Likelihood-Based Estimation of a Proportional-Hazard, Competing- Risk Model with Grouped Duration Data

This short paper demonstrates two important results related to the estimation of competing-risk models under the proportional-hazards assumption with grouped duration data. First I show that the model with non-parametric baseline hazards is unidentifiable with only grouped duration data. Therefore one has to make functional form assumption for any meaningful inference. Secondly I demonstrate that under some parametric assumption such as piecewise constant baseline hazards, the sample likelihood function has explicit analytical form. Therefore there is no need for approximation. The approximation formula adopted by Deng et al (2000) and religiously followed by others is only a quasi likelihood function.