A Bayesian approach to survival analysis of COVID-19 data using the additive flexible Weibull extension-Lomax distribution

This study investigates the Bayesian estimation for the additive flexible Weibull extension-Lomax (AFWE-L) distribution, a versatile model designed to capture complex survival data patterns. Using Type II censored samples and a joint bivariate informative prior, Bayes estimators are derived for the distribution's unknown model parameters, reliability metrics such as the hazard and reversed hazard rate functions. Bayesian inference is conducted with the squared error (symmetric) and linear-exponential (asymmetric) loss functions, allowing flexibility in handling estimation errors. Credible intervals are constructed to quantify parameter uncertainty, providing a measure of precision for the Bayes estimates. The effectiveness of the Bayes estimators under various censoring levels is evaluated through a comprehensive simulation study, specifically 0% and 30%, revealing increased estimation efficiency with larger sample sizes and reduced censoring. The simulation study is performed through the implementation of the adaptive Metropolis algorithm. The simulation results demonstrate the efficacy of the proposed methodology in capturing diverse survival patterns and highlight the impact of censoring on estimation accuracy. Furthermore, The AFWE-L distribution model is utilized to analyze three real-world datasets concerning COVID-19, showcasing its practical utility in analyzing complex survival data characterized by competing risks. This research advances Bayesian survival analysis techniques, providing a robust framework for modeling lifetime data with competing risks in medical and reliability studies.