# RE: st: Survival analysis: Interpretation of Cox regression

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject RE: st: Survival analysis: Interpretation of Cox regression Date Sun, 1 Jan 2006 10:57:21 +0000 (GMT)

```> 1) What is the proper interpretation of a significant result in
> Cox regression?

It is easiest to think about this as comparing groups (group 1 and the reference category) but the
same also applies to continuous variables. A significant effect would be that the hazard of
experiencing the event for patients in group 1 is different from the hazard of experiencing the
event in reference category. You can tell more by looking at the hazard ratios, they tell you by
how much these groups are different: e.g. an hazard ratio of .2 means that group 1 has a 80%
smaller hazard than the reference category. An hazard ratio of 1.4 means that group 1 has a 40%
higher hazard than the reference category. The mechanics of interpreting hazard ratios is the same
as the mechanics of interpreting odds ratios.

> 2) How can I verify if survivor function at a particular time
> (e.g. 5 years) are statistically different?

It is an assumption of the Cox model that the hazard of group one is always proportional to the
hazard of the reference category. So if you find an hazard ratio of 1.4, than the hazard of group
one is always 40% higher than the hazard of the reference category. If this effect is significant
than the groups are, by assumption, always significantly different.

> 3) How do I perform the above comparison adjusting for other
> factors?

If we just want to know the differnce between group 1 and the reference category, we would make a
dummy variable (called group1) which is 1 when the person is a member of group 1 and zero if he is
a member of the reference category. You properly -stset- your data, and than type -stcox group1-.
Say you want to controll for age, smoking history, and whether or not they came in the hospital
wairing a pink tutu. Than you type -stcox group1 age smoke tutu-

A while ago I wrote a short introduction to survival analysis as an appendix to another report. It
also discusses Cox regression. I just put it on my website: http://home.fsw.vu.nl/m.buis/ Another
excelent source of information is the book by Mario Cleves, William Gould, Roberto Gutierrez, "An
Introduction to Survival Analysis Using Stata", from Stata Press.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z214

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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