Multivariate Exact Discrepancy: A New Tool for PK/PD Model Evaluation

Pharmacokinetic models are evaluated using three types of metrics: those based on estimating the typical pharmacokinetic parameters, those based on predicting individual pharmacokinetic parameters and those that compare data and model distributions. In the third groups of metrics, the best-known methods are Visual Predictive Check (VPC) and Normalised Prediction Distribution Error (NPDE). Despite their usefulness, these methods have some limitations, especially for the analysis of dependent concentrations, i.e., evaluated in the same patient.

In this work, we propose an evaluation method that accounts for the dependency between concentrations.

Thanks to the study of the distribution of simulated vectors of concentrations, the method provides one probability per individual that its observations (i.e., concentrations) come from the studied model. The higher the probability, the better the model fits the individual. By examining the distribution of these probabilities for a set of individuals, we can evaluate the model as a whole.

We demonstrate the effectiveness of our method through two examples. Our approach successfully detects misspecification in the structural model and identifies outlier kinetics in a set of kinetics.

We propose a straightforward method for evaluating models during their development and selecting a model to perform therapeutic drug monitoring. Based on our preliminary results, the method is very promising but needs to be validated on a larger scale.