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

Approximate inferences for nonlinear mixed effects models with scale mixtures of skew-normal distributions