[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Measures of frequency and association](https://durgical.com/en/epidemiology/areas/measures/) › Incidence rate and person-time

# Incidence rate and person-time

- Measure

New cases divided by the total time each person was observed; it is used when follow-up differs between people.

Updated Nov 5, 2026

## Key points

- Incidence rate = new cases / total person-time at risk.
- Each person contributes time until they become ill, leave the study or follow-up ends.
- Units are cases per person-time (per 1,000 person-years, for example).
- Rate ratio = rate in the exposed / rate in the unexposed; it is read like a relative risk.
- It assumes roughly constant risk over time: 100 people for one year count the same as 10 people for ten years.

## What it is

In a real cohort people enter and leave at different times: some move away, some die of other causes, some become ill. The incidence rate adds up the time each person was at risk (person-time, for example person-years) and divides new cases by that total. This compares how fast disease appears in different groups even when follow-up is unequal, and the ratio of two rates is the rate ratio.

## Formula and reading

- IR = cases / Σ time at risk. It ranges from 0 to infinity; it is not a proportion.
- Rate ratio = IR exposed / IR unexposed. 1 = no association; above 1 = more cases with exposure; below 1 = fewer.
- A person who becomes ill stops contributing time at risk from the moment of diagnosis.

## Worked example

- Data: 100 night-shift workers: 60 are followed 3 years without injury, 30 leave at 2 years and 10 are injured, on average at 1 year.
- Person-time: 60 × 3 = 180, 30 × 2 = 60 and 10 × 1 = 10; total 250 person-years.
- Night-shift rate = 10 / 250 = 0.04 per person-year = 40 per 1,000 person-years.
- Day shift: 6 injuries in 400 person-years = 0.015 = 15 per 1,000 person-years.
- Rate ratio = 40 / 15 ≈ 2.7 (rounded to one decimal).
- Reading: in this example injuries occur about 2.7 times as fast on the night shift.

## Markers

- person-years
- IR
- rate ratio

## How to read it

- Cancer registries and surveillance reports give incidence per 100,000 person-years.
- Trials with uneven follow-up report events per 100 patient-years.

## Common pitfalls

- Dividing by the number of people instead of person-time.
- Continuing to add time after the person became ill.
- Assuming constant risk when risk changes a lot over time (for example, right after surgery).

## Memory aid

Everyone brings their own clock: a rate does not count heads, it counts the time each head spent at risk.

## Test yourself

Think of the answer, then tap the question to see it.

## Ten people are followed 5 years each and another 20 for 1 year. How much person-time do they contribute?

10 × 5 + 20 × 1 = 70 person-years.

## Why is person-time used instead of the number of people?

Because follow-up varies; person-time weights how long each person was actually at risk.

## What does a rate ratio of 0.5 indicate?

Disease appears at half the speed in the exposed compared with the unexposed: exposure is linked to fewer cases.

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## Connections

## Related 5

- [Incidence](https://durgical.com/en/epidemiology/incidence/)
- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Prevalence, incidence and duration](https://durgical.com/en/epidemiology/prevalence-incidence-and-duration/)
- [Cohort study](https://durgical.com/en/epidemiology/cohort-study/)
- [Survival analysis and censoring](https://durgical.com/en/epidemiology/survival-analysis-and-censoring/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [Principles of Epidemiology | Lesson 3 - Section 2](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html) (Centers for Disease Control and Prevention, 2012); [Principles of Epidemiology | Lesson 3 - Section 5](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section5.html) (Centers for Disease Control and Prevention, 2012).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/incidence-rate-and-person-time/