After spending weeks on modelling with little progress it occurred to us that the problem might lie with the diagnostic – not the model.
Background: A VPC (visual predictive check) is a graphically representation of multiple simulations of a model. Percentiles of both the observed and the simulated data are plotted against an independent variable (typically time); comparison of the percentiles allows the modeller to assess the models ability to reproduce the central tendency and the variability in the observed data. The VPC has become a cornerstone diagnostic method in model evaluation. It is often useful for comparing models, for suggesting how a model might be improved and for assessing how useful a model might be (1). However, in cases where predictions differ largely due to different dosing or influential covariates the interpretation of the traditional VPC may be misleading; and in cases where dose is adapted to drug concentrations (or effects) the traditional VPC can be completely uninformative. In such cases, the prediction corrected VPC (pcVPC) has been suggested to be a useful alternative (2). Dosage of tacrolimus, a key immunosuppressant agent used in solid organ transplantation, is currently adjusted according to trough concentration measurements due to its large pharmacokinetic variability and narrow therapeutic window. Use of a pcVPC during population PK (popPK) modelling of tacrolimus may be more useful than a traditional VPC.
Aims: The primary goal of this research is to develop a popPK model of tacrolimus in adult kidney transplant recipients that can then be used for future Bayesian forecasting based- therapeutic drug monitoring of this agent. This abstract/poster attempts to demonstrate a case where the traditional VPC inappropriately caused model rejection.
Methods: Pharmacokinetic and demographic data were collected from kidney transplant recipients from the Princess Alexandra Hospital in Brisbane, Australia. PopPK modelling was performed using NONMEM 7. Traditional and prediction corrected VPCs were created in R (www.r-project.org) with XPOSE4 (www.xpose.sf.net) from a 1,000 simulations performed in NONMEM7 using PsN (www.psn.sf.net).
Results: A total 1,554 tacrolimus concentration-time measurements were collected from 173 patients on 326 occasions. Trough (~20% of data) as well as non-trough tacrolimus concentrations were available for model development. In the modelling process traditional VPCs changed little and repeatedly caused model rejection. Typically the VPC would satisfactorily describe the central tendency, but fail to describe the variability. Eventually, it occurred to us that the traditional VPC might be inappropriate and instead we adopted the pcVPC. The difference was remarkable; a pcVPC of our basic model (2-compartment model with lag time absorption) now describes both the central tendency and the variability in a satisfactory way.
Discussion: We present a modelling scenario where the traditional VPC is significantly different from the pcVPC; the former caused model rejection, the latter acceptance. In the case at hand we believe that the pcVPC is an appropriate diagnostic as tacrolimus doses ranged from 0.5 to 18 mg [10th;90th percentile 3mg;8mg] and individual dosing is adapted by the physician to meet a target concentration.
Bergstrand et al(2) offer no severe pitfalls for using the pcVPC, but point out that one possible drawback is that the pcVPC changes the scale for predictions and observations to a less intuitive one. While this might be reason enough not to use the pcVPC as first choice in standard popPK model building we believe that our example demonstrates that the pcVPC is valuable to consider before rejecting a model.
References:
(1) Karlsson MO, Holford N. A tutorial on visual predictive checks. PAGE 17 (2008). Abstract 1434. www.page-meeting.org/?abstract=1434. Accessed January 2012.
(2) Bergstrand M, Hooker AC, et al. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS Journal 2011;13(2): 143-51.