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
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
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
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
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
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
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