Joint bent-cable Tobit models for longitudinal and time-to-event data

In this article, we show how to estimate a transition period for the evolvement of drug resistance to antiretroviral (ARV) drug or other related treatments in the framework of developing a Bayesian method for jointly analyzing time-to-event and longitudinal data. For HIV/AIDS longitudinal data, developmental trajectories of viral loads tend to show a gradual change from a declining trend after initiation of treatment to an increasing trend without an abrupt change. Such characteristics of trajectories are also associated with a time-to-event process. To assess these clinically important features, we develop a joint bent-cable Tobit model for the time-to-event and left-censored response variable with skewness and phasic developments. Random effects are used to determine the stochastic dependence between the time-to-event process and response process. The proposed method is illustrated using real data from an AIDS clinical study.