Let's say I perform a Cox regression including 3 predictors that relate to the survival:
Hazard ratios (HR) for predictors
- Sex: Hazard ratio for males = HR 1.5
- Treatment: Hazard ratio for being treated, as compared with controls = HR 1.5
- Race: Being black, as compared with being white = HR 1.5.
If I wonder what the hazard will be for a black male with treatment, can I simply add upp the HRs; 1.5 + 1.5 + 1.5 = 4.5?
I understand how interactions work and how they should apply. An interaction term between these predictors can definitely be recommended, but I was wondering whether the simple addition of coefficients will convey their additive risk?
Textbooks of Cox regression often mention the terms additivity and multiplicatively, but they seldom elaborate on them.
I guess any answer to this would also extend to linear and logistic regression.