# SAS/STAT Software

## 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 interval-censored data
• ICPHREG Procedure — Proportional hazards regression models to interval-censored 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 product-limit method (also called the Kaplan-Meier 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 interval-censored 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 transformation-based confidence intervals produces survival plots provides the weighted generalized log-rank 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 multiple-comparison 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 interval-censored 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, log-logistic, and three-parameter gamma distributions. The following are highlights of the LIFEREG procedure's features:

 estimates the parameters by maximum likelihood with a Newton-Raphson 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 p-values 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 sampling-based 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 right-censored 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 longer-lived 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 product-limit method (also called the Kaplan-Meier 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 (life-table method ) produces the Nelson-Aalen estimates of the cumulative hazards and the corresponding standard errors performs nonparametric analysis of competing-risks data provides nonparametric k-sample 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: log-rank test Wilcoxon test Tarone-Ware test Peto-Peto test modified Peto-Peto test Fleming-Harrington Gρ 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 (log-rank 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 Anderson-Gill 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 case-control studies fits multinomial logit choice models for discrete choice data performs sampling-based 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 user-specified 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) delete-1 jackknife produces the following observation-level 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 time-dependent 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