External validation with sparse, adaptive-design
data for evaluating the predictive performance
of a population pharmacokinetic model of
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.
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 Prediction corrected visual predictive checks with the three compared models
PK model of tacrolimus with the intent of
capturing this process. This model has MPE RMSE
been used to suggest a revised initial Objectives: Wallin 1.1 5.8
dosing schedule and forms the basis for a To evaluate the predictive performance of Staatz 2.2 7.9
dose adaptation tool. our population model, in comparison to Sam 2.1 7.7
two previously published models (2, 3),
Mean prediction error and root mean squared error
To validate the model and compare it to using data collected from an independent with the three compared models
previously published models, an group of paediatric liver patients and
independent dataset was used. The based on model diagnostics suitable for
nature of this dataset, comprising of use with TDM data. Accuracy of early Results:
sparse adaptive-type TDM data, measurements as well as avoiding Accuracy and precision expressed as
necessitate some caution in model fit overprediction was of special concern. MPE and RMSE was better for the
evaluation. Population predictions can proposed model compared to the Sam
only be used for data prior to and Staatz models. Graphical diagnostics
individualization, and individual confirmed the increased predictive
predictions does not serve as an unbiased Data on the PK of tacrolimus in the first capability with the proposed model.
guide in model structure discrimination. two weeks following liver transplantation
was collected retrospectively from the
medical records of 12 paediatric patients.
Commonly used simulation based Population predicted drug concentrations
diagnostics are also unsuitable when from the three models were compared to
using adaptive design data, but visual measured concentrations using samples
evaluation of the predictive performance drawn prior to TDM associated dosage
can be performed with prediction adaption. Individual predicted drug
corrected VPC (pcVPC), where observed concentrations based on all data were
and simulated observations are compared to all the measured
normalized based on the population concentrations.
DV 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 Baysian predictions based on only the previously
corrected VPC:s (pcVPC), were measured concentrations, mimicking Bayesian
constructed using the PsN software and forecasting.
the Xpose graphical analysis toolpack.
Population prediction of samples drawn prior Simulation based diagnotics was a
to a posteriori dose individualisation 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-
1. M Bergstrand, A.C Hooker, J.E Wallin, M.O Karlsson. Prediction Corrected Visual
Predictive Checks. ACoP (2009) Abstr F7.
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