Survival Function

Survival data arise when we are interested in the time of occurrence of an event, and the survival function describes the cumulative probability of surviving beyond a given time point in a given group of individuals. Methods to estimate the survival function can be classified in nonparametric and model-based methods and the main ones are described here. Among the nonparametric ones, the product limit, the life table, the Fleming–Harrington, and Bayesian methods are considered. Assumptions on right censoring and left truncation are discussed, with practical advices on how to present and read the survival curve. Aspects that are special to estimation of survival in the presence of time-dependent variables and competing risks are mentioned. Among the model-based methods, the use of estimators derived by the Cox model and parametric models is shown. Finally, relative survival and period analysis estimators are presented as useful tools in describing the survival experience in disease (cancer) registries, and survival estimators that account for special features in (nonrandom) designs are also briefly mentioned.