Evaluating pharmacokinetic/pharmacodynamic models using the posterior predictive check.

Area of Science:

• Pharmacometrics
• Statistical Modeling
• Model Evaluation

Background:

• The posterior predictive check (PPC) is a key tool for evaluating statistical models.
• Its application in pharmacokinetic (PK) and pharmacodynamic (PD) modeling requires careful examination.
• Understanding PPC performance is crucial for reliable model assessment in drug development.

Purpose of the Study:

• To investigate the properties of the posterior predictive check (PPC) for pharmacokinetic (PK) and pharmacodynamic (PD) model evaluation.
• To assess the type-I error rate and statistical power of the PPC under various simulation and analysis scenarios.
• To determine the influence of different statistics and posterior distribution approximations on PPC performance.

Main Methods:

• Simulated extensive sampling data from single individuals using simple PK/PD and error models.
• Applied PPC to analyze models, comparing them against simulation models (null vs. alternative hypotheses).
• Evaluated five specific PK/PD models (mono- and biexponential PK, Emax and sigmoid Emax PD) with different error structures.

Main Results:

• The PPC demonstrated conservatism under the null hypothesis, rarely invalidating correct models.
• Statistical power was generally low, particularly for statistics that were functions of both data and parameters.
• No significant advantage was observed for different methods of approximating the posterior distribution on model parameters.

Conclusions:

• The PPC is a reliable tool that tends to be conservative, minimizing incorrect model rejections.
• Enhancing the power of PPC requires careful selection of statistics, especially those not heavily reliant on parameter estimates.
• The choice of posterior approximation method did not substantially impact PPC performance in this study.