Metrics for External Model Evaluation with an Application to the Population Pharmacokinetics of Gliclazide

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Abstract
Purpose The aim of this study is to define and illustrate metrics for the external evaluation of a population model. Materials and Methods In this paper, several types of metrics are defined: based on observations (standardized prediction error with or without simulation and normalized prediction distribution error); based on hyperparameters (with or without simulation); based on the likelihood of the model. All the metrics described above are applied to evaluate a model built from two phase II studies of gliclazide. A real phase I dataset and two datasets simulated with the real dataset design are used as external validation datasets to show and compare how metrics are able to detect and explain potential adequacies or inadequacies of the model. Results Normalized prediction errors calculated without any approximation, and metrics based on hyperparameters or on objective function have good theoretical properties to be used for external model evaluation and showed satisfactory behaviour in the simulation study. Conclusions For external model evaluation, prediction distribution errors are recommended when the aim is to use the model to simulate data. Metrics through hyperparameters should be preferred when the aim is to compare two populations and metrics based on the objective function are useful during the model building process.