships or activities that could appear to have influenced the submitted work.

We thank Karen Poole for manuscript editing. The authors have no conflict of interest to declare.

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Appendix S1

Brief description of the three modeling approaches