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External validation with sparse, adaptive-design
data for evaluating the predictive performance
of a population pharmacokinetic model of
tacrolimus
Johan E. Wallin1,2, Martin Bergstrand1, Mats O. Karlsson1, Henryk Wilczek3, Christine E. Staatz1,4
1. Department of Pharmaceutical Biosciences, Uppsala University, Sweden, 2. PK/PD/TS, Eli Lilly, Erl Wood Windlesham, UK, 3. Division of Transplantation
Surgery, Karolinska Institute, Stockholm, Sweden 4. School of Pharmacy, University of Queensland, Brisbane, Australia.
Introduction:
Tacrolimus is a potent immunosuppressant used to prevent and treat organ
rejection in paediatric liver transplantation.
Tacrolimus has a narrow therapeutic
window and displays considerable
between and within-subject pharmacokinetic (PK) variability. The PK of
tacrolimus change markedly in the
immediate post-transplant period. We
have previously developed a population
PK model of tacrolimus with the intent of
capturing this process. This model has
been used to suggest a revised initial
dosing schedule and forms the basis for a
dose adaptation tool.
To validate the model and compare it to
previously
published
models,
an
independent dataset was used. The
nature of this dataset, comprising of
sparse
adaptive-type
TDM
data,
necessitate some caution in model fit
evaluation. Population predictions can
only be used for data prior to
individualization,
and
individual
predictions does not serve as an unbiased
guide in model structure discrimination.
Commonly
used
simulation
based
diagnostics are also unsuitable when
using adaptive design data, but visual
evaluation of the predictive performance
can be performed with prediction
corrected VPC (pcVPC), where observed
and
simulated
observations
are
normalized based on the population
prediction (1).
Prediction corrected visual predictive checks with the three compared models
Objectives:
To evaluate the predictive performance of
our population model, in comparison to
two previously published models (2, 3),
using data collected from an independent
group of paediatric liver patients and
based on model diagnostics suitable for
use with TDM data. Accuracy of early
measurements as well as avoiding
overprediction was of special concern.
Methods:
Data on the PK of tacrolimus in the first
two weeks following liver transplantation
was collected retrospectively from the
medical records of 12 paediatric patients.
Population predicted drug concentrations
from the three models were compared to
measured concentrations using samples
drawn prior to TDM associated dosage
adaption.
Individual predicted drug
concentrations based on all data were
compared
to
all
the
measured
concentrations.
PRED
Population prediction of samples drawn prior
to a posteriori dose individualisation
RMSE
Wallin
1.1
5.8
Staatz
2.2
7.9
Sam
2.1
7.7
Mean prediction error and root mean squared error
with the three compared models
Results:
Accuracy and precision expressed as
MPE and RMSE was better for the
proposed model compared to the Sam
and Staatz models. Graphical diagnostics
confirmed the increased predictive
capability with the proposed model.
To evaluate the models’ potential for
Bayesian forecasting in dose adaptation,
individual predicted drug concentrations
based on prior samples were compared to
measured
concentrations.
Model
predictive performance was compared by
calculation of MPE and RMSE. Prediction
corrected
VPC:s
(pcVPC),
were
constructed using the PsN software and
the Xpose graphical analysis toolpack.
DV
MPE
Baysian predictions based on only the previously
measured concentrations, mimicking Bayesian
forecasting.
Conclusions:
Simulation based diagnotics was a
valuable aid in determining that the
proposed PK model predicted the
validation data set reasonably well, and
performing better than the previously
published models in this early posttransplantation phase.
References:
1.
M Bergstrand, A.C Hooker, J.E Wallin, M.O Karlsson. Prediction Corrected Visual
Predictive Checks. ACoP (2009) Abstr F7.
[http://www.go-acop.org/sites/all/assets/webform/Poster_ACoP_VPC_091002_two_page.pdf]
2.
Sam WJ, Aw M, Quak SH, et al. Population pharmacokinetics of tacrolimus in Asian
paediatric liver transplant patients. Br J Clin Pharmacol 2000; 50 (6): 531.
3.
Staatz CE, Taylor PJ, Lynch SV, Willis C, Charles BG, Tett SE. Population
pharmacokinetics of tacrolimus in children who receive cut-down or full liver transplants.
Transplantation 2001; 72 (6): 1056.
Posthoc Bayesian individual predictions of the three compared models representing
the overall fit to data