# How should I interpret the exp(coef) hazard ratio in Cox regression?

I know it looks like a duplicate, but wait!

I am analysing survival data in R, and have a little trouble correctly interpreting the results of the Cox-Regression. I have read the other (amazing) CrossValidated posts about the subject, but still have a little doubt.

For instance, I am looking at if radiation therapy has an effect on survival of cancer patients. R returns an exp(coef) for radiation therapy yes of 0.5882. I understand this represents the hazards ratio (I guess the hazard represents the average probability to be dead at any specific time), i.e. the ratio between the hazard of a patient who received radiation therapy and the hazard of a patient who did not.

However, how can I understand which population actually survive better here (imagine I don't have any Kaplan-Meier curve)? How does the fact that R returns the HR for radiation therapy yes influence the way I interpret the HR?

Alright, a couple things.

First: The hazard is defined as the instantaneous probability of an event at time t, conditional on it not having occured in any previous time.