Specialty › Tests on summarized data

Incidence rate CI (Poisson)

The exact (Garwood) Poisson interval bounds an incidence rate computed as events divided by person-time.

What is Incidence rate CI (Poisson)?

When you observe e events over T person-time, the rate estimate is λ̂ = e / T with the Poisson CI from the χ² distribution: λ_L = ½ · χ²_{2e, α/2} / T and λ_U = ½ · χ²_{2(e+1), 1 − α/2} / T. This is exact regardless of e (works even when e = 0).

Asymptotic alternatives (Wald, Wilson on √e) are wrong for small e; always prefer exact Garwood for incidence rates.

When should I use Incidence rate CI (Poisson)?

Reporting an incidence rate from a single-arm study or registry.

What data does it need?

Event count + person-time + confidence level.

What does it report?

Rate with exact Poisson CI.

How do I interpret the result?

Exact CI is asymmetric; for e = 0 events the lower bound is 0 and the upper is non-zero — informative even with no observed events.