What is the distinction between incidence rate and cumulative incidence?

Incidence rate (incidence density) measures the rate of new events per unit of dynamic person-time at risk (e.g., person-years). Cumulative incidence (risk or incidence proportion) measures the proportion of an initially disease-free closed cohort that develops the event over a defined follow-up period.

Can person-time rates be expressed as a percentage?

No. A rate with person-time in the denominator has dimensions of 1/time and can exceed 1.0 (or 100 per unit time). Percentages are strictly proportions (dimensionless numbers bounded between 0% and 100%) and apply only to cumulative incidence.

Which confidence interval formulas are applied?

For person-time rates, exact two-sided Garwood Poisson intervals derived from the Chi-square / Poisson relationship are calculated. For cumulative incidence, the Wilson score interval without continuity correction is used, as recommended by NIST and epidemiological standards.

What are the conversion relationships between time units?

Standard epidemiological approximations define 1 person-year ≈ 12 person-months ≈ 365.25 person-days. However, this calculator preserves the denominator unit entered without automated conversion to prevent follow-up cadence distortion.

Incidence Rate & Cumulative Incidence Calculator

Compute person-time incidence rates (PY, PM, PD) or population-at-risk cumulative incidence with verified 95% confidence intervals.

Study Parameters

Measure Type

New Cases (Events)

Observed new incident events during the observation window.

Total Person-Time at Risk

Sum of individual disease-free observation periods.

Display Base Multiplier

Per 1,000 Per 10,000 Per 100,000

Evidence Presets

Enter case and denominator parameters to view rate estimates, exact 95% confidence intervals, and reference scales.

Incidence Rate

—

per 1,000 person-years

95% CI Lower

—

Garwood limit

95% CI Upper

—

Garwood limit

Events (Cases)

—

numerator

Denominator

—

person-years

Multi-Scale Comparison

Scale	Estimate	95% Confidence Interval

Interpretation

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Formula & Method Exact Poisson (Garwood)

Rate = (New Cases ÷ Person-Time) × Multiplier

Epidemiological Unit Relationships

Incidence Rate (Incidence Density): Measures event frequency per unit of aggregate observation time. Standard reference ratios: 1 person-year is observationally equivalent to 12 person-months or ~365.25 person-days. Rates are rates of occurrence, not percentages; when follow-up time is short or risk is high, a rate can validly exceed 1.0.

Cumulative Incidence (Incidence Proportion / Risk): Measures probability of event occurrence in a fixed cohort initially at risk: Risk = Cases ÷ N_initial. Because numerator is a subset of denominator, values are strictly bounded within [0, 1] (or 0% to 100%).

Statistical Interval Methods & Authorities

Garwood Poisson Limits: Exact limits for observed count k at confidence 100(1 - α)%: Lower = χ²_2k(α/2) / 2; Upper = χ²_2k+2(1 - α/2) / 2. When k = 0, the lower bound is exactly 0 and upper bound is -ln(α/2) = -ln(0.025) ≈ 3.688879.

Wilson Score Interval: Recommended for binomial proportions without ad-hoc continuity adjustments (NIST Handbook §2.4.1).

Primary authorities: CDC Principles of Epidemiology (Lesson 3.2) • CDC U.S. Cancer Statistics (Poisson CIs) • NIST e-Handbook §2.4.1.

Educational Limitation: This calculator provides statistical point and interval estimation for research, teaching, and surveillance analysis. It does not provide clinical diagnoses or individualized prognostic recommendations.

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Summary