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The aim of survival analysis is to explain and predict the survival, usually defined along the time domain. In this work we study it by means of regression models. In statistical data analysis it is common to consider the regression set up in which a given response variable depends on some factors and/or covariates. The model selection problem mainly consists in choosing the covariates which better explain the dependent variable in a precise and hopefully fast manner. This process usually has several steps: the first one is to collect considerations from an expert about the set of covariates, then the statistician derives a prior on model parameters and constructs a tool to solve the model selection problem. We consider the model selection problem in survival analysis when the response variable is the time to event. Under an objective Bayesian approach, some commonly used tools in literature are the Intrinsic Bayes factor (IBF) and the Fractional Bayes factor (FBF). In this thesis we deal with the variable selection problem for censored data.