Summary: Infectious diseases that can be spread directly or indirectly from one person to another are caused by pathogenic microorganisms such as bacteria, viruses, parasites, or fungi. Infectious diseases remain one of the greatest threats to human health and the analysis of infectious disease data is among the most important application of statistics. In this article, we develop Bayesian methodology using parametric bivariate accelerated lifetime model to study dependency between the colonization and infection times for Acinetobacter baumannii bacteria which is leading cause of infection among the hospital infection agents. We also study their associations with covariates such as age, gender, apache score, antibiotics use 3 months before admission and invasive mechanical ventilation use. To account for singularity, we use Singular Bivariate Extreme Value distribution to model residuals in Bivariate Accelerated lifetime model under the fully Bayesian framework. We analyze a censored data related to the colonization and infection collected in five major hospitals in Turkey using our methodology. The data analysis done in this article is for illustration of our proposed method and can be applied to any situation that our model can be used.