Bayesian segmental growth mixture Tobit models with skew distributions

This paper presents an extension of the standard Tobit to simultaneously address segmental phases, subpopulation heterogeneity, lower limit of detection, and skewness in outcomes of human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) longitudinal data. A major problem often encountered in an HIV/AIDS research is the development of drug resistance to antiretroviral (ARV) drug or therapy. For dealing with drug resistance problem, estimating the time at which drug resistance would develop is usually sought. Following ARV treatment, the profile of each subject’s viral load tends to follow a ‘broken stick’ like growth trajectory, indicating multiple phases of decline and increase in viral loads. Such multiple phases with multiple change-points are captured by subject-specific random parameters of growth curve models. To account subpopulation heterogeneity of drug resistance among patients, the turning-points are also allowed to differ by latent classes of patients on the basis of trajectories of observed viral loads. These features of viral longitudinal data are jointly modeled in a unified framework of segmental growth mixture Tobit mixed-effects models with skew distributions for a response variable with left censoring and skewness under the Bayesian approach. The proposed methods are illustrated using real data from an AIDS clinical study.