A Bathtub Hazard Function Model Assuming a Mixture of Two Weibull Parametric Hazard Functions under a Bayesian Approach

Abstract

This study introduces a parametric survival model based on a mixture of two Weibull hazard functions to accommodate bathtub-shaped hazard rates. The proposed formulation provides flexible modeling of lifetime data in applications such as engineering and medical studies. Inference for the model, in the presence of censored observations and covariates, is conducted within a Bayesian framework. Prior distributions for the model parameters are specified using empirical Bayesian methods based on a preliminary data analysis. Posterior summaries of interest are obtained via Markov Chain Monte Carlo (MCMC) simulation methods using the OpenBUGS software to generate samples from the joint posterior distribution of the model parameters. The methodology is illustrated through three real data applications, including two engineering datasets and one medical dataset from oncology.