Bayesian inference in nonlinear mixed-effects models using normal independent distributions

Nonlinear mixed-effects (NLME) models are popular in many longitudinal studies, including human immunodeficiency virus (HIV) viral dynamics, pharmacokinetic analyses, and studies of growth and decay. Generally, the normality of the random effects is a common assumption in NLME models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize normal/independent distributions as a tool for robust modeling of NLME models under a Bayesian paradigm. The normal/independent distributions is an attractive class of symmetric heavy-tailed distributions that includes the normal distribution, the generalized Student-t, Student-t, slash and the contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of normal distributions in this type of models. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the q-divergence measure. Further, some discussions on model selection criteria are given. These analysis are computationally possible due to an important result that approximating the likelihood function of a NLME model with normal/independent distributions for a simple normal/independent distribution with specified parameters. The new methodologies are exemplified through simulated and a real data set of AIDS/HIV infected patients that was initially analyzed using a normal NLME model, illustrating the usefulness of the proposed methodology.