Survival Analysis Procedures

There are three SAS procedures for analyzing survival data: LIFEREG, LIFETEST and PHREG. PROC LIFEREG is a parametric regression procedure for modeling the distribution of survival time with a set of concomitant variables . PROC LIFETEST is a nonparametric procedure for estimating the survivor function, comparing the underlying survival curves of two or more samples, and testing the association of survival time with other variables. PROC PHREG is a semiparametric procedure that fits the Cox proportional hazards model.

The LIFEREG Procedure

The LIFEREG procedure fits parametric accelerated failure time models to survival data that may be left, right, or interval censored. The parametric model is of the form

where y is usually the log of the failure time variable, x is a vector of covariate values, ² is a vector of unknown regression parameters, ƒ is an unknown scale parameter, and ˆˆ is an error term. The baseline distribution of the error term can be specified as one of several possible distributions, including, but not limited to, the log normal, log logistic, and Weibull distributions. Several texts that discuss these parametric models are Kalbfleisch and Prentice (1980), Lawless (1982), and Nelson (1990).

The LIFETEST Procedure

The LIFETEST procedure computes nonparametric estimates of the survival distribution function. You can request either the product-limit (Kaplan and Meier 1958) or the life-table (actuarial) estimate of the distribution. The texts by Cox and Oakes (1984)andKalbfleisch and Prentice (1980) provide good discussions of the product-limit estimator, and the texts by Lee (1992)andElandt-Johnson and Johnson (1980) include detailed discussions of the life-table estimator . PROC LIFETEST computes nonparametric tests to compare the survival curves of two or more groups. The procedure also computes rank tests of association of the survival time variable with other concomitant variables as given in Kalbfleisch and Prentice (1980, Chapter 6).

The PHREG Procedure

The PHREG procedure fits the proportional hazards model of Cox (1972; 1975)to survival data that may be right censored. The Cox model is a semiparametric model in which the hazard function of the survival time is given by

where » ( t ) is an unspecified baseline hazard function, x ( t ) is a vector of covariate values, possibly time-dependent, and ² is a vector of unknown regression parameters. The model is referred to as a semiparametric model since part of the model involves the unspecified baseline function over time (which is infinite dimensional) and the other part involves a finite number of regression parameters. Several texts that discuss the Cox regression models are Collett (1994), Cox and Oakes (1984), Kalbfleisch and Prentice (1980), and Lawless (1982).