Discrete-time approach is used in survival data analysis when only the time interval in which the event of interest has occurred is known or when this event occurs in a discrete-time scale. The work presented in this paper is motivated by the analysis of HIV/AIDS follow-up data collected in Burkina Faso during the 5-YEAR Global Fund program implemented to fight AIDS, Tuberculosis and Malaria. The research question that motivated the work is the likely existence of different mortality risk profiles of people infected with HIV/AIDS, depending on their characteristics and health status at the beginning of their care. In order to answer these questions, we considered a binary tree regression approach for survival data analysis since such a model owns the ability to handle interaction effects between the outcome covariates without a tight specification of such effects during the model statement step. This helps to prevent specification and interpretation errors. The fitted model resulted in splitting patients into three disjoint subgroups, corresponding each to a specific hazard profile.