Development and Evaluation of Nonparametric Mixed Effects Models
Abstract: A nonparametric population approach is now accessible to a more comprehensive network of modelers given its recent implementation into the popular NONMEM application, previously limited in scope by standard parametric approaches for the analysis of pharmacokinetic and pharmacodynamic data.The aim of this thesis was to assess the relative merits and downsides of nonparametric models in a nonlinear mixed effects framework in comparison with a set of parametric models developed in NONMEM based on real datasets and when applied to simple experimental settings, and to develop new diagnostic tools adapted to nonparametric models.Nonparametric models as implemented in NONMEM VI showed better overall simulation properties and predictive performance than standard parametric models, with significantly less bias and imprecision in outcomes of numerical predictive check (NPC) from 25 real data designs. This evaluation was carried on by a simulation study comparing the relative predictive performance of nonparametric and parametric models across three different validation procedures assessed by NPC. The usefulness of a nonparametric estimation step in diagnosing distributional assumption of parameters was then demonstrated through the development and the application of two bootstrapping techniques aiming to estimate imprecision of nonparametric parameter distributions. Finally, a novel covariate modeling approach intended for nonparametric models was developed with good statistical properties for identification of predictive covariates.In conclusion, by relaxing the classical normality assumption in the distribution of model parameters and given the set of diagnostic tools developed, the nonparametric approach in NONMEM constitutes an attractive alternative to the routinely used parametric approach and an improvement for efficient data analysis.
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