### Sunday, January 01, 2006

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

> 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

visiting adress: Buitenveldertselaan 3 (Metropolitan), room Z214

+31 20 5986715

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

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