Analysis of progressively censored competing risks data

In several studies in Survival Analysis, the cause of failure / death of items or individuals may be attributable to more than one cause. In this chapter, we consider the competing risks model when the data is progressively Type-II censored. We provide di®erent techniques for the analysis of the model under the assumption of independent causes of failure and exponential lifetimes. The maximum likelihood estimators of the di®erent parameters and the UMVUE's are obtained. In addition, the exact distributions of the di®erent estimators are derived. We also derive the UMP and UMPU test for the equality of the failure rates of the competing risks. We consider the Bayesian estimation using the Inverse Gamma distribution as a prior. To assess the performance of all these estimators, con¯dence intervals are developed using the exact, asymptotic, and bootstrap distributions. In the Bayesian context, we develop credible intervals for the parameters. The di®erent methods are compared through a simulation study, and the analysis of a real dataset. Finally, we also provide some insight into inference under the Weibull model and dependent causes of failure