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Different probability models are used to model survival data. However, it is important to know which model describe best the data because if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret and helps in predictions. This article presents the Bayesian censored data modeling assuming Gumbel, double exponential, exponentially modified Gaussian, Weibull, and lognormal distributions as sampling models. In particular, a historical Leukemia data set is used to show the comparison among different models. Markov Chain Monte Carlo (MCMC) methods are used to compute the posterior summaries. Different model selection criteria, like, Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), Leave-one-out Cross-Validation (LOOCV), and Watanabe-Akaike Information Criterion (WAIC) are used for model selection. It is observed from the comparative study that the lognormal model has the minimum values of different model selection criteria and considered to be the best for this Leukemia data.

A Comparison of Different Bayesian Models for Leukemia Data