Question about how to correctly interpet Cox proportional hazards model for continuous variables I'm having an hard time trying to understand how to interpret the coefficients after fitting a Cox proportional hazards (CPH) model. I think I understand it when the variables are binary, in this case, the exponentiated coefficient refers to the hazard ratio between the two classes. However, this doesn't make sense when we're talking about a continuous variable, because we can't compare two groups. I've tried looking at other examples using CPH, but every time they only use binary variables to interpret the coefficients.
 A: This isn't fundamentally different from interpreting the coefficient for a continuous predictor in ordinary linear regression. A coefficient still represents the change in outcome for a one-unit change in the predictor. The difference is in the way the change in outcome is represented in the model.
In a Cox survival model, changes in outcomes are represented by changes in log hazards or by hazard ratios. The original regression coefficient for a continuous predictor is the change in the log-hazard of an event associated with a one-unit change in the predictor. If you exponentiate the coefficient to get a hazard ratio, then you get the hazard ratio associated with a one-unit change in the predictor.
If you are interested in the hazard ratio associated with some change other than one unit in the predictor, it's most straightforward to multiply the coefficient (in log-hazard scale) by that change of predictor and only then exponentiate to get the corresponding hazard ratio.
A: You can interpret the exponentiated coefficients as the hazard ratio associated with increasing the independent variable in 1 unit. For example, if the coefficient is $\beta=0.7$, we have $\exp(\beta)\approx2.0$, so increasing the independent variable by 1 doubles the hazard function ($\text{HR}=2.0$).
Interpretation is less straightforward than in the binary case and requires you to understand the units of your data. It may make sense to rescale your independent variables, so that 1 unit corresponds to something like 1 standard deviation or 10 years of age.
