## 9.4. Survival Analysis

- Survival Variable Selection
- Life Table
- Kaplan-Meier Analysis
- Survival Comparison Statistics
- Cox Regression

Survival Analysis is useful when the dependent variable represents the time elapsed between an initial event and a termination event. This is most often the case in medical research, where detection of the disease is the initial event and the patient’s death is the termination event. This type of data frequently occurs in other disciplines as well, such as engineering (e.g. failure time of components) or social sciences (e.g. survival of marriages). In these types of problems, researchers are often faced with the task of estimating a survival function (the probability that an individual is alive at time t) or a hazard function (the probability of failure at a time period t + Dt, given that the individual has survived until time t).

In principle, one could use standard parametric statistics for describing the average survival times and comparing effects of treatments. However these methods would not consider censored data, that is, data where the termination event has never occurred. Data may be censored because the patient has entered the study too late, patients may have survived the whole study period, or because of patients with whom we have lost contact.

When there are no censored cases in data, it is a relatively straightforward exercise to estimate the survival function. The empirical survival function is defined simply as:

However, when there are censored cases in data or when we want take into consideration other factors that may affect the survival times (categorical variables such as sex, region, etc. or continuous variables such as temperature, age), then one of the Survival Analysis methods available in this section should be used. UNISTAT will also estimate the empirical survival function when a censor variable is not selected.