Example Data Table
| Scenario |
Rate |
Follow-up |
Confidence |
Precision |
Design Effect |
Loss |
| Rare safety event |
2 per 1000 |
2 years |
95% |
25% relative |
1.00 |
10% |
| Hospital infection rate |
8 per 1000 |
1 year |
95% |
20% relative |
1.20 |
15% |
| Community surveillance |
35 per 100000 |
3 years |
99% |
10 absolute |
1.50 |
5% |
Formula Used
The calculator uses a normal approximation for a Poisson incidence rate.
Incidence rate: λ = expected rate ÷ rate denominator
Absolute half-width: d = relative margin × λ, or absolute margin ÷ denominator
Effective person-time: PT = Z² × λ ÷ d²
Minimum event person-time: PT events = minimum events ÷ λ
Adjusted person-time: max(PT, PT events) × design effect
Final sample: n = adjusted person-time ÷ average follow-up ÷ retention factor
Expected events: events = λ × retained subjects × average follow-up
How to Use This Calculator
Enter the expected incidence rate and choose its denominator.
Add the average follow-up time expected for each subject.
Select the confidence level for the planning interval.
Choose relative precision when the margin should scale with the rate.
Choose absolute precision when the margin has a fixed value.
Add a design effect for cluster or complex sampling designs.
Enter expected loss to follow-up to inflate the sample.
Press the calculate button and review the result above the form.
Planning Incidence Rate Studies
An incidence rate study measures how often new events occur during observed time. It is different from a simple proportion. A proportion counts people with an event. An incidence rate also counts how long people were followed. This is useful when follow up differs between people. It also helps when events are rare.
Why Sample Size Matters
A small study may produce a wide confidence interval. That interval can be hard to interpret. A large study gives a narrower estimate. Yet large studies cost more money and time. A sample size calculator helps balance precision and resources before recruitment begins.
Person Time Is Central
The main input is the expected incidence rate. The calculator converts that rate into events per one person time unit. It then uses the desired margin of error and confidence level. The result first appears as required person time. Subject count is then found by dividing person time by average follow up.
Precision Choices
You can enter relative or absolute precision. Relative precision is a percent of the expected rate. It is helpful when the rate may be small. Absolute precision uses the same rate scale as the input. It is useful when a clinical or operational limit is already known.
Practical Adjustments
Real studies rarely keep every participant. Loss to follow up reduces usable person time. The calculator inflates the sample for that loss. Clustered designs may also reduce effective information. A design effect adjusts for that issue. You can also require a minimum expected event count.
Reading The Results
The final sample size is rounded upward. The retained sample is shown after loss. Expected cases are estimated from retained person time. The confidence interval is approximate. It is meant for planning, not final reporting. Final analysis should follow the approved protocol and use observed data.
Important Limits
This tool uses a normal planning approximation for a Poisson rate. It works best when the expected number of events is not very small. For very rare outcomes, confirm the plan with exact Poisson methods or simulation. Also check exposure definitions, censoring rules, inclusion criteria, and calendar limits before locking the final sample size. Keep assumptions documented for reviewers and future audits clearly.
FAQs
What is an incidence rate sample size?
It is the number of subjects needed to estimate a new event rate with planned confidence and precision. It also depends on total person-time.
Why does person-time matter?
Incidence rate uses both events and observation time. More follow-up time adds information, even when the number of enrolled subjects stays lower.
What is relative precision?
Relative precision sets the margin as a percent of the expected rate. For example, 20% means the half-width equals 20% of the rate.
What is absolute precision?
Absolute precision sets a fixed half-width using the same denominator as the entered rate. It is useful when a fixed clinical limit matters.
What does design effect mean?
Design effect inflates the required sample when clustering or complex sampling reduces independent information. Use 1 for a simple independent design.
Why include loss to follow-up?
Some subjects may not complete observation. Loss adjustment increases enrollment so retained person-time remains close to the required planning target.
Can this calculator handle rare events?
It can provide planning estimates for rare events. For extremely rare outcomes, confirm the design with exact Poisson methods or simulation.
Is the confidence interval final?
No. The interval shown is a planning approximation. Final reporting should use observed data and the approved statistical analysis plan.