  Nonlinear mixed effects models have received a great deal of attention in the
statistical literature in recent years because of their flexibility in handling
longitudinal studies, including human immunodeficiency virus viral dynamics,
pharmacokinetic analyses, and studies of growth and decay. A standard
assumption in nonlinear mixed effects models for continuous responses is that
the random effects and the within-subject errors are normally distributed,
making the model sensitive to outliers. We present a novel class of asymmetric
nonlinear mixed effects models that provides efficient parameters estimation in
the analysis of longitudinal data. We assume that, marginally, the random
effects follow a multivariate scale mixtures of skew--normal distribution and
that the random errors follow a symmetric scale mixtures of normal
distribution, providing an appealing robust alternative to the usual normal
distribution. We propose an approximate method for maximum likelihood
estimation based on an EM-type algorithm that produces approximate maximum
likelihood estimates and significantly reduces the numerical difficulties
associated with the exact maximum likelihood estimation. Techniques for
prediction of future responses under this class of distributions are also
briefly discussed. The methodology is illustrated through an application to
Theophylline kinetics data and through some simulating studies.
