Abstract
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.