Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes

Abstract

In this paper, studies of left-truncated and right-censored data with dependent competing risks are discussed. When the latent lifetime of competing failure causes is modeled by a bivariate Marshall–Olkin Weibull distribution, a dependent competing risks model is established for left-truncated and right-censored data with partially observed causes of failure, and classical and Bayesian estimations are presented in consequence. Maximum likelihood estimators along with the associated existence and uniqueness of the model parameters are established, and the asymptotic likelihood theory is used to construct approximate confidence intervals based on asymptotic theory. Further, based on general flexible priors, Bayes estimators and the associated highest posterior density credible intervals of the parameters are also obtained, and an importance sampling technique is used to generate samples from the posterior distribution and in turn to compute the Bayes estimates. Finally, extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicabilities of the proposed methods. The numerical results show that our proposed methods work satisfactory.