Bayesian analysis for partially complete time and type of failure data

Abstract

In this paper, we consider the Bayesian analysis of competing risks data, when the data are partially complete in both time and type of failures. It is assumed that the latent cause of failures have independent Weibull distributions with the common shape parameter, but different scale parameters. When the shape parameter is known, it is assumed that the scale parameters have Beta–Gamma priors. In this case, the Bayes estimates and the associated credible intervals can be obtained in explicit forms. When the shape parameter is also unknown, it is assumed that it has a very flexible log-concave prior density functions. When the common shape parameter is unknown, the Bayes estimates of the unknown parameters and the associated credible intervals cannot be obtained in explicit forms. We propose to use Markov Chain Monte Carlo sampling technique to compute Bayes estimates and also to compute associated credible intervals. We further consider the case when the covariates are also present. The analysis of two competing risks data sets, one with covariates and the other without covariates, have been performed for illustrative purposes. It is observed that the proposed model is very flexible, and the method is very easy to implement in practice.

Keywords:

• latent failure time model
• competing risks model
• importance sampling
• Weibull distribution
• prior distribution
• credible interval

Acknowledgements

The author would like to thank the referees for their constructive comments.