Date:         Thu, 1 Jul 2004 15:47:01 -0500
Reply-To:     "Howells, William" <Howells_W@BMC.WUSTL.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Howells, William" <Howells_W@BMC.WUSTL.EDU>
Subject:      PHREG: comparing coefficients across models
Content-Type: text/plain; charset="US-ASCII"

We have two plain vanilla Cox regression models.  In model 1 we have
covariates x1 and x2.  In model 2 we have covariates x1 and x3.  x2 and
x3 measure the same thing, but x2 is categorical and x3 is continuous.
The question came up as to how to compare x2 and x3.  Can't put them
both in the same model because of collinearity.  Hazard ratios may not
be compared because the scales are different.  The best we could come up
with was to compare the t value from the Wald test, beta divided by its
standard error, and the resulting p-value.  x3 certainly has a bigger t
value, and a smaller p value.  Can we conclude that x3 is a "stronger
predictor than" x2?  I think I remember some cautions comparing
coefficients across Cox models due to the baseline hazard not being
modeled.  Some in the meeting wanted to say x3 "explains more of the
variance" than x2.  But we don't have an R2 (R-squared) like linear
regression.  I don't believe we can make any statements about percent of
variance explained in Cox models, again due to lack of modeling the
baseline hazard.  Any ideas?

Bill Howells, MS
Wash U Med, St Louis MO