Analysis of Incomplete Data in Presence of Competing Risks

摘要

In medical studies or in reliability analysis an investigator is often interested with the assessment of a specific risk in presence of other risk factors. In the Statistical literature it is known as the analysis of competing risks model. The competing risks model assumes that the data consists of a failure time and an indicator denoting the cause of failure. Several studies have been carried out under this assumption for parametric and nonparametric set up. Unfortunately in many situations, the causes of failure are not observed, even if the failure time is observed. Miyawaka (1984) obtained some of the results under the assumption that the failure time distribution is exponential. He obtained the maximum likelihood estimators and the minimum variance unbiased estimators of the unknown parameters. We provide the approximate and asymptotic properties of these estimators. Using the approximate and the asymptotic distributions we obtain confidence bounds of the parameters and also propose two different bootstrap confidence bounds. We consider the case when the failure distribution may not be exponential and use one data set to see how different methods work in real life situations.