Cox regression interaction interpretation

[joldham1]

Hello, I'm a stats lightweight and am having trouble interpreting the interaction term in the Cox model I've constructed. I've read previous posts regarding interaction terms in nonlinear models which have helped but I still can't quite tell if I'm interpreting my outputs correctly. Below is a Cox model with 3 terms - SNP (0, 1), treat (0, 1) and treat#SNP interaction term. From what I've read you can't directly interpret the interaction HR from the output so my question is how to determine the HR in individuals for whom SNP==1 and treat==1 compared to those for whom SNP==0 and treat==0. Thx much.
Cox regression -- Breslow method for ties

No. of subjects = 151 Number of obs = 151
No. of failures = 35
Time at risk = 7268.285718
LR chi2(6) = 20.33
Log likelihood = -156.00389 Prob > chi2 = 0.0024

---------------------------------------------------------------------------------
_t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
SNP | 1.319208 .5351759 0.68 0.495 .5956595 2.921652
|
treat |
1 | 1.459607 .7583516 0.73 0.467 .5272138 4.040966
|
treat#SNP |
1 | .1727357 .1479031 -2.05 0.040 .0322515 .9251545
|
---------------------------------------------------------------------------------

[Joe Canner]

What command did you use to get this output?

In any case, if you do stcox SNP#treat you should get coefficients for all combinations of SNP and treat (01, 10, and 11) versus both equal 0.

[Marcos Almeida]

Hello "jodham1" (please re-register with your name and family name by clicking on "contact us" sign, below to right),

I would interpret your results this way: SNP = 1 has non-significant p-value related to the outcome; treat =1, also, has no significant p-value related to the outcome. However, for those who are at the same time "treat" =1 and SNP =1, there are significant p-values related to the outcome.

By the way, with regards to the use of interaction terms without the main terms in a Cox regression (and I'm not saying I'm in favor or against it), please see this comment from the book "An Introduction to Survival Analysis Using Stata" (by Cleves, Gutierrez, Gould and Marchenko, third edition, StataPress):


"It is commom to read that interaction effects should be included in the model only when the corresponding main effects are also included, but there is nothing wrong with including interaction effects by themselves [...] . The goal of the researcher is to parameterize what is reasonably likely to be true for the data considering the problem at hand and not merely following a prescription".

Hopefully it helps.

Best,
Marcos

[Clyde Schechter]

You can do this directly as:

lincom SNP + treat + treat#SNP, hr

But assuming you're using a recent version of Stata, better still is to use

margins treat#SNP

to get the hazard ratios associated with all four combinations of treat and SNP.

[Maarten Buis]

The other suggestions aren't wrong, but you can directly interpret the HR, but not as a hazard ratio but as a ratio of hazard ratios, see: http://maartenbuis.nl/publications/interactions.html This site also contains a link to an example using Cox regression. Also see http://maartenbuis.nl/publications/ref_cat.html to get what Clyde suggested without the need of post-estimation command.

A very useful way to understand this is to play around with the different methods in one example until you find out that they are exactly equivalent, that is, they are just different ways of saying exactly the same thing.