Bayesian Estimation and Model Assessment of the Exponentiated Rayleigh Survival Model Using Laplace and MCMC Techniques: Applications with Right-Censored Medical Data

This paper presents a comprehensive comparative study of Bayesian and classical estimation techniques for the Exponentiated Rayleigh (expRay) survival model, particularly in the presence of right-censored medical data. Using both analytic and simulation-based Bayesian methods—including Laplace approximation, Independent Metropolis (IM), and Gibbs sampling via JAGS—the model's flexibility and robustness are evaluated. Two real-world datasets, Intrauterine Device (IUD) discontinuation times and bladder cancer remission durations, are analyzed to illustrate the model's practical applications. Results from Maximum Likelihood Estimation (MLE) are benchmarked against Bayesian estimates, representing that the IM algorithm offers the best balance between computational efficiency and statistical accuracy. Model diagnostic including the posterior predictive checks (ppc) confirms the model's adequacy. The study highlights the suitability of the expRay model for modeling varying hazard rates in clinical survival data and establishes the IM-based Bayesian framework as an effective tool for medical survival analysis.