Terry and all:
I appreciate deeply Terry's point about it not being clear what reduction of
unexplained variability means in a Cox analysis, and that there are not
unique definitions of this concept. Actually, my intent in using this
concept in the paper that I am preparing goes very much along the line one
part of the discussion in the Korn paper. I am doing a "Baseline
Covariates" type of paper following a clinical trial. What I want to make
clear to the reader is that, although there are many nominally significant
independent baseline predictors, only the first few make any substantial
contribution to the overall efficiency of the model, and even all of them in
aggregate only explain about a third of the variability. The measure
computed in Terry's summary.coxph makes that point sufficiently clear. I
personally have pretty strong reservations about the whole business of a
"baseline predictors" approach to prognostication, though identifying
factors that are strong predictors has some utility in trying to make a bit
more precise and to add power to other ad hoc retrospective analyses. So
from my point of view the exact measure that I use is probably not too
important. Ease of computation is important, and in this particular case,
the ease of computation is complete, as the number falls out of the analyses
that I am doing anyhow, thanks to Terry's including it in his summary.coxph
function.
Larry Hunsicker
-----Original Message-----
From: Terry Therneau [mailto:therneau@mayo.edu]
Sent: Monday, January 05, 2004 10:11 AM
To: lawrence-hunsicker@uiowa.edu; s-news@lists.biostat.wustl.edu
Cc: Michael.Schemper@vm230.AKH-WIEN.AC.AT
Subject: Re: [S] Exact meaning of "rsquare" at end of summary(coxph)
There are dozens of definitions for an R-square for a Cox model. I really
liked the following paper
Korn, Edward L. , and Simon, Richard (1990), ``Measures of explained
variation for survival data'', Statistics in Medicine, 9 , 487-503
which highlights, for me, one of the main issues. Say that we are following
patients with advanced lung cancer (a median survival of < 2 years), a
model has predicted 10 year survival for patient X, and the patient actually
lived 20 years. Any physician would say that this was perfect prediction,
and most R-square statistics would say that it was very bad -- worse than
telling a 3 year survivor that he had only 6 months.
What exactly R-squared SHOULD be for survival studies is a hard question.
What is used in coxph is a moderately good measure proposed by Nagelkirke,
that also has the virtue of being easy to compute.
Michael Schemper has given, I think, the most thought to the issues and
has published several papers. (He also points out that Nagelkirke's idea
appears earlier due to someone else -- I forget who). To dig deeper I would
recommend looking at his work.
Terry Therneau
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