Survival analysis for the inverse Gaussian distribution with the Gibbs sampler

Abstract

This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters μ and λ and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter ($\varphi =\lambda /\mu$) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered.

Keywords:

• Bayesian inference
• bootstrap test
• censoring
• fiducial inference
• Gibbs sampler
• Kernel density estimate

Acknowledgments

The authors thank three anonymous referees and the associate editor for their constructive and very useful comments and suggestions on an earlier manuscript which led to a substantial improvement. The authors would also like to thank Colin Hamman who previously made similar computations and simulations for this study using software packages MATLAB and Scilab as a part of his capstone research project performed under the guidance of Professor Raj S. Chhikara [17]. Also, the authors would like acknowledge the R Core Team [25] and the contributors of the R packages by [8,14–16,24].

Disclosure statement

No potential conflict of interest was reported by the author(s).