Bayesian Extension of the Weibull AFT Shared Frailty Model with Generalized Family of Distributions for Enhanced Survival Analysis Using Censored Data

In survival analysis, the Accelerated Failure Time (AFT) shared frailty model is a widely used framework for analyzing time-to-event data while accounting for unobserved heterogeneity among individuals. This paper extends the traditional Weibull AFT shared frailty model using half logistic-G family of distributions (Type I, Type II and Type II exponentiated) through Bayesian methods. This approach offers flexibility in capturing covariate influence and handling heavy-tailed frailty distributions. Bayesian inference with MCMC provides parameter estimates and credible intervals. Simulation studies show improved model predictive performance compared to existing models, and real-world applications demonstrate its practical utility. In summary, our Bayesian Weibull AFT shared frailty model with Type I, Type II and Type II exponentiated half logistic-G family distributions enhances time-to-event data analysis, making it a versatile tool for survival analysis in various fields using STAN in R.