Hi:
There is also a nice paper by Kent and Quigley (Biometrika, 1988) that
describes a measure of dependence between the explanatory variables and
the response variable, under more general regression settings.
Best,
Ravi.
----- Original Message -----
From: "Hunsicker, Lawrence" <lawrence-hunsicker@uiowa.edu>
Date: Wednesday, January 7, 2004 10:00 am
Subject: Re: [S] Exact meaning of "rsquare" at end of summary(coxph)
> 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
> significantindependent 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.coxphfunction.
>
> 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
> followingpatients 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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