Survival Analysis: A 2 Minute Introduction

Introduction

Survival analysis is a collection of statistical procedures for data analysis for which the outcome variable of interest is time until an event occurs. The event can be death, the occurrence of a disease, or recovery.

Although more than one event may be considered in the same analysis, we will assume that only one event is of designated interest. When more than one event is considered (e.g., death from and of several causes), the statistical problem can be characterized as either recurrent events or a competing risk problem.

Let us take an example: How long patients can survive after receiving a heart transplant.

In this case, the event of interest is the death of a patient, but in other situations, it might be a cure for a disease, relief from symptoms, or the recurrence of a particular condition. Such observations are generally referred to by the generic term survival data even when the endpoint or event being considered is not death but something else.

The time variable usually referred to as survival time, because it gives them time that an individual has “survived” over some follow-up period(Days, Weeks, Years). We also typically refer to the event(Death, relief, etc) as a failure, because the event of interest usually is death, disease incidence, or some other negative individual experience. Failure can be a positive event.

Survival data are generally asymmetrically distributed and are positively skewed often, with a few people surviving a very long time compared with the majority. Thus, assuming a normal distribution will not be reasonable.

Censoring

Censoring occurs when we have some information about individual survival time, but we don’t know the survival time exactlyAt the completion of the study, some patients may not have reached the endpoint of interest (cured, relief, death, etc.) and then the exact survival time is unknown.

The most commonly encountered form is right censoring. Suppose patients are followed in a study for 20 weeks. A patient who does not experience the event of interest for the duration of the study is said to be right-censored.

Why Censor?

There are three reasons why censoring may occur

1. Study ends—no event:

A person does not experience the event before the study ends.(Person B).

2. Lost to follow-up

A person is lost to follow-up during the study period.(Person E).

3. Withdraws

A person withdraws from the studybecause of death (if death is not the event of interest) or some other reason. (Person C)

Note: If an event occurs then there will be no censoring.

Conclusion

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