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The incidence rate relates new events to accumulated time at risk.
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Formula
Rate in events/person-time · D event count · Ti time at risk
| Symbol | Meaning | Unit |
|---|---|---|
| Incidence rate during the observation period | events per person-year or similar | |
| Number of new events | events | |
| Observed time at risk for person i | time |
IR=\frac{D}{\sum_i T_i}A rate differs from cumulative incidence, which is the proportion developing an outcome over a fixed period. Person-time is interpretable with a clear event definition and suitable follow-up; a constant rate is an extra model assumption, not a property of the formula. Recurrent events require a defined counting rule.
Requires accurately measured time at risk and consistent event definition; rate need not be constant.
Accumulated observed time enables comparison when follow-up duration differs.
Solve for a quantity
Expected event count under an assumed constant rate.
6 events in 300 person-years: rate per 100 PY?
6/300·100=2 events per 100 person-years.
Interpreting incidence rate as a percentage of people.
A rate uses person-time in the denominator; cumulative incidence uses people.
Formula cluster
Rate comparisons require similar event definitions and observation contexts.
With 12 new events in 600 person-years, rate=12/600=0.02 per person-year, or 2 per 100 person-years. Check: scaling numerator and denominator equally leaves the rate unchanged.
Comparing new events when observation time differs across people
Here is how to work through a typical Incidence rate per person-time (IR = Ereignisse / Personenzeit) task step by step:
Task
6 events in 300 person-years: rate per 100 PY?
Solution path
6/300·100=2 events per 100 person-years.
Incidence rate divides new events by accumulated person-time and has units such as events per 100 person-years. Cumulative incidence is the proportion of a defined population developing the event over a fixed period; it is dimensionless. With varying follow-up, the rate may be more informative, but still requires clear time at risk. The measures are not interchangeable and answer different questions. Report event definition, inclusion criteria and person-time. Rate and cumulative incidence differ; recurrent events need a clear rule. Uncertainty can remain high with few events despite large person-time. State confidence interval and observation window.
First divide events by total person-years, then multiply by 100. Twelve events over 600 person-years gives 0.02 per person-year or 2 per 100 person-years. This scaling is a more readable unit, not a percentage probability. When follow-up differs, each person contributes time at risk until event, censoring or end of observation. Report event definition, inclusion criteria and person-time. Rate and cumulative incidence differ; recurrent events need a clear rule. Uncertainty can remain high with few events despite large person-time. State confidence interval and observation window.
Events divided by person-time is a descriptive rate and does not automatically require constant hazard. But deriving risk over time from a Poisson or exponential model often assumes a constant rate within groups and intervals. If risk changes with age or duration, stratified rates, time-varying models or survival analysis may be needed. Report follow-up time and event definition. Report event definition, inclusion criteria and person-time. Rate and cumulative incidence differ; recurrent events need a clear rule. Uncertainty can remain high with few events despite large person-time. State confidence interval and observation window.
Reproduce the example calculation: With 12 new events in 600 person-years, rate=12/600=0.02 per person-year, or 2 per 100 person-years. Incidence rate per person-time uses IR = Ereignisse / Personenzeit. In plain terms, the incidence rate relates new events to accumulated time at risk. Unit check: Rate in events/person-time · D event count · Ti time at risk. Requires accurately measured time at risk and consistent event definition; rate need not be constant. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.
A key limit of Incidence rate per person-time is this: Requires accurately measured time at risk and consistent event definition; rate need not be constant. Do not use the metric without its reference; it is useful for Comparing new events when observation time differs across people. The incidence rate relates new events to accumulated time at risk. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.
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