Survival Analysis
Data that measure lifetime or the length of time until the occurrence of an event are called lifetime, failure time, or survival data.
For example, variables of interest might be the lifetime of diesel engines, the length of time a person stayed on a job, or the survival
time for heart transplant patients. The purpose of survival analysis is to model the underlying distribution of the failure time variable
and to assess the dependence of the failure time variable on the independent variables.
The SAS/STAT survival analysis procedures include the following:
 ICLIFETEST Procedure — Nonparametric survival analysis for intervalcensored data
 ICPHREG Procedure — Proportional hazards regression models to intervalcensored data
 LIFEREG Procedure — Parametric models for failure time data that can be uncensored, right censored, left censored, or interval censored
 LIFETEST Procedure — Nonparametric estimates of the survivor function either by the productlimit method (also called the KaplanMeier method) or by the lifetable
method (also called the actuarial method)
 PHREG Procedure — Regression analysis of survival data based on the Cox proportional hazards model
 SURVEYPHREG Procedure — Regression analysis of survival data based on the Cox proportional hazards model for complex survey sample designs
ICLIFETEST Procedure
The ICLIFETEST procedure performs nonparametric survival analysis for intervalcensored data.
You can PROC ICLIFETEST to compute nonparametric estimates of the survival functions
and to examine the equality of the survival functions through statistical tests.
The following are highlights of the ICLIFETEST procedure's features:
 uses the efficient EMICM algorithm to estimate survival functions by default
 supports Turnbull's algorithm and the iterative convex minorant (ICM) algorithm
 computes standard errors of the survival estimates by using a multiple imputation method or a bootstrap method
 supports several transformationbased confidence intervals
 produces survival plots
 provides the weighted generalized logrank test

 supports a variety of weight functions for testing early or late differences
 supports a stratified test for survival differences within predefined populations
 supports a trend test for ordered alternatives
 supports multiplecomparison functionalities
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
ICLIFETEST Procedure
ICPHREG Procedure
The ICPHREG procedure fits proportional hazards regression models to intervalcensored data. You can fit models that have a variety of
configurations with respect to the baseline hazard function, including the piecewise constant model and the cubic spline model.
PROC ICPHREG maximizes the full likelihood instead of the Cox partial likelihood to estimate the regression coefficients.
Standard errors of the estimates are obtained by inverting the observed information matrix that is derived from the full likelihood.
The following are highlights of the ICPHREG procedure's features:
 tests linear hypotheses about the regression coefficients
 computes customized hazard ratios
 estimates and plots the survival function and the cumulative hazard function for a new set of covariates
 creates a SAS data set that contains the predicted values
 enables you to include an offset variable in the model

 enables you to weight the observations in the input data
 supports BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
ICPHREG Procedure
LIFEREG Procedure
The LIFEREG procedure fits parametric models to failure time data that can be uncensored, right censored, left censored, or
interval censored. The models for the response variable consist of a linear effect composed of the covariates and a random
disturbance term. The distribution of the random disturbance can be taken from a class of distributions that includes the
extreme value, normal, logistic, and, by using a log transformation, the exponential, Weibull, lognormal, loglogistic, and
threeparameter gamma distributions. The following are highlights of the LIFEREG procedure's features:
 estimates the parameters by maximum likelihood with a NewtonRaphson
algorithm
 estimates the standard errors of the parameter estimates from the
inverse of the observed information matrix
 fits an accelerated failure time model that assumes that the effect
of independent variables on an event time distribution is multiplicative
on the event time
 computes least square means and least square mean differences for classification effects
 performs multiple comparison adjustments for the pvalues and confidence limits for the least
square mean differences
 estimates linear functions of the model parameters

 tests hypotheses for linear combinations of the model parameters
 performs samplingbased Bayesian analysis
 performs weighted estimation
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that contains the parameter estimates, the maximized log likelihood,
and the estimated covariance matrix
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
LIFEREG Procedure
LIFETEST Procedure
A common feature of lifetime or survival data is the presence of rightcensored observations due either to withdrawal of experimental
units or to termination of the experiment. For such observations, you know only that the lifetime exceeded a given value; the exact
lifetime remains unknown. Such data cannot be analyzed by ignoring the censored observations because, among other considerations,
the longerlived units are generally more likely to be censored. The analysis methodology must correctly use the censored observations
in addition to the uncensored observations. The LIFETEST procedure computes nonparametric estimates of the survivor function either by
the productlimit method (also called the KaplanMeier method) or by the lifetable method (also called the actuarial method).
The following are highlights of the LIFETEST procedure's features:
 estimates the probability density function (lifetable method )
 produces the NelsonAalen estimates of the cumulative hazards and the corresponding standard errors
 performs nonparametric analysis of competingrisks data
 provides nonparametric ksample tests based on weighted comparisons of the estimated hazard rate
of the individual population under the null and alternative hypotheses
 enables you to specify the following tests:
 logrank test
 Wilcoxon test
 TaroneWare test
 PetoPeto test
 modified PetoPeto test
 FlemingHarrington G_{ρ} family of tests
 provides corresponding trend tests to detect ordered alternatives
 provides stratified tests to adjust for prognostic factors that affect the events rates in the various populations

 provides a likelihood ratio test, based on an underlying exponential model to compare the survival curves of the samples
 computes censored data linear rank statistics based on the exponential scores (logrank test) and the Wilcoxon scores (Wilcoxon test)
 provides five transformations to be used in the calculation of confidence limits for the quartiles of survival time
 supports weighted estimation
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
LIFETEST Procedure
PHREG Procedure
The PHREG procedure performs regression analysis of survival data based on the Cox proportional hazards model.
Cox's semiparametric model is widely used in the analysis of survival data to explain the effect of explanatory variables on hazard rates.
The following are highlights of the PHREG procedure's features:
 fits a superset of the Cox model, known as the multiplicative hazards model or the AndersonGill model
 fits frailty models
 fits competing risk model of Fine and Gray
 performs stratified analysis
 includes four methods for handling ties in the failure times
 provides four methods of variable selection
 permits an offset in the model
 performs weighted estimation
 enables you to use SAS programming statements within the procedure to modify values of the explanatory variables or to create ne explanatory variables
 tests linear hypotheses about the regression parameters
 estimates customized hazard ratios
 performs graphical and numerical assessment of the adequacy of the Cox regression model

 creates a new SAS data set that contains the baseline function estimates at the event times of each stratum for every specified set of covariates
 outputs survivor function estimates, residuals, and regression diagnostics
 performs conditional logistic regression analysis for matched casecontrol studies
 fits multinomial logit choice models for discrete choice data
 performs samplingbased Bayesian analysis
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates an output data set that contains parameter and covariance estimates
 creates an output data set that contains userspecified statistics
 creates a SAS data set that corresponds to any output table
 automatically created graphs by using ODS Graphics

For further details, see
PHREG Procedure
SURVEYPHREG Procedure
The SURVEYPHREG procedure performs regression analysis based on the Cox proportional hazards model for sample survey data.
Cox's semiparametric model is widely used in the analysis of survival data to estimate hazard rates when adequate explanatory variables are available.
The following are highlights of the SURVEYPHREG procedure's features:
 computes hazard ratios estimates
 computes variances of the regression parameters by using the following methods:
 Taylor series (linearization)
 balanced repeated replication (BRR)
 delete1 jackknife
 produces the following observationlevel output statistics:
 predicted values and their standard errors
 martingale residuals
 Schoenfeld residuals
 score residuals
 deviance residuals
 enables you to employ Fay's method with BRR
 enables you to input or output a SAS data set containing a Hadamard matrix for BRR
 enables you to import or export SAS data sets containing replicate weights for BRR or jackknife methods
 provides analysis for subpopulations, or domains, in addition to analysis for the entire study population

 supports programming statements that enable you to include timedependent covariates in the model
 performs BY group processing, which enables you to obtain separate analyses on grouped observations (distinct from subpopulation analysis)
 enables you to test linear hypotheses about the regression parameters
 enables you to estimate a linear function of the regression parameters
 creates a SAS data set that contains the estimated linear predictors and their standard error estimates, the residuals from the linear regression, and the
confidence limits for the predictors
 creates a SAS data set that contains the jackknife coefficients
 saves the context and results in an item store that can be processed with the PLM procedure
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
SURVEYPHREG Procedure