Survival time data and their first statistical analysis: Review

In the life testing, medical follow-up studies, and other fields, it is often impossible to observe the lifetimes of all experimental units in the study. These types of data are called survival data. Because of the nature of the data, we cannot obtain the full information of the survival data. Therefore, it is not possible to apply the standard statistical techniques to analysis such survival data. In this paper, I mainly focus onright censoring data and explain how to derive the basic nonparametric estimators of cumulative distribution (Kaplan-Meier estimator), hazard, and cumulative hazard function using observed data. In addition to that I discuss how to compare the survival probabilities in two or more groups by using log-rank test. I also introduce the proportional hazard model (Cox’s model) to incorporate the other related covariates to the experiment. Finally, I present some simulation study and real data application.