Piecewise mixed-effects models with skew distributions for evaluating viral load changes: A Bayesian approach

Studies of human immunodeficiency virus dynamics in acquired immuno deficiency syndrome (AIDS) research are very important in evaluating the effectiveness of antiretroviral (ARV) therapies. The potency of ARV agents in AIDS clinical trials can be assessed on the basis of a viral response such as viral decay rate or viral load change in plasma. Following ARV treatment, the profile of each subject's viral load tends to follow a 'broken stick'-like dynamic trajectory, indicating multiple phases of decline and increase in viral loads. Such multiple-phases (change-points) can be described by a random change-point model with random subject-specific parameters. One usually assumes a normal distribution for model error. However, this assumption may be unrealistic, obscuring important features of within- and among-subject variations. In this article, we propose piecewise linear mixed-effects models with skew-elliptical distributions to describe the time trend of a response variable under a Bayesian framework. This methodology can be widely applied to real problems for longitudinal studies. A real data analysis, using viral load data from an AIDS study, is carried out to illustrate the proposed method by comparing various candidate models. Biologically important findings are reported, and these findings also suggest that it is very important to assume a model with skew distribution in order to achieve reliable results, in particular, when the data exhibit skewness.