Using continuous variables that can be negative in a Cox Model

[Wladislav Diegelow]

Hi there,

a brief question on the sense (or nonsense) of a model, that I am setting up right now:

I am setting up a cox regression. I have measured the difference of a language variable of my participants BEFORE and AFTER a certain event, i.e., it may take the value 3 BEFORE the event and 1 AFTER the event. The language difference variable would then be "-2" (1 minus 3), i.e., the language variable decreases after the first event.

I would then like to test, if the change in this variable effects the likelihood of the occurrence of a second event.

Is the following interpretation correct: If the Hazard Ratio of my Language_difference variable is 0.98, this means that an increase in my language variable (AFTER-value is higher then the BEFORE-value, i.e. the language variable increases after the first event), this would mean a decrease in the probability of the occurrence of the second event. Vice versa, if the Language_difference would be negative (i.e., the AFTER-value is lower then the BEFORE-value), the Hazard Ratio of 0.98 would mean that a decrease in my Language variable would lead to an increase in the probability of the occurrence of my second event?

I tried to keep my description as narrow as possible. My main issue is, if the variable in the cox model is allowed to take negative values and how the hazard ratio could then be interpreted.

If you need some additional information, or if anything is unclear, feel free to ask!

Best regards

[Chris Boudreaux]

Yes you sound correct. The way you interpret the hazard ratio is a 1 unit increase in x is associated with a | 1.00 - exp(beta)| change in the hazard rate. Your hazard rate indicates that a 1 unit increase in the language variable is associated with a 2 percent decrease (1.00 -0.98) in the hazard of a second event.

With that said, it sounds like you should use a logit or probit model and not a cox model. Your outcome appears binary (1= received second language event; 0= did not). Cox models are used to measure survival as time to event outcomes and have right or left hand censoring