Metropolis Algorithm Based Bayesian Analysis of a Competing Risk Data Using Copula-Frailty Model

Competing risks can play a significant role in the design and analysis of critical intelligent systems which experience several risks of failure but actually fail due to a single cause that occurs first. The failure time of various components of these systems may be correlated as one failure may lead to another. In order to model such a dependence structure, copula models and frailty models have been developed for such competing risk data. The frailty term is used to describe the underlying heterogeneity among the units and the copula function is utilized to represent the dependence between the failure times. A Bayesian analysis using the Weibull distribution as the underlying failure time distribution to describe the competing risk data is carried out. The paper also considers some other models and compares them using a few standard Bayesian model comparison tools. Lastly, a real data set is studied to illustrate the proposed Bayesian approach.