Inference of dependent left-truncated and right-censored competing risks data from a general bivariate class of inverse exponentiated distributions

Abstract

In this paper, inference is discussed for left-truncated and right-censored (LTRC) competing risks data. For modelling the dependent competing risks variables, a flexible bivariate lifetime model is constructed with a class of inverse exponentiated distribution, and associated distribution properties are provided correspondingly. When the LTRC competing risks data is available with partially observed failure causes, a dependent competing risks model is further established. Maximum likelihood estimators of the unknown parameters and the reliability indices are established, and the approximate confidence intervals are also constructed based on asymptotic theory. In addition, Bayesian estimators are obtained based on flexible priors, Markov Chain Monte Carlo sampling approach is also proposed for computing the Bayesian estimates as well as the highest posterior density credible intervals. Finally, simulation studies are carried out to investigate the performances of our results, and a real-life data set is analysed to illustrate the applicability of the proposed methods.

Keywords:

• Dependence competing risks model
• left-truncated and right-censored data
• a general class of inverse exponentiated distributions
• maximum likelihood estimation
• posterior analysis

Acknowledgments

The authors would like to thank the Editor and the referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper.

Disclosure statement

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

Additional information

Funding

This work of Liang Wang was supported by the National Natural Science Foundation of China [grant number 12061091], the Yunnan Fundamental Research Projects of China [grant number 202101AT070103] and the Doctoral Research Foundation of Yunnan Normal University [grant number 00800205020503129]. Fode Zhang was supported by the National Natural Science Foundation of China [grant number 12071372].