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st: R: Proportional hazards assumption in Cox model


From   "Carlo Lazzaro" <carlo.lazzaro@tin.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: R: Proportional hazards assumption in Cox model
Date   Wed, 25 Feb 2009 09:14:05 +0100

Dear Mingfeng,
the usual test for checking the fulfilment of Cox proportional hazard
assumption requirements is Schoenfeld residuals [in Stata 9.2/SE -
schoenfeld(newvars)-].
Unfortunately, Cox proportional hazard assumption may not hold. 
An example about this lack of holding of Cox proportional hazard assumption
(more frequent than usually reported I scientific articles, I suspect) can
be found in Jes S Lindholt, Svend Juul, Helge Fasting and Eskild W
Henneberg. Screening for abdominal aortic aneurysms: single centre
randomised controlled trial. BMJ 2005;330;750-; originally published online
9 Mar 2005; doi:10.1136/bmj.38369.620162.82. 
The authors wrote "We used Cox proportional hazards regression to
compare specific mortality due to abdominal aortic aneurysm
and overall mortality. As the proportional hazards assumption
was not fulfilled, we decided to carry out separate analyses for the
periods before and after 1.5 years after randomisation".
Hence, the moved to Kaplan-Meier estimates of mortality (a non parametric
method that makes no assumptions about the underlying risk function).
As an aside, Svend Juul is an epidemiologist and also a relevant contributor
to Stata List. 

For further details on Survival analysis, I will recommend you to take a
thorough look at:
 Cleves MA, Gould WG, Gutierrez R. An Introduction To Survival Analysis
Using Stata. Revised edition. College Station: StataPress, 2006; 
[ST] Stata manual. Survival analysis and epidemiological table. Release 9.

Kind Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Mingfeng Lin
Inviato: mercoledì 25 febbraio 2009 6.09
A: statalist@hsphsun2.harvard.edu
Oggetto: st: Proportional hazards assumption in Cox model

Greetings!

I have a quick question about Cox models: I understand that we need to
test for the assumption of proportional hazards for all covariates,
and if any one fails the test, we should be concerned about the
statistical inference on that variable; plus we should consider things
such as time varying effects, stratification, and so on.  But what if
none of these solves the problem? In particular, is it appropriate to
say that if one set of variables passes the test, we can still be
confident about the estimates of their coefficients - despite the
failure of other variables and global tests? In other words, while we
know that Cox models tend to be quite robust, how much latitude do we
have in terms of the proportional hazards assumption? How robust is
this model, just to be specific?

I'm still learning event history analysis, and the papers that I have
came across so far (empirical papers in social sciences) do not seem
to actually test that assumption (or maybe they forgot to report the
results), so I am just curious.

Thank you very much for any suggestions you can provide.  If you could
refer me to specific papers on this, it would be really helpful.

Mingfeng
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