In this paper we study the Cox proportional hazards model for survival data in the presence of long-term survivors. Both semiparametric and full parametric versions of the Cox model are considered. Partial likelihood and full likelihood are used to obtain the estimators of the coefficients of covariates and the long-term survivor proportion. Their asymptotic properties are also derived based on counting process and martingale theory. Simulations are carried out to check and compare the performance of the estimators between semiparametric and full parametric models.
- Counting process
- Cox proportional hazards model
- Long-term survivor
- Maximum likelihood estimation
- Partial likelihood