Jointly modeling means and variances for nonlinear mixed effects models with measurement errors and outliers

In longitudinal data analyses, the within-individual repeated measurements often exhibit large variations and these variations appear to change over time. Understanding the nature of the within-individual systematic and random variations allows us to conduct more efficient statistical inferences. Motivated by human immunodeficiency virus (HIV) viral dynamic studies, we considered a nonlinear mixed effects model for modeling the longitudinal means, together with a model for the within-individual variances which also allows us to address outliers in the repeated measurements. Statistical inference was then based on a joint model for the mean and variance, implemented by a computationally efficient approximate method. Extensive simulations evaluated the proposed method. We found that the proposed method produces more efficient estimates than the corresponding method without modeling the variances. Moreover, the proposed method provides robust inference against outliers. The proposed method was applied to a recent HIV-related dataset, with interesting new findings.