# Survival Analysis

Survival analysis helps the researcher assess if, any why, certain individuals are exposed to a higher risk of experiencing an event of interest, such as death, machine failure, drug relapse, etc.  This is also referred to as event history analysis.

Survival analysis consists of a wide variety of techniques that help the researcher analyze time-to-event models.  Survival analysis can be used to study many things and is extremely helpful in studying the cause of births and deaths.  It can also be used by the researcher in order to understand the cause(s) of marriages and divorces, and even the cause of wars and revolutions.

### Questions Answered:

What proportion of a given population will survive past a set date?

Of the population that survived, what is the rate they will die/fail?

Do certain factors (e.g., age and gender) effect the probability of survival?

The first step in survival analysis is for the researcher to establish what event is to be analyzed.  For example, suppose in a study of marital histories, four types of states are  obtained: ‘never married,’ ‘married,’ ‘divorced,’ and ‘widowed.’  The term ‘event’ is a transition from one state to another.  In this example, the event can be referred to as ‘married,’ which is a transition from the origin of ‘never married’ to the final state of ‘married.’

The next step is to ensure that the data consists of a longitudinal record of when the event has occurred for individuals or group of individuals.  Using the example above, this may include ages and marriage dates, as well as other explanatory variables (e.g., gender, income, etc.).

The dependent variable can be survival time or transition rate, and analyses can be conducted to describe the varying proportions of surviving cases at different times or to assess the relationship between survival time and a set of covariates/predictors.

The most common event analyzed in survival analysis is death.  Other common events are unemployment, graduation from school, machine failure, etc.  The survival time data in survival analysis has two important special characteristics.  The survival time data in survival analysis is not negative and is usually positively skewed.

The survival time, which is the object of study in survival analysis, should be differentiated from the calendar time.  The survival time in survival analysis should always be measured related to some appropriate time origin.