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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?

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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.

So yes, the hazard ratio is a ratio of hazards - in your case, Hazard(Radiation=Yes)/Hazard(Radiation=No).

That ratio is all you need to know. It indicates that someone who receives radiation has about half the hazard of one who doesn't - that is, they are less likely to have the event (and by extension, survive, if your event is 'died of cancer'). If you're familiar with odds ratios or relative risks, you can think about these in broadly the same way for interpretation.

For a single binary exposure like what you are describing, which one R returns doesn't really change things. The HR for Radiation=No is just 1/0.5882 = 1.70, which has the same interpretation but changing the focus - that is, people who don't receive radiation have a little under twice the hazard as those who do.

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  • $\begingroup$ may I ask why you say that the hazard ratio may broadly be have the same interpretation as an odds ratio? ( I am also teaching my self survival analysis). $\endgroup$ – Guilherme Marthe Jun 15 '17 at 3:08
  • $\begingroup$ @GuilhermeMarthe In this context, I'm speaking in the sense of 1 = a null result, >1 = the exposure is harmful, <1 the exposure is protective. $\endgroup$ – Fomite Jun 15 '17 at 3:11
  • $\begingroup$ Huuum I see. The interpretation seems a little looser than in parametric estimation, I believe. Another question: is log hazard a thing, like log odds is? $\endgroup$ – Guilherme Marthe Jun 15 '17 at 3:14
  • $\begingroup$ @GuilhermeMarthe It depends on what you mean by "a thing"? But a Cox model is made up of a linear combination of variables on the log scale. $\endgroup$ – Fomite Jun 15 '17 at 3:19
  • $\begingroup$ @Fomite, thanks, great answer. Really helpful. I still have a doubt about the interpretation of one of my results, but I think it is better if I ask another question. $\endgroup$ – francoiskroll Jun 15 '17 at 7:47

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