Incidence Rate and Person-Time Analyzer

Scope

This calculator estimates an incidence rate from an aggregate event count and person-time, or compares rates from two independent populations. It does not calculate cumulative incidence, risk, prevalence, odds, hazard ratios, adjusted estimates, or person-time from individual dates.

Formula and inference

The incidence rate is the event count divided by accumulated time at risk. Each group uses a two-sided Garwood exact Poisson confidence interval. The incidence-rate ratio uses a central exact conditional interval and matching central exact conditional test. The incidence-rate difference uses an approximate MOVER interval formed from the two Garwood component intervals. No continuity correction is added to zero counts.

Assumptions and limitations

• The two groups are independent and use comparable event definitions, ascertainment, person-time units, and risk-period rules.
• Counts follow a Poisson model closely enough for the stated inference and each aggregate rate adequately summarizes its group.
• An incidence rate is not a risk or probability and may exceed one per selected time unit.
• Repeated events within a participant may be correlated or overdispersed. Individual-level Poisson, negative-binomial, GEE, frailty, or recurrent-event models may then be preferable.
• Crude aggregate rates do not account for confounding, clustering, time-varying exposure, competing risks, or informative follow-up.
• A non-significant result does not establish equivalence or equal rates.

Validation

Version 1.0.0 was checked against independent R calculations for Garwood intervals, central exact conditional rate-ratio inference, and MOVER rate-difference intervals. Automated tests cover ordinary, sparse, zero-event, unequal-person-time, parsing, direction, scaling, reporting, privacy, and responsive-interface cases. Version 1.1.0 retains these statistical methods with a harmonized interface. Owner review, native PDF pagination and screen-reader listening checks remain pending. Availability does not constitute regulatory validation.

Privacy

All calculations use aggregate values in browser memory. The app does not transmit, upload, or persist entered counts, labels, person-time, or results. Do not enter identifiable or confidential information.

References

1. Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice. Lesson 3: Measures of Risk.
2. Garwood F. Fiducial limits for the Poisson distribution. Biometrika. 1936;28:437–442.
3. Zou GY, Donner A. Construction of confidence limits about effect measures: a general approach. Stat Med. 2008;27:1693–1702.
4. Li HQ, Tang ML, Poon WY, Tang NS. Confidence intervals for difference between two Poisson rates. Commun Stat Simul Comput. 2011;40:1478–1493.
5. R Core Team. stats::poisson.test: Exact Poisson tests.