Bayesian two-part bent-cable Tobit models with skew distributions: Application to AIDS studies

Abstract

This paper presents a new development of a bent-cable two-part Tobit model to identify both phasic patterns and mixture of advancing (to AIDS) and non-advancing patients of HIV. In identification of such phasic patterns, estimation of a transition period for the development of drug resistance to antiretroviral (ARV) drug or therapy is carried out using longitudinal data that have a gradual change from a declining phase to an increasing phase. In addition to phasic changes, there are also problems of skewness and left-censoring in the response variable because of a lower limit of detection. A relatively large percentage of data below limit of detection are recorded more than expected under an assumed skew-distribution. To properly accommodate these features, we present an extension of the random effects bent-cable Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for a response with left-censoring, skewness and phasic patterns. The proposed methods are illustrated using real data from an AIDS clinical study.