Bayesian Laplace regression for C-in ated survival data

In this paper, we propose the use of Bayesian quantile regression for the analysis of survival data with mixed discrete-continuous distribution with a point mass at C, where these observations of the response variable may be censored at C, where these observations may be right censored or true C. The censoring mechanism is assumed random and possibly dependent on the covariates. Quantile regression allow us to permit covariates to affect survival at different stages in the follow up period, so providing a comprehensive study of the survival distribution. We take a Baysian quantile regression approach for continuous part by considering the quantile process as a linear combination of covariates. Also the probability of being censored given that the observed value is equal to C, will be analyzed. We build up a Markov Chain Monte Carlo method from related models in the literature to obtain samples from the posterior distribution. We demonstrate the suitability of the model to analyze this censoring probability with a simulated study.