Analysis of Type-II hybrid censored competing risks data

TL;DR

This paper develops new estimation and inference methods for Type-II hybrid censored competing risks data with exponential distributions, including modified estimators, exact distributions, confidence intervals, and Bayesian approaches, validated through simulations and real data.

Contribution

It introduces modified estimators for scale parameters, derives their exact distributions, and proposes Bayesian inference methods for Type-II hybrid censored competing risks data.

Findings

Modified estimators perform well in simulations

Exact distributions enable precise confidence intervals

Bayesian methods provide reliable parameter estimates

Abstract

Kundu and Gupta (2007, Metrika, 65, 159 - 170) provided the analysis of Type-I hybrid censored competing risks data, when the lifetime distribution of the competing causes of failures follow exponential distribution. In this paper we consider the analysis of Type-II hybrid censored competing risks data. It is assumed that latent lifetime distributions of the competing causes of failures follow independent exponential distributions with different scale parameters. It is observed that the maximum likelihood estimators of the unknown parameters do not always exist. We propose the modified estimators of the scale parameters, which coincide with the corresponding maximum likelihood estimators when they exist, and asymptotically they are equivalent. We obtain the exact distribution of the proposed estimators. Using the exact distributions of the proposed estimators, associated confidence intervals are obtained. The asymptotic and bootstrap confidence intervals of the unknown parameters are also provided. Further, Bayesian inference of some unknown parametric functions under a very flexible Beta-Gamma prior is considered. Bayes estimators and associated credible intervals of the unknown parameters are obtained using Monte Carlo method. Extensive Monte Carlo simulations are performed to see the effectiveness of the proposed estimators and one real data set has been analyzed for the illustrative purposes. It is observed that the proposed model and the method work quite well for this data set.