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.
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).
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.
Connections
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 (Centers for Disease Control and Prevention, 2012); Principles of Epidemiology | Lesson 3 - Section 5 (Centers for Disease Control and Prevention, 2012).
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Representative model, for educational purposes only.