Consequences of misspecifying assumptions in nonlinear mixed effects models
The nonlinear mixed effects model provides a framework for inference in a number of applications, most notably pharmacokinetics and pharmacodynamics, but also in HIV and other disease dynamics and in a host of other longitudinal-data settings. In these models, to characterize population variation, individual-specific parameters are modeled as functions of fixed effects and mean-zero random effects. A standard assumption is that of normality of the random effects, but this assumption may not always be realistic, and, because the random effects are not observed, it may be difficult to verify. An additional issue is specifying the form of the function relating individual-specific parameters to fixed and random effects. Again, because this relationship is not observed explicitly, it may be difficult to specify. Popular methods for fitting these models are predicated on the normality assumption, and past studies evaluating their performance have assumed that normality and the form of the model are correct specifications. We investigate the consequences for population inferences using these methods when the normality assumption is inappropriate and/or the model is misspecified.
random effects nonnormality laplace approximation linearization