Analysis of incomplete data in presence of competing risks

In medical studies or in reliability analysis an investigator is often interested in the assessment of a specific risk in the presence of other risk factors. In statistical literature this 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 both the parametric and non-parametric set up. Unfortunately in many situations, the causes of failure are not observed, even if the failure times are observed. Miyawaka (1984, IEEE Trans. Reliability Anal. 33(4), 293-296) obtained some 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 compute confidence intervals for different parameters and compare them with the two different bootstrap confidence bounds. We also consider the case when the failure distributions are Weibull. One data set is used to see how different methods work in real-life situations. (C) 2000 Elsevier Science B.V. All rights reserved.