Skew-normal Bayesian nonlinear mixed-effects models with application to AIDS studies.

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. Nonlinear mixed-effects (NLME) models have been used for modeling between-subject and within-subject variations in viral load measurements. Mostly, normality of both within-subject random error and random-effects is a routine assumption for NLME models, but it may be unrealistic, obscuring important features of between-subject and within-subject variations, particularly, if the data exhibit skewness. In this paper, we develop a Bayesian approach to NLME models and relax the normality assumption by considering both model random errors and random-effects to have a multivariate skew-normal distribution. The proposed model provides flexibility in capturing a broad range of non-normal behavior and includes normality as a special case. We use a real data set from an AIDS study to illustrate the proposed approach by comparing various candidate models. We find that the model with skew-normality provides better fit to the observed data and the corresponding estimates of parameters are significantly different from those based on the model with normality when skewness is present in the data. These findings suggest that it is very important to assume a model with skew-normal distribution in order to achieve robust and reliable results, in particular, when the data exhibit skewness.