I'm using a Cox survival analysis model in Stata. My covariates include a series of mutually-exclusive dummies. As in other regression models, I leave one out as a reference.
If I change the reference dummy, the significance and hazard ratios are changing where I wouldn't expect it.
A fictional example:
6 race/ethnicity categories.
I leave out "white" as the reference.
"Asian" has a hazard ratio of 1.3, and is significant.
I take that to mean the Asian population is 1.3 times more likely to have the event occur.
Now I leave out "Asian" instead of "white", because I want to look at the difference between the Asian population and other groups.
I would expect "white" to have a hazard ratio of 0.7 and be significant, since its relative to Asian. However, it has a vastly different hazard ratio, and/or the difference is no longer significant.
What is the explanation for that? Is there some sort of instability in my model? Is this a mathematical thing my brain is not grasping well?
To simplify (and make up for formatting difficulties), I've included just the dummies, hazard ratio, and z-score.
Model 1: variable haz. ratio z category1 .567 -2.41 category2 .906 -0.76 category3 .842 -1.16 category4 .940 -0.49 category5 .654 -3.02 ** category6 2.26e-14 -0.00 category7 .437 -3.14 category8 (I omitted; placeholder)** category9 .809 -0.46 category10 2.16e-14 -0.00 Model 2: variable haz. ratio z category1 .868 -0.58 category2 1.38 2.08 category3 1.29 1.50 category4 1.44 2.50 category5 (I omitted; placeholder)** category6 2.16e-19 -0.00 category7 .669 -1.50 category8 1.53 3.02** category9 1.24 0.46 category10 7.47e-20 -0.00
I'm trying to figure out why the relationship between categories 5 and 8 is changing, depending on which is omitted.