# Introduction

Survival data often consists of a response variable that measures the
duration of time until a specified event occurs and a set of
independent variables thought to be associated with the event-time
variable. Component lifetimes in industrial reliability, durations of
jobs, and survival times in a clinical trial are examples of event
times. The purpose of survival analysis is to model the underlying
distribution of event times and to assess the dependence of the event
time on other explanatory variables. In many situations, the event
time is not observed due to withdrawal or termination of the study;
this phenomenon is known as *censoring*. Survival analysis
methods correctly use both the censored and uncensored observations.

**Figure 14.1:** Survival Analysis Menu

Usually, a first step in the analysis of survival data is the
estimation of the distribution of the survival times. The survival
distribution function (SDF), also known as the survivor function, is
used to describe the lifetimes of the population of interest. The SDF
evaluated at time *t* is the probability that an experimental unit
from the population will have a lifetime exceeding *t*. The
product limit and actuarial methods are popular techniques for
estimating survival distributions.

Proportional hazards regression is a useful technique for assessing
the relationship between survival times and a set of explanatory
variables. The proportional hazards model of Cox (1972) assumes a
parametric form for the effects of explanatory variables on survival
times and allows an unspecified form for the underlying survivor
function. The proportional hazards model is also known as Cox
regression.

*Survival Analysis Task Features*

The Life Tables task provides both the actuarial (also known as
life-table) method and product-limit method (also known as the
Kaplan-Meier method).
You can define strata and test the homogeneity
of survival functions across strata with rank tests and a likelihood
ratio test based on an underlying exponential distribution. In
addition, you can test the association between covariates and the
lifetime variable with the log-rank test and the Wilcoxon test.
Plots provided are the survival function, -log (survival function),
log(-log(survival function)), hazard function, and probability density
function.
The Proportional Hazards task performs Cox regression. You can choose
from five different model selection techniques, select from four
different methods for handling tied event times, and produce a
survivor function plot with confidence intervals.

The examples in this chapter demonstrate how you can use the Survival
tasks in the Analyst Application to analyze survival data.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.