# Crude incidence rate ratios giving different results to conditional Poisson regression model

I am analysing the treatment effect of a compound, namely the rate at which an event occurs during treatment. I have calculated the crude incidence rate ratio for a group of subjects, each of whom has exposure time and non-exposure time, using $$IRR = \frac{\textrm{# of events during exposure} / \textrm{Total person years during exposure}}{\textrm{# of events during non-exposure} / \textrm{Total person years during non-exposure}}.$$

I got an IRR of $$\frac{0.47}{0.16} = 2.94$$, which I interpret as meaning the event rate during exposure is 2.94 times greater than during non-exposure.

However, if I run a conditional Poisson regression with a formula $$EventNumber \sim Exposure + strata(subject\_id) + offset(log(duration)),$$ I get a coefficient for the exposure variable where $$\exp(coefficient) = \exp (-0.38) = 0.68,$$ which indicates that the incidence rate for exposure is less than that of baseline (non-exposure).

I'm confused about these conflicting results. If I try running a non-conditional Poisson regression, I get a similar number as 0.68. Is it reasonable that I get two completely different results by computing these two values? Whilst I'm not surprised they are different, I was a bit taken aback that they were so different.

• I figured out what was wrong -- I was not using the natural logarithm when calculating the log(duration), I was using log10. – as646 Jul 1 at 15:01