Basic epidemic metrics: what they measure
In outbreaks and public health reporting, the key distinction is new cases versus existing cases.
Incidence measures how fast new cases are occurring in a defined time window, while prevalence measures
how common the condition is at a specific time (or over a period).
Quick memory hook: incidence = new cases; prevalence = existing cases.
Formulas used in this calculator
1) Incidence proportion (risk) and attack rate
Incidence proportion (also called cumulative incidence or risk) is the fraction of an
at-risk population that becomes a new case during a specified time window. In outbreaks, the same calculation
is commonly reported as the attack rate.
Step 1. Identify numerator (new cases) and denominator (population at risk).
\[
\begin{aligned}
\text{New cases} &= C_{\text{new}} \\
\text{At-risk population} &= N_{\text{risk}}
\end{aligned}
\]
Step 2. Compute incidence proportion (risk).
\[
\begin{aligned}
\text{Incidence proportion} &= \frac{C_{\text{new}}}{N_{\text{risk}}}
\end{aligned}
\]
Step 3. Express it as a percent or per K people (optional scaling).
\[
\begin{aligned}
\text{Percent} &= \frac{C_{\text{new}}}{N_{\text{risk}}}\cdot 100\% \\
\text{Per }K &= \frac{C_{\text{new}}}{N_{\text{risk}}}\cdot K
\end{aligned}
\]
Important denominator rule: “At-risk” means people who could become a new case during the window. If some
individuals already have the condition at the start, they should not be counted as at-risk for incidence.
2) Incidence rate (requires person-time)
Incidence rate uses person-time in the denominator, which accounts for different follow-up times
(open cohorts, dropouts, varying observation lengths). It is reported as cases per person-time, often scaled per
1 000 or 100 000 person-units.
Step 1. Use person-time directly, or compute it from population and time length (when appropriate).
\[
\begin{aligned}
\text{Person-time (given)} &= PT \\
\text{If approximated for a closed cohort:}\quad PT &\approx N_{\text{risk}}\cdot T
\end{aligned}
\]
Step 2. Compute incidence rate and optional scaling.
\[
\begin{aligned}
\text{Incidence rate} &= \frac{C_{\text{new}}}{PT} \\
\text{Rate per }K\text{ person-time} &= \frac{C_{\text{new}}}{PT}\cdot K
\end{aligned}
\]
Units matter: if person-time is entered in person-days, the rate is “cases per person-day” (and similarly
for weeks/months/years). Keep the time unit consistent with how you report the result.
3) Prevalence (point or period)
Point prevalence is the fraction of the population that is a case at a single time point. It is a
snapshot of burden, not speed.
Point prevalence at a time point.
\[
\begin{aligned}
\text{Point prevalence} &= \frac{C_{\text{existing at time }t}}{N_{\text{total at time }t}} \\
\text{Percent} &= \frac{C_{\text{existing}}}{N_{\text{total}}}\cdot 100\%
\end{aligned}
\]
Period prevalence is the fraction of the population that was a case at any time during a defined period.
A common “basic” approach is to use the total number of people who were cases at any time in the period divided by an
average (or mid-period) population size.
Period prevalence over a window (basic reporting form).
\[
\begin{aligned}
\text{Period prevalence} &= \frac{C_{\text{cases during period}}}{N_{\text{average population}}}
\end{aligned}
\]
Interpretation caution: period prevalence can be defined in more than one way depending on surveillance
rules (e.g., counting anyone who was a case at any time in the period). Always label the period and case definition.
4) Case fatality ratio (CFR)
Case fatality ratio describes severity among identified cases: the fraction of cases that die from the disease
(within the defined follow-up/episode period). It is not the same as a population mortality rate.
Compute CFR from deaths among cases and total cases.
\[
\begin{aligned}
\text{CFR} &= \frac{D}{C_{\text{cases}}} \\
\text{CFR (\%)} &= \frac{D}{C_{\text{cases}}}\cdot 100\%
\end{aligned}
\]
Common reporting tips
-
Always report the time window for incidence (e.g., “over 14 days”) and the time unit for incidence
rates (e.g., “per 100 000 person-days”).
-
For incidence proportion, use at-risk population whenever possible (exclude existing cases at baseline).
-
For prevalence, specify whether it is point or period, and include the date/time (or the start/end).
-
For CFR, ensure the deaths counted correspond to the cases counted (same outbreak, same follow-up window).
