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Incidence Rate Calculator
Enter your event count and total person-time at risk to calculate a crude incidence rate, along with the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
Incidence rate measures how quickly new cases of an outcome occur in a population followed over time. Instead of dividing by a fixed number of people, it divides the number of new events by the total person-time each participant contributed while they were at risk — so someone followed for five years contributes five times as much person-time as someone followed for one year.
This calculator computes the rate of new events per unit of person-time at risk from the numbers you enter, with an exact Poisson 95% confidence interval, then shows the R command, poisson.test(), which returns the same interval, so you can check the result yourself.
When to Use the Incidence Rate Calculator
Incidence rate is the right tool when you are tracking new events in a group followed over time and follow-up length differs between participants — for example, new diagnoses per 1,000 person-years in a screening cohort, or new infections per 100 patient-days on a hospital ward. It answers “how fast are new cases occurring,” not “how many people currently have this.”
Incidence rate vs. prevalence: these two measures are among the most frequently confused in epidemiology. Incidence rate counts only new events and divides by person-time at risk, so it reflects how quickly a condition is occurring. Prevalence counts all existing cases — new and old — at a single point or period, divided by the population, so it reflects how common a condition is right now. A disease can have high prevalence but low incidence if cases are chronic and long-lasting, or high incidence but low prevalence if cases resolve quickly.
Once you have incidence rates for an exposed and an unexposed group, the natural next step is often to compare them directly and quantify the excess rate attributable to the exposure (see Related Calculators below). If you are not sure which epidemiological or statistical measure actually fits your data before you compute anything, our Test Selector can help you confirm the right method.
events <- {events}; pt <- {pt}
poisson.test(events, pt) # exact CI per unit of person-time
poisson.test(events, pt)$conf.int * {mult_n} # 95% CI per {mult_n}User guide
When to use. Calculate the rate of new events per unit of person-time at risk.
Assumptions. Person-time is correctly accumulated; events are independent.
Common mistakes. Do not confuse incidence (new cases over time) with prevalence (existing cases).
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. 2008.
Worked Examples
Example 1: Cohort Study — Crude Rate
A cohort study recorded 45 new events over 1,000 person-time units of follow-up (for example, 1,000 person-years). Dividing events by person-time gives IR = 45 ÷ 1,000 = 0.045 events per person-time unit — the direct output of the IR = events / person-time formula, before any multiplier is applied.
Example 2: Same Data, Rescaled with a Multiplier
A rate of 0.045 is rarely reported as-is — it is rescaled with a multiplier so it is easier to read and compare. Using the same 45 events over 1,000 person-time units: ×100 gives 4.5 per 100 person-time units; ×100,000 (a common convention for rarer outcomes) gives 4,500 per 100,000 person-time units. The calculator reports the exact Poisson 95% CI of 3.28 to 6.02 per 100, the same interval poisson.test(45, 1000) gives in R.
Assumptions to Check
Person-time is correctly accumulated. Every participant’s contribution should stop being counted at the moment they have the event, are lost to follow-up, or the study ends — whichever comes first. Under- or over-counting person-time directly biases the rate.
Events are independent. The Poisson model behind this calculator assumes one event does not change another participant’s risk of an event. This can break down with contagious outcomes (e.g., outbreaks) or when the same person can have repeat events without being properly re-entered into the risk set.
The population is reasonably homogeneous, or you are prepared to stratify. A single crude rate can mask large differences between subgroups (age, calendar period, exposure status) — consider stratum-specific or age-standardized rates if your population is heterogeneous.
The multiplier matches your reporting convention. Make sure the denominator (per 100, per 1,000, per 100,000 person-years) matches how you intend to compare against published benchmarks.
Common Mistakes
Confusing Incidence with Prevalence
Do not confuse incidence (new cases occurring over time) with prevalence (existing cases at a point in time) — they answer different questions and are not interchangeable. See the Prevalence Calculator in Related Calculators below for the companion measure.
Using Person-Count Instead of Person-Time
Dividing events by the number of people at the start of follow-up — rather than by total person-time — produces a cumulative incidence (risk), not an incidence rate. The two have different units and are not numerically interchangeable when follow-up time varies across participants.
Dropping Withdrawals from the Denominator
Participants who leave a study early still contributed person-time up to the point they left, and that time must be counted. Excluding them entirely, rather than including their partial follow-up, understates total person-time and inflates the rate.
Reporting the Rate Without a Multiplier or Time Unit
A rate of “0.0003” is unreadable and easy to misquote. Always state the multiplier and time unit together (e.g., “per 1,000 person-years”), and keep them consistent when comparing rates across studies or subgroups.
Frequently Asked Questions
What is the difference between incidence rate and incidence proportion (risk)?
Incidence rate divides new events by total person-time at risk, so its units are events per person-time (e.g., per 1,000 person-years). Incidence proportion (cumulative incidence, or risk) divides new events by the number of people at risk at the start of follow-up, giving a unitless proportion between 0 and 1. Use incidence rate when follow-up time varies between participants; use risk when everyone is followed for the same fixed period.
Why does the R code use a Poisson test?
Event counts observed over person-time are typically modeled as a Poisson process. poisson.test() uses this model to return an exact confidence interval around your rate and, if you provide a comparison value, a p-value testing whether your observed rate differs from it. The calculator reports the exact Poisson interval, so it stays valid with few events: for 3 events in 250 person-years it gives 2.47 to 35.07 per 1,000, the same as poisson.test(3, 250).
What multiplier should I use when reporting my rate?
It depends on convention in your field and how rare the outcome is: common outcomes are often reported per 100 or per 1,000 person-time units, while rarer outcomes (certain cancers, rare adverse events) are typically reported per 100,000. Match whatever multiplier the studies you are comparing against use.
Can I use this calculator for adjusted or stratified incidence rates?
This calculator returns the crude (overall) incidence rate for the events and person-time you enter. For age-adjusted or stratum-specific rates, calculate the rate within each stratum separately and combine them using standard weights, or consult a biostatistician for direct or indirect standardization.
Related Calculators
References
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008.
- Breslow NE, Day NE. Statistical Methods in Cancer Research, Volume II: The Design and Analysis of Cohort Studies. IARC Scientific Publications No. 82. Lyon: International Agency for Research on Cancer; 1987.
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