No intercept is used in the underlying Cox regression model fit by PROC PHREG. Hence, PROC PHREG does not estimate an intercept parameter.

Essentially, the intercept is absorbed into the unknown and unspecified baseline hazard, h₀(t). Suppose an intercept, β₀, exists. Then the underlying Cox proportional hazards model is h(t) = h₀(t) exp(β₀ + β₁x₁ + ... + β_kx_k) or equivalently h(t) = h₀^*(t) exp(β₁x₁ + β₂x₂ + ... + β_kx_k), where h₀^*(t) = h₀(t) exp(β₀). So, the intercept is involved as just another constant that is part of the baseline hazard. The baseline hazard is unknown and unspecified and is done away with in the partial likelihood method as discussed by Cox (1972).

An intercept term could potentially be introduced using the OFFSET= option. However, this would not affect the results and, in particular, the intercept would cancel out of any hazard ratio(s).

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Cox, D. R. 1972. "Regression Models and Life-Tables (with Discussion)." Journal of the Royal Statistical Society Series B, 34:187-220.

Operating System and Release Information

Product Family	Product	System	SAS Release
			Reported	Fixed*
SAS System	SAS/STAT	All	n/a

* For software releases that are not yet generally available, the Fixed Release is the software release in which the problem is planned to be fixed.

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Because it is absorbed into the unknown and unspecified baseline hazard function.

Type:	Usage Note
Priority:	low
Topic:	SAS Reference ==> Procedures ==> PHREG

Date Modified:	2017-10-31 10:50:54
Date Created:	2005-11-14 16:28:57