Bayesian Survival Analysis of Lung Cancer Data under Uncertainty: A Fuzzy Environment Approach

This study proposes a Bayesian framework for estimating the parameters of two Weibull populations with a common shape parameter from fuzzy survival data. Triangular fuzzy numbers are used to represent imprecise survival times, and Bayesian estimation is performed using Lindley’s approximation, Hamiltonian Monte Carlo(HMC), and Metropolis-Hastings(MH), while KDE is used to obtain marginal posterior density estimates and posterior modes from the MCMC samples. A comprehensive simulation study is conducted under different sample sizes to compare the performance of the proposed estimators using bias and mean squared error. The results show that estimation accuracy improves with increasing sample size, while the Bayesian methods provide stable and reliable parameter estimates under uncertainty. The proposed methodology is further illustrated using survival data from male and female patients with Stage III lower-lobe lung cancer. Goodness-of-fit assessments indicate that the Weibull distribution adequately represents the observed survival pattern, and the Bayesian methods produce consistent survival estimates. The proposed framework combines fuzzy uncertainty modeling with computational Bayesian techniques to provide an effective approach for survival analysis when survival times are subject to imprecision.