# Big picture on survival analysis and life data analysis

I have heard of survival analysis and life data analysis, but don't quite get the big picture.

I was wondering what topics they are covering?

Is it pure statistics, or just application of statistics on some specific area?

Is life date analysis part of survival analysis?

Thanks and regards!

-

The concept of censoring is the key to survival analysis and life data analysis. This issue can also enter via industrial statistics. When monitoring the length of time it takes for a sample of units to fail, you can have

• Complete data: the exact time a unit fails is known
• Censored to the right: the time to fail for a unit is beyond the present run time
• Censored to the left: the known time is after the time a unit failed

Other issues that enters the data mix are

• Singly censored: all unfailed units have a common run time
• Multiply censored: the unfailed units have different run times
• Interval censored: the time to fail is known to be between a particular set of times.
• Time censored: the censoring time is fixed
• Failure censored: a test is stopped when a fixed number of units fail
• Competing failure modes: the sample units fail for different reasons

Common distributions capable of handling these situations are: lognormal, Weibull, and extreme value. The issues become interesting because there are graphical procedures to handle analysis as well as MLE and Method of Moments methods.

Systems reliability is an off-shoot of this topic which gets involved with Bayesian methods, renewal theory, and accelerated life testing. Wayne Nelson and Bill Meeker have several good books on the topics.

-
(+1) Censoring is the key idea; time is just a particular (and the most common) application. For instance, Dennis Helsel has applied survival analysis to chemical measurements having detection limits (left censoring). There's no time involved, but the model and the techniques are still useful. –  whuber Apr 4 '11 at 14:40

In survival analysis, or time-to-event analysis, the variable or interest measures the time from a starting point to a point of interest like death due to some disease. So the response variable is a positive variable which is in most cases skewed. As a consequence the usual assumption of normality fails and, for instance, the classical regression techniques are not applicable. (Though, note that sometimes a transformation of the variable could make the situation better). But the main difference is censoring: a very common feature when dealing with time-to-event data. In its most common form (right censoring), you do not know the exact time for a given individual but you do know that it is larger than some value $t^{\star}$. For example, suppose you follow a patient up to death. At time $t=10$ days, he is alive. At time $t=30$ days he is still alive but then he is lost to follow-up. Then you do not know the exact time of death but you do know that $t > 30$. Ignoring censoring is clearly not the best think to do; instead, you can record $t^{\star} = 30$ as a censored observation. Techniques of survival analysis (e.g., Kaplan-Meier estimator, Cox regression, ...) are specially designed to deal with censoring.

To my point of view Modelling Survival Data in Medical Research is a very good choice as a first book in survival analysis... but there are many others.

-
5, 10, 12+, 14, 17, 18+, 20+

A first approximation description of survival analysis: Analysing data where the dependent variable has (1) precise values (the complete observations) and (2) values know to be above a given threshold (the censored observations). The above may be a survival data sample, values without + are precisely known; values with + are known to be more, but not how much more. (And there are many extensions.)