Enhancing Survival Analysis with Bayesian Modeling: A Comparative Study of Type II Half Logistic-Weibull Cox-PH, Weibull Cox-PH and Weibull Models

Survival analysis plays a crucial role in understanding time-to-event data and modeling the underlying hazard rates. In this study, we propose a novel Bayesian survival analysis approach by incorporating the Type II half-logistic Weibull Cox-proportional hazard (Cox-PH) model. This model combines the advantages of the half-logistic Weibull distribution with the flexibility of the Cox-PH framework, allowing for efficient estimation of survival probabilities and hazard ratios. This study aims to apply Bayesian Analysis of Type II half-logistic Weibull Cox-PH model and compare it with Weibull Cox-PH, and Weibull models. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language Stan. To incorporate censored mechanisms within the Stan framework, customized codes are developed. The models are then compared using information criteria under Bayesian paradigm.