Bayesian Inference of a Dependent Competing Risk Data

TL;DR

This paper develops a Bayesian approach for competing risks data analysis using Gamma-Dirichlet priors, offering advantages over classical methods and extending to various censoring schemes.

Contribution

It introduces a Bayesian inference framework for the Marshall-Olkin bivariate Weibull model with Gamma-Dirichlet priors, including partial ordering and different censoring schemes.

Findings

Bayesian estimates outperform classical inference in this context.

The method effectively handles various censoring schemes.

Partial ordering priors incorporate cause severity information.

Abstract

Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks data set using four-parameter Marshall-Olkin bivariate Weibull distribution when the failure of an unit at a particular time point can happen due to more than one cause. The aim of this paper is to provide the Bayesian analysis of the same model based on a very flexible Gamma-Dirichlet prior on the scale parameters. It is observed that the Bayesian inference has certain advantages over the classical inference in this case. We provide the Bayes estimates of the unknown parameters and the associated highest posterior density credible intervals based on Gibbs sampling technique. We further consider the Bayesian inference of the model parameters assuming partially ordered Gamma-Dirichlet prior on the scale parameters when one cause is more severe than the other cause. We have extended the results for different censoring schemes also.