External validation with sparse, adaptive-design data for evaluating the predictive performance of a population pharmacokinetic model of tacrolimus

1
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
immunosuppr-essant used to prevent and treat
organ rejection in paediatric liver
transplantation. Tacrolimus has a narrow
therapeutic window and displays considerable
between and within-subject pharmaco-kinetic (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. 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
VPCs (pcVPC), were constructed using the PsN
software and the Xpose graphical analysis
toolpack.
MPE 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.



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
post-transplantation phase.
Population prediction of samples drawn prior to a
posteriori dose individualisation
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