Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions

Marc Lavielle, Benjamin Ribba

For nonlinear mixed-effects pharmacometric models, diagnostic approaches often rely on individual parameters, also called empirical Bayes estimates (EBEs), estimated through maximizing conditional distributions. When individual data are sparse, the distribution of EBEs can "shrink" towards the same population value, and as a direct consequence, resulting diagnostics can be misleading. Instead of maximizing each individual conditional distribution of individual parameters, we propose to randomly sample them in order to obtain values better spread out over the marginal distribution of individual parameters. We evaluated, through diagnostic plots and statistical tests, hypothesis related to the distribution of the individual parameters and show that the proposed method leads to more reliable results than using the EBEs. In particular, diagnostic plots are more meaningful, the rate of type I error is correctly controlled and its power increases when the degree of misspecification increases. An application to the warfarin pharmacokinetic data confirms the interest of the approach for practical applications. The proposed method should be implemented to complement EBEs-based approach for increasing the performance of model diagnosis.