Comparison of Mixed-Effects Models for Skew-Normal Responses with an Application to AIDS Data: A Bayesian Approach

The potency of antiretroviral agents in AIDS clinical trials can be assessed on the basis of a viral response such as viral decay rate or change in viral load (number of HIV RNA copies in plasma). Linear, nonlinear, and nonparametric mixed-effects models have been proposed to estimate such parameters in viral dynamic models. However, there are two critical questions that stand out: whether these models achieve consistent estimates for viral decay rates, and which model is more appropriate for use in practice. Moreover, one often assumes that a model random error is normally distributed, but this assumption may be unrealistic, obscuring important features of within- and among-subject variations. In this article, we develop a skew-normal (SN) Bayesian linear mixed-effects (SN-BLME) model, an SN Bayesian nonlinear mixed-effects (SN-BNLME) model, and an SN Bayesian semiparametric nonlinear mixed-effects (SN-BSNLME) model that relax the normality assumption by considering model random error to have an SN distribution. We compare the performance of these SN models, and also compare their performance with the corresponding normal models. An AIDS dataset is used to test the proposed models and methods. It was found that there is a significant incongruity in the estimated viral decay rates. The results indicate that SN-BSNLME model is preferred to the other models, implying that an arbitrary data truncation is not necessary. The findings also suggest that it is important to assume a model with an SN distribution in order to achieve reasonable results when the data exhibit skewness.