Poisson Incidence Rate & Incidence Rate Ratio (IRR)
In follow-up studies outcomes accumulate over "person-time" (person-years/person-months). One group gives the incidence rate with an exact Poisson confidence interval; two groups give the incidence rate ratio IRR (with a Wald log-CI and an exact conditional CI). Suited to cohort studies, adverse-event rates, recurrence rates and other person-time outcomes.
① Input
| Event count e | Person-time t | |
|---|---|---|
| Group 1 | ||
| Group 2 |
How to use & methodology
How does an incidence rate differ from a 'proportion'?
A proportion has people in the denominator; an incidence rate has 'person-time' (person-years/person-months), counting how long each person was observed — appropriate for cohort studies with unequal follow-up and censoring.
How does IRR relate to RR and HR?
IRR is the ratio of two incidence rates, assuming the rate is roughly constant over the observation period (Poisson); RR uses the cumulative incidence proportion; HR comes from a survival model and lets the rate change over time. IRR is most natural for person-time outcomes with a stable rate.
Which CI — Wald or exact?
When event counts are large the two are close, so reporting the Wald log CI is fine; when events are few or one group is 0, the exact conditional CI is more robust (Wald is then unreliable or undefined).
How is person-time calculated?
Sum each individual's observation time (e.g. 2 years of follow-up = 2 person-years). The clock stops at the outcome or at censoring. The total person-time is the denominator.