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I have survival data with 1 column for time, one for survival, and one for treatment group. Time is in units years. I created a cox model

   coxph(Surv(time,event)~treatment_group)

I have obtained the hazard ratio and p-value for treatment group. However, how do I determine the event rate per year, taking into account censoring. Essentially, I'm looking for x%/year in treatment group had the event.

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That kind of constant hazard rate corresponds to an exponential model. A Cox model does not assume that the hazard function can be expressed I that way. In fact, Cox tegressio makes no assumption on the hazard function other than it being affected proportionally by any model terms.

Assuming that an approximately constant hazard function makes sense in your case, you could proceed as follows: For each group/categorical covariate level you can get am estimate simply from (number of subjects with event)/(total time in years to first event or censoring) applied to each group. Alternatively, you can explicitly fit an exponential time to event model. This can be done either with survival analysis packages or a function for Poisson regression with event yes/no as the outcome and log (time to event or censoring) as an offset (the resulting likelihoods are equivalent up to constants).

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  • $\begingroup$ When you say: "(number of subjects with event)/(total time in years to first event or censoring)" for an estimate, do you essentially mean for example: Time: 5,4,7,4 Event: 0,1,1,0 then: 2 events/(5+4+7+4) = .1 events/year = 10% events/year is it accurate to say 10% event rate/year? $\endgroup$
    – RA_R
    Commented Sep 23, 2017 at 17:36
  • $\begingroup$ That's a hazard rate of 0.1/year. Thou get the percentage per 1 year from the cdf as $1-e^{-\lambda \times 1}$. $\endgroup$
    – Björn
    Commented Sep 24, 2017 at 7:08

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