Parametric inference of incomplete data with competing risks among several groups

We develop parametric inferential methods for the competing risks problem where data arise due to multiple causes of failure in several groups with censoring and possibly missing causes. We provide the general likelihood method and the closed-form maximum-likelihood estimators for the exponential model. Parametric tests are given for comparing different causes and groups. An extensive numerical and graphical investigation is presented to substantiate the proposed methods. A real-data example is illustrated.