The SURVEYPHREG Procedure
- Overview
- Getting Started
-
Syntax
PROC SURVEYPHREG Statement BY Statement CLASS Statement CLUSTER Statement DOMAIN Statement ESTIMATE Statement FREQ Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement NLOPTIONS Statement OUTPUT Statement Programming Statements REPWEIGHTS Statement SLICE Statement STORE Statement STRATA Statement TEST Statement WEIGHT Statement -
Details
Notation and Estimation Failure Time Distribution Time and CLASS Variables Usage Partial Likelihood Function for the Cox Model Specifying the Sample Design Missing Values Variance Estimation Domain Analysis Hypothesis Tests, Confidence Intervals, and Residuals Output Data Sets Displayed Output ODS Table Names ODS Graphics
-
Examples
- References
Overview: 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 procedure provides design-based variance estimates, confidence intervals, and hypothesis tests concerning the parameters and model effects. See Chapter 3, Introduction to Statistical Modeling with SAS/STAT Software, and Chapter 14, Introduction to Survey Sampling and Analysis Procedures, for an introduction to the basic concepts of survey data analysis; see Chapter 13, Introduction to Survival Analysis Procedures, for an introduction to the basic concepts of survival analysis.
The survival time of each member of a finite population is assumed to follow its own hazard function, 
, expressed as
 |
where 
is an arbitrary and unspecified baseline hazard function, 
is the vector of explanatory variables for the 
th population unit at time 
, and 
is the vector of unknown regression parameters.
The SURVEYPHREG procedure produces a sample-based estimate 
of finite-population proportional hazards regression parameters 
by maximizing the partial pseudo-log-likelihood 
based on observed covariates and observed survival time 
. The procedure also produces an estimate of the sampling variance 
, which assumes the values of the finite population 
are fixed. For statistical inference, PROC SURVEYPHREG incorporates complex survey sample designs, including designs with stratification, clustering, and unequal weighting.
The procedure also allows time-dependent explanatory variables. An explanatory variable is time-dependent if its value for any given individual can change over time. Time-dependent variables have many useful applications in survival analysis. You can include time-dependent variables such as blood pressure or blood chemistry measures that vary with time during the course of a study. You can also use time-dependent variables to test the validity of the proportional hazards model.
Several optimization techniques are available in SURVEYPHREG to maximize the log likelihood. Hazard ratio estimates can also be obtained along with parameter estimates. Sampling errors of the regression parameters and hazard ratios are computed by using either the Taylor series (linearization) method or one of the replication (resampling) methods that are based on complex sample designs (Binder; 1983; Wolter; 2007; Särndal, Swensson, and Wretman; 1992; Binder; 1992; Lohr; 2009; Fuller; 2009). These variance estimators essentially assume the finite population as fixed and estimate the variability due to the random sample selection mechanism.
The remaining sections of this chapter contain information about how to use PROC SURVEYPHREG, information about the underlying statistical methodology, and some applications of the procedure. The section Getting Started: SURVEYPHREG Procedure introduces PROC SURVEYPHREG with an example. The section Syntax: SURVEYPHREG Procedure describes the syntax of the procedure. The section Details: SURVEYPHREG Procedure summarizes the statistical techniques employed in PROC SURVEYPHREG. The section Examples: SURVEYPHREG Procedure includes some additional examples of useful applications. Experienced SAS/STAT software users might decide to proceed to the "Syntax" section, while other users might choose to read both the "Getting Started" and "Examples" sections before proceeding to "Syntax" and "Details."