# Effects of right-censoring on Poisson IRR estimates

I have some time-to-event data with right-censoring.

Details Added: Each subject is followed up until first event (no recurrent events) or loss to follow-up. Let's assume there are no competing risks.

Given that rates are constant (and other Poisson assumptions hold), and censoring is non-informative, am I correct in thinking that Poisson regression gives unbiased estimates of the incidence rate ratio in the following model?

glm(status ~ trt, offset = log(time), family = poisson(link = "log"), data = df)


A few test datasets have yielded very similar results between the Cox HR and Poisson IRR, but I want to understand whether this is general.

My logic is that any bias in the estimation of the rates is balanced between both groups, leaving ratios unaffected?

• It's not clear to me from your description where the right censoring comes from and how you are handling right-censored observations in your model. Is this a situation where an individual can have at most one event, and you are simply not recording an event at the last observation time? What determines that last observation time? Or might an individual experience more than one event, and you are recording the number of events over an observation duration?
– EdM
Commented May 15, 2023 at 11:34
– ZKA
Commented May 15, 2023 at 17:36
• If censoring is non-informative, how exactly is either model providing a biased estimation of rates? How is the Cox model providing an estimate of rates at all? Commented May 15, 2023 at 17:44
• I think that this page provides the theoretical justification that you're looking for. Please look that over and edit this question further if it doesn't do so. @AdamO I think it's the rate ratio between trt groups that's being estimated in the Cox model.
– EdM
Commented May 15, 2023 at 18:40
• @EdM a hazard is an instantaneous rate. If the hazards are non-proportional, I can believe that these models estimate fundamentally different things, but otherwise they should be consistent for the same value. Correct? Commented May 15, 2023 at 18:47