Bayesian Weibull quantile regression via Barker’s MCMC proposal: application to cancer survival data

This paper discusses Bayesian framework for Weibull quantile regression in the context of censored survival data, offering a flexible alternative to traditional mean-based survival models. Because the posterior distribution is too difficult to analyze analytically, Bayesian inference is performed using sample-based methods based on the Metropolis-Hastings algorithm extended with gradient-informed Barker’s acceptance mechanism. A theoretical analysis is also presented to confirm the unimodality of the resulting joint posterior distribution, ensuring the stability and reliability of the proposed inference method. The proposed methodology’s practical utility is demonstrated by its use with cancer survival data, where survival outcomes are modeled as functions of clinically significant covariates such as patient age, pathological stage, and the USC73 score. The most important predictors are identified using Bayesian variable selection, pseudo marginal likelihood measures, and the deviance information criterion. Extensive simulation studies are conducted with various parameter configurations to determine the proposed Bayesian quantile regression methodology’s accuracy and practical viability.