Population pharmacokinetics and dosing regimen optimisation of
tacrolimus in Chinese pediatric hematopoietic stem cell
transplantation patients
Abstract
1. Several tacrolimus population pharmacokinetic (PPK) models in hematopoietic
stem cell transplantation (HSCT) patients have been set up to recommend an
optimal dosage schedule. However, the PPK model of Chinese pediatric HSCT
patients has not been reported. The study is to investigate whether published PPK
models of HSCT patients can be used to simulate Chinese pediatric HSCT patients
and establish the tacrolimus PPK model of Chinese pediatric HSCT patients.
2. Published PPK models were collected from the literature and assessed using
Chinese pediatric HSCT patients via the individual prediction error method. The
establishment of tacrolimus PPK model in Chinese pediatric HSCT patients were
characterized with nonlinear mixed-effects modeling (NONMEM).
3. Three published HSCT PPK models were identified, two of which could be applied
to our external dataset. However, these models were dissatisfactory in terms of
individual prediction error and hence, inadequate for extrapolation. Finally, a new
tacrolimus PPK model in Chinese pediatric HSCT patients was established. Based
on the simulation results of our model, new initial dosage suggestions were
recommendated. In conclusion, the tacrolimus PPK model in Chinese pediatric
HSCT patients was presented and the model could be used to predict individualized
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dosing regimens in children with HSCT.
Keywords: population pharmacokinetics, tacrolimus, Chinese pediatric hematopoietic
stem cell transplantation, real world study, ursodeoxycholic acid
Introduction
Hematopoietic stem cell transplantation (HSCT) is increasingly used to treat many
malignant and nonmalignant diseases (Jacobson et al., 2001). However, post-
transplant immunologic complications, for example, acute and chronic graft-versus-
host disease (GVHD), are barriers to successful transplantation. Thus, it is critical to
reduce the risk of GVHD. Fortunately, tacrolimus has been used as an drug therapy
for the prevention of GVHD following HSCT (Fay et al., 1995; Nash et al., 1995; Fay
et al., 1996; Nash et al., 1996; Przepiorka et al., 1996; Uberti et al., 1997; Nash et al.,
2000).
However, tacrolimus has a narrow therapeutic range (Venkataramanan et al.,
1995), high concentrations seem to be associated with toxicity and lower
concentrations are connected with an increased risk of acute rejection episodes (Staatz
and Tett, 2004; Passey et al., 2011). Additionally, tacrolimus has considerable inter-
and intra-individual variabilities in pharmacokinetics. Tacrolimus, given orally is
absorbed incompletely with a lag time of average 0.4 h (range 0-2 h) and absorption
rates spanning from very fast to slow (Jusko et al., 1995a). In spite of such variation,
the trough concentrations of tacrolimus correlate well with the area under the
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concentration-time curve (AUC) (Grevel and Kahan, 1991; Jusko et al., 1995a; Jusko
et al., 1995b; Venkataramanan et al., 1995).
Population pharmacokinetics (PPK) can collect pharmacokinetic information
from sparse data in patients (Marsot et al., 2017). What is more, PPK analysis could
distinguish inter- and intra-individual variabilities (Vadcharavivad et al., 2016; Wang
et al., 2018). Hence, PPK has greater statistical power to ascertain the effects of
multiple factors on pharmacokinetics of tacrolimus compared to traditional
pharmacokinetic method (Vadcharavivad et al., 2016; Wang et al., 2018), and makes it
possible to design an optimal dosage regimen.
Several tacrolimus population pharmacokinetic (PPK) models in HSCT have
been established to design an optimal dose schedule (Wallin et al., 2009; Xue et al.,
2009). However, the PPK model of Chinese pediatric HSCT patients has not been
reported. Therefore, it is vital to investigate whether published PPK models of HSCT
patients can be used to simulate Chinese pediatric HSCT patients and to establish
tacrolimus PPK model of Chinese pediatric HSCT patients and formulate an ideal
dose regimen for personalized medicine.
Materials and method
Review of published PPK models
Literatures were collected with the PubMed, Web of Sci, CNKI and Wanfang
databases up to 9 January 2019. The included criteria for publications were as
follows: (I) studies involving HSCT patients with tacrolimus treatment and (II)
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studies involving PPK modeling.
Patients and data collection
Chinese pediatric HSCT patients between June 2015 and June 2018 from Children’s
Hospital of Fudan University were retrospectively analyzed. Drug concentration data
and relevant clinical information were collected from therapeutic drug monitoring
(TDM) records and medical records, respectively. The study was approved by the
Research Ethics Committee of Children’s Hospital of Fudan University.
Information extracted from the medical records included gender, age, weight,
post transplant day (POD), albumin (ALB), globulin (GLB), alanine transaminase
(ALT), aspartate transaminase (AST), creatinine (Cr), Urea (Ur), total protein (TP),
total bile acid (TBA), direct bilirubin (DBIL), total bilibrubin (TBIL), hematocrit
(HCT), hemoglobin (HGB), mean corpuscular hemoglobin (MCH), mean corpuscular
hemoglobin concentration (MCHC) and concomitant drugs.
Dosing and sampling schedule
Tacrolimus was orally administered and the starting dosage was 0.12 mg/kg/day
splited into two doses. The drug concentration of tacrolimus was measured twice
weekly or more frequently if required (e.g., in case of suspicion of intolerance or
adverse events) by therapeutic drug monitoring (TDM). Tacrolimus dose was later
adjusted according to the clinical efficacy and adverse effect as well as its trough
concentration in TDM. All of the blood concentrations were collected before next
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administration and the tacrolimus concentrations used in the current research were
trough concentrations.
Generally, the target trough concentrations range cited was 10-20 ng/ml. The
upper limit of 20 ng/ml comes from the analysis correlating toxicity with higher blood
levels (Wingard et al., 1998; Przepiorka et al., 1999b). The lower limit of 10 ng/ml
was due to the fact that there is less published experience using lower target levels
(Przepiorka et al., 1999a). A number of centers have used an upper level of 15 ng/ml,
which allowed for an interval of 5 ng/ml before getting into the range of increased
risk of nephrotox-icity (Przepiorka et al., 1999a). Therefore, in the present study, the
target therapeutic range is 10-15ng/ml.
Analytical method
Blood concentrations of tacrolimus were measured by Emit® 2000 Tacrolimus Assay
(Siemens Healthcare Diagnostics Inc, Newark, US). Several different measurement
techniques were used in the included studies and there were system deviations among
the different analysis methods (Agrawal et al., 2014). For adjusting the differences,
the tacrolimus concentrations of the external data were converted to their
corresponding equivalents according to previously published bioassay methodology
with the following formulae (Hesse et al., 2002), Equation 1:
MEIA=(EMIT−0.05)/0.96 (1)
where EMIT was the concentration of the external data measured via the enzyme
multiplied immunoassay technique and MEIA was the after-conversion equivalent
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analyzed using the microparticle enzyme immunoassay.
Evaluation of external predictiveness
The external evaluation was carried out by a non-linear mixed-effects modeling
(NONMEM) software (edition 7, ICON Development Solutions, Ellicott City, MD,
USA). The results were performed with the R package (version 3.4.2, http://www.r-
project.org). PPK models from published papers were rebuilt using parameters set
based on the published values. Given the sparse PK sampling, maximum a posterior
(MAP) Bayesian was used to assess the influence of observations on model
predictability (Brooks et al., 2016; Zhao et al., 2016). The predictive performances of
these PPK models with the external data were evaluated using the individual
prediction error method, which compared differences between observations with
individual predictions, Equation 2:
IPE = (IP−OB)/OB×100% (2)
where IPE was individual prediction error, IP represented the individual predicted
concentration and OB was the observation.
Establishment of a new model
Data were analyzed with NONMEM. The first-order conditional estimation method
with interaction (FOCE-I) option was used to estimate pharmacokinetic (PK)
parameters and their variability. One-compartment model with first-order elimination
was used to describe the absorption phase because all the tacrolimus concentrations in
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the study were trough concentration. The PK parameters were comprised of apparent
oral clearance (CL/F) and apparent volume of distribution (V/F). The absorption rate
constant (Ka) of the model was fixed to 4.48h-1 through literature study (Yang et al.,
2015; Wang et al., 2018).
Random effect model
Inter-individual variability was evaluated by Equation 3:
θi =θ×exp (ηi) (3)
where θi was the individual parameter value, θ was the typical population value of
the pharmacokinetic parameter. ηi was symmetrical distribution, which was zero-
mean chance variables with variance term.
Random residual variability was evaluated using Equation 4:
OB=IP×(1+ε1)+ε2 (4)
where OB was the observation, IP represented the individual predicted
concentration. εn represented symmetrical distribution, which was zero-mean chance
variables with a variance.
Covariate model
The correlation between PK parameters and weight was described using Equation 5:
Pi=Pstd×(WTi /WTstd) PWR (5)
Pi represented the ith individual PK parameter, WTi represented the ith individual
weight. WTstd was the standard weight of 70 kg. Pstd represented the typical individual
parameter, whose weight was WTstd. PWR represented the allometric coefficient: 0.75
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for the CL/F and 1 for the V/F (Anderson and Holford, 2008).
The correlation between PK parameters and continuous covariates and categorical
covariates was described using Equations 6 and 7, respectively.
Pi=T(P)×(Covi /Covmedian)θ (6)
Pi=T(P)×(1+θ×Covi) (7)
where Pi was the individual parameter value, T(P) was the typical individual
parameter value. θ was the parameter to be estimated and Covi was the covariate of
the ith individual. Covmedian was the population median for the covariate.
The potential covariates included gender, age, weight, POD, ALB, GLB, ALT,
AST, Cr, Ur, TP, TBA, DBIL, TBIL, HCT, HGB, MCH, MCHC and concomitant
drugs. The covariate model was established in a stepwise way (Yang et al., 2015). To
compare hierarchical models, a likelihood ratio test was adopted. The change in the
objective function values (OFV) caused by the inclusion of a covariate is proportional
to twice the negative log likelihood of the data and approximates a chi-square
distribution. In the univariate analysis, a decrease in the OFV > 3.84 (P < 0.05, degree
of freedom = 1) was used as a criterion for inclusion of the covariate in the base
model. The significant covariate-parameter relationships were reserved in the model.
When a full regression model was built, the model was further testified by dropping
the covariate from each parameter one at a time to acquire the final model. An
increase in the OFV > 6.64 (P < 0.01, degree of freedom = 1) was used as a criterion
for retaining significant covariate-parameter relationships in the model.
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Model validation
An internal validation method of bootstrap was used for assessing the stability and
reliability of the final parameters (Jolling et al., 2005; Brendel et al., 2007). Bootstrap
was produced by repeated random sampling with replacement from the original data.
This procedure was performed with the software package Wings for NONMEM and
repeated 1000 times with different random draws. The medians and 2.5-97.5%
percentiles of the bootstrap result were compared to the final PK parameter estimates.
Visual inspection of routine diagnostic plots, histogram, QQ figures and prediction-
corrected visual predictive check plots were used to evaluate the new model.
Simulation of tacrolimus dosing regimens
The parameter estimates obtained from the final model were used to perform the
initial dosing regimen simulations. The influence of the covariate on the probability to
achieve the target concentration was investigated using Monte Carlo simulations
based on the established model. We estimated the probability to achieve both 10-
15ng/ml based on the established model without drug combination. 1000 virtual
patients were simulated in each of the seven weight groups (5, 7.5, 10, 12.5, 15, 17.5
and 20 kg) and for nine dosing regimens (0.5mg/0.5mg q24h, 1.0mg/0.5mg q24h,
1.0mg/1.0mg q24h, 1.5mg/1.0mg q24h, 1.5mg/1.5mg q24h, 2.0mg/1.5mg q24h,
2.0mg/2.0mg q24h, 2.5mg/2.0mg q24h, 2.5mg/2.5mg q24h).
Result
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Published PPK models
Three studies were included, finally (Figure 1 and Table 1). One study (Wallin et al.,
2009) focused on children and the other two studies (Jacobson et al., 2001; Xue et al.,
2009) had a wide range of ages from children to adult. Because the model from
Jacobson et al (Jacobson et al., 2001) is incomplete (lack of information on apparent
volume of distribution), only two models could be applied to our external dataset.
Evaluation of external predictiveness
The data obtained from 17 Chinese pediatric HSCT patients were available. Patient
characteristics and drug combination were summarized in Table 2 and Table 3,
respectively. As shown in Figure 2, the individual prediction errors obtained from the
two models were not satisfactory and it was required to produce a new model to apply
to Chinese pediatric HSCT patients.
Production of the new model and model evaluation
A one-compartment model with first absorption and elimination best fitted the data.
The PK parameters of tacrolimus, CL/F and V/F, were estimated by NONMEM. The
final covariate models were as follows:
CL/F = 15.4 × (WT/70)0.75 × (1+URSO×0.964) (8)
V/F = 6250 × (WT/70) (9)
where CL/F was apparent oral clearance, V/F was apparent volume of distribution,
WT and URSO were weight and ursodeoxycholic acid, respectively. Figure 3 showed
the covariate relationships.
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Validation of new model
In Figure S1, visual inspection of routine diagnostic plots were shown. In Table 4,
parameter estimates of final model and bootstrap validation were shown. The median
values of the parameter estimate from bootstraps were close to the respective values
from the final population model, and the absolute value of all bias were < 15%,
showing that the estimates for the PK parameters in the final population model were
accurate, and the model was reliable. In Figure S2, the distribution of weighted
residuals for the final model was shown. In Figure S3, the prediction-corrected visual
predictive check plot of the final model was shown. Most of the observed
concentrations are within the 95% prediction intervals from the simulation data,
revealing that the prediction-corrected concentrations were well predicted by the final
model.
Simulation of weight effect at different dose
The predicted median (2.5-97.5%) and probability to achieve the target concentration
with respect to body weight for different dosing regimens were were shown in Table
5. Based on the simulation results of our model, new initial dosage suggestions were
recommendated. The 1.0mg/0.5mg q24h regimen is appropriate for children with a
weight of 5kg; the 1.0mg/1.0mg q24h regimen is suitable for children with a weight
of 7.5kg; the 1.5mg/1.0mg q24h regimen is fit for children with a weight of 10kg; the
1.5mg/1.5mg q24h regimen is appropriate for children with a weight of 12.5kg; the
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2.0mg/1.5mg q24h regimen is appropriate for children with a weight of 15kg; the
2.5mg/2.0mg q24h regimen is appropriate for children with a weight of 17.5kg; the
2.5mg/2.5mg q24h regimen is appropriate for children with a weight of 20kg.
Discussion
Currently, different tacrolimus PPK models have been built in many populations
including renal transplant patients (Zhao et al., 2009; Benkali et al., 2010; Zuo et al.,
2013; Bergmann et al., 2014; Han et al., 2014; Andreu et al., 2015), liver transplant
patients (Wallin et al., 2011; Zhang et al., 2012; Musuamba et al., 2014; Lu et al.,
2015; Yang et al., 2015; Zhu et al., 2015), and lung transplant patients (Monchaud et
al., 2012). However, only several tacrolimus PPK models in HSCT have been
established (Jacobson et al., 2001; Wallin et al., 2009; Xue et al., 2009) and the PPK
model of Chinese pediatric HSCT patients has not been reported. The study is to
investigate whether published PPK models of HSCT patients can be used to simulate
Chinese pediatric HSCT patients and establish the tacrolimus PPK model in Chinese
pediatric HSCT patients.
In our study, three published HSCT PPK models were identified, two of which
could be applied to our external dataset. However, these models were dissatisfactory
in terms of individual prediction error and hence, inadequate for extrapolation. In
Wallin et al study (Wallin et al., 2009), all patients aged from birth to 18 years who
underwent HSCT between 2002 and 2007 at Queen Silvia Children’s Hospital in
Gothenburg, Sweden, and received tacrolimus as initial prophylaxis against GVHD
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were eligible for inclusion in study. Pharmacokinetic, demographic, and other clinical
data were collected retrospectively from patient electronic medical records. However,
the patients were limited to Swede and the effect of concomitant medications is
unknown (Wallin et al., 2009). In Xue et al study (Xue et al., 2009), the age range
was 12-60 years, which was not fitted to our age group.
To explore the influence of demographic features, biological characteristics, and
concomitant medications on tacrolimus CL/F in Chinese pediatric HSCT patients, our
model was built. Our present study is the first report, to our knowledge, of a
population pharmacokinetics model of tacrolimus in Chinese pediatric HSCT patients
based on real world study. The typical values of CL/F and V/F in final tacrolimus
PPK model were 15.4L/h and 6250L. However, in Xue et al study (Xue et al., 2009).
The population typical values of tacrolimus CL and V were 12.1L/h and 686L,
respectively. In Wallin et al study (Wallin et al., 2009), Typical clearance was 106
mL/h/kg-0.75, typical distribution volume was 3.71 L/kg. This may partly explain the
possible mechanism for why our new PPK model differs from other models.
Furthermore, the database used to build models varied from study to study. It was
mainly referring to potential differences in areas of: patient eligibility based on
inclusion/exclusion criteria, patient's baseline disease status, use of concurrent-
medications, and potential differences in their treatment dose regimen and
demographic information. All of these may attribute to the inability of extrapolating
these models to describe the our dataset.
We also examined various covariates on different parameters and the following
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covariates were determined to be meaningful: weight and ursodeoxycholic acid were
included as significant covariates for CL/F, weight was for V/F. Many studies have
demonstrated a non-linear relationship between drug clearance and body weight in
pediatric patients, and it may be well described with allometric scaling using a
coefficient of 0.75 for clearance and 1 for volume (Holford, 1996; Anderson and
Holford, 2008; 2011). Body weight is the most important predictor of clearance and
volume in children with maturation of elimination processes (Anderson and Holford,
2011) and is also considered to be the primary factor determining clearance and
volume because of theory explaining the link between mass, function and structure
and the extensive support for this theory across many orders of magnitude of body
weight (Savage et al., 2008). Therefore, the factor for body weight for clearance may
be expected to scale to weight with a power 0.75 and a coefficient of 1 for volume
(Holford, 1996; Anderson and Holford, 2008; 2011). For ease of comparison with
other results, the body weight is usually standardized to a value of 70 kg (Anderson
and Holford, 2011). It is especially valuable to use a standard when reporting the
results of studies in children and neonates (Anderson and Holford, 2011). The major
differences between age groups of differing body weights require standardization to a
common size to make meaningful comparisons (Anderson and Holford, 2011). Even
if the age groups appear to be comparable, different studies may have substantial
differences in typical weights (Anderson and Holford, 2011). Interpretation of
parameter estimates is more convenient when comparing standard values (Anderson
and Holford, 2011). In addition, biliary elimination is the major excretion pathway for
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tacrolimus (Moller et al., 1999) and ursodeoxycholic acid can promote bile excretion,
increasing tacrolimus clearance.
Although the TDM was not originally designed to research the pharmacokinetics
of tacrolimus, the PPK method provides a powerful tool to extract useful information
from sparse drug concentrations (Thomson and Whiting, 1992) from traditional TDM.
Thus, PPK can promote to optimize the use for tacrolimus to realize satisfactory
therapeutic concentrations. Additionally, it is ethical suitable in studying pediatric
patients prohibited excessive blood sampling compared with traditional
pharmacokinetic studies (Kauffman and Kearns, 1992). Consequently, the tacrolimus
PPK model has clinical value in predicting pharmacokinetic process in individual
pediatric patients who has HSCT condition. In terms of model application, 1000
virtual patients were simulated in each of the seven weight groups and for nine dosing
regimens and new initial dosage suggestions were recommendated. Current starting
dosing recommendations for tacrolimus is based on weight and is fixed at 0.12
mg/kg/day, which is lacking of individualized treatment options. In our study, we
simulated more accurate individualized drug treatment for different body weights.
The 1.0mg/0.5mg q24h regimen is appropriate for children with a weight of 5kg; the
1.0mg/1.0mg q24h regimen is suitable for children with a weight of 7.5kg; the
1.5mg/1.0mg q24h regimen is fit for children with a weight of 10kg; the 1.5mg/1.5mg
q24h regimen is appropriate for children with a weight of 12.5kg; the 2.0mg/1.5mg
q24h regimen is appropriate for children with a weight of 15kg; the 2.5mg/2.0mg
q24h regimen is appropriate for children with a weight of 17.5kg; the 2.5mg/2.5mg
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q24h regimen is appropriate for children with a weight of 20kg.
The same as three published articles, there were limitations in our study. As for
HSCT patients pharmacogenomic consideration hasn’t been used in clinical, whether
the inclusion of genotyping in our model would better explain the variabilities of
tacrolimus in Chinese pediatric HSCT patients should be studied in future. In
addition, small group of patients, use of trough concentrations only instead of
intensive sampling were also limitations in our study.
In a word, the tacrolimus PPK model in Chinese pediatric HSCT patients was
established and the model could be used to predict individualized dosing regimens in
children with HSCT. A large external evaluation of our model will be conducted in
future studies.
Funding
This work was supported by the Clinical Pharmacy Key Specialty Construction
Project of Shanghai under Grant number YZ2017/5; the Young Medical Talents of
Wuxi under Grant number QNRC020; the Young Project of Wuxi Health and Family
Planning Research under Grant number Q201706; the Wuxi science and technology
development guidance plan (medical and health care) under Grant number
CSZON1744; the AOSAIKANG pharmaceutical foundation under Grant number
A201826.
Declaration of interest
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The authors report no declarations of interest. The authors alone are responsible for
the content and writing of this article.
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Figure legend
Figure 1. Overview of the strategy used in the literature search.
Figure 2. Box plots of individual prediction error.
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Individual prediction error, IPE (%)=(IP−OB)/OB×100%
IP: individual predicted concentration; OB: observation concentration.
Blue dashed line and red dashed lines are reference lines indicating IPE% of 0% and
± 30%, respectively.
Figure 3. The covariate relationships.
(A) apparent oral clearance (CL/F) vs. weight (WT)
(B) apparent oral clearance (CL/F) vs. ursodeoxycholic acid (URSO)
(C) apparent volume of distribution (V/F) vs. weight (WT)
Figure S1. Visual inspection of routine diagnostic plots.
(A) observations vs. population predictions (B) observations vs. individual predictions
(C) conditional weighted residuals (WRES) vs. population predictions (D) conditional
weighted residuals (WRES) vs. time after the start of therapy.
Figure S2. Distribution of weighted residuals for the final model.
(A) density vs. weighted residuals (B) quantiles of weighted residuals vs.quantiles of
normal
Figure S3. Prediction-corrected visual predictive check (VPC) for the final model.
The middle red solid line represents the median of the prediction-corrected
concentrations. The lower and upper red dashed lines are the 2.5th and 97.5th
percentiles of the prediction-corrected concentrations, respectively, representing the
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lower and upper limits of the 95% confidence interval of predicted values.
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