Introduction: Several Classical Data Examples for Survival Analysis

The proportional hazards (PH) model was proposed by Sir David Cox just over 40 years ago (Cox 1972). Today, the Cox model is the most important model in survival analysis , reliability and quality of life research, epidemiology, clinical trials , and biomedical studies. There have also been tremendous applications of the Cox model in demography , econometrics , finance, pharmacology, biology, gerontology , insurance, etc. These have marked the great success of the Cox PH model which further induced extended studies of competitive survival regression models and the corresponding development of semiparametric estimation theory, likelihood principle, counting process modeling and applications.