Concept Architecture
Concept
Theoretically, Attack Rate is an epidemiological measure that quantifies the proportion of an at-risk population that develops a specified disease during a defined outbreak or exposure period. Despite its name, it is a cumulative incidence measure rather than a true rate because it does not incorporate person-time. Attack rate exists to measure disease occurrence rapidly during outbreaks and to compare transmission across exposed populations.
Mathematically, Attack Rate is represented as the proportion of new cases divided by the total population at risk during a specified period, typically expressed as a percentage. Variants include the overall attack rate, primary attack rate and secondary attack rate, each describing disease occurrence within different epidemiological contexts.
In practice, Attack Rate is calculated using surveillance or outbreak investigation data by counting confirmed or probable cases and dividing by the number of individuals at risk. Health economists use attack rates to estimate disease burden, model infectious disease transmission, evaluate preventive interventions and parameterise decision-analytic and transmission models.
Purpose
Used to quantify the occurrence of disease during outbreaks, compare transmission across populations and provide key epidemiological inputs for infectious disease modelling and health economic evaluation.
Mathematical Formulae
Primary Formula
Attack Rate = (Number of new cases during the outbreak � Population at risk at the beginning of the outbreak) ? 100%
Supporting Formulae
Secondary Attack Rate:
Secondary Attack Rate = (Number of cases among contacts � Number of susceptible contacts) ? 100%
Primary Attack Rate:
Primary Attack Rate = (Primary cases � Population at risk) ? 100%
Related Mathematical Methods
Cumulative Incidence
Secondary Attack Rate
Incidence Proportion
Risk Ratio
Basic Reproduction Number
Effective Reproduction Number
Example
An outbreak of norovirus occurs in a residential care facility housing 180 residents. During the outbreak, 54 residents develop gastroenteritis.
Attack Rate = (54 � 180) ? 100%
Attack Rate = 30%
This indicates that 30% of residents became ill during the outbreak.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| COUNT | =COUNT(B2:B181) | Count confirmed outbreak cases |
| COUNTA | =COUNTA(A2:A181) | Count individuals at risk |
| COUNTIF | =COUNTIF(B2:B181,"Case") | Count disease cases meeting the case definition |
| IFERROR | =IFERROR((COUNTIF(B2:B181,"Case")/COUNTA(A2:A181))*100,0) | Calculate attack rate as a percentage |
| ROUND | =ROUND(C2,1) | Report attack rate to the required precision |
VBA (Optional)
VBA can automate attack rate calculations across multiple outbreaks and generate epidemiological summary reports for surveillance datasets.
Sources
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology.
- Gordis L. Epidemiology.
- Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice.
- World Health Organization. Communicable Disease Surveillance and Response.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Dynamic Transmission Modeling: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-5 — Pitman, Fisman, Zaric, Postma, Kretzschmar, Edmunds & Brisson, Task Force Report 5 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on dynamic transmission models for infectious disease, capturing indirect (herd) effects that static models cannot, and their use in cost-effectiveness analysis of vaccination and control programmes.
Journal ArticleView source →
Frequently Asked Questions (6)
What is an attack rate?
A measure of disease incidence in a specific outbreak, the proportion of an at-risk population that develops the disease over the outbreak period.
Source: Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 3rd ed. Lippincott Williams & Wilkins; 2008.
Why is an attack rate suited to a defined outbreak?
An attack rate is a form of incidence tailored to a specific outbreak, giving the proportion of a defined at-risk group that falls ill over the outbreak's short course. It suits an outbreak because the population and time window are clearly bounded, so a simple proportion captures the risk without needing to track person-time. Comparing attack rates across groups, such as those who did and did not eat a suspect food, helps pinpoint the source. It measures who succumbed among those exposed. Gordis (2014) describes this measure.
Source: Gordis 2014
How is an attack rate calculated?
An attack rate is calculated as the number of people who develop the disease during the outbreak divided by the number of people at risk in the population, usually over the outbreak period, expressed as a proportion or percentage. For example, in a foodborne outbreak, the attack rate among those who ate a particular food is the number who became ill divided by the number who ate it. Comparing attack rates across exposure groups helps identify the source. So the attack rate quantifies the proportion of the at-risk group affected.
Source: Rothman, Greenland & Lash 2008
How is the attack rate used in outbreak investigation?
In outbreak investigation, the attack rate is used to measure the extent of illness and to identify the likely source by comparing attack rates among those exposed and not exposed to suspected causes, such as particular foods or settings. A much higher attack rate among those with a specific exposure points to it as a probable source. Attack rates for different exposures are compared, often through relative risks, to find the exposure most strongly associated with illness. So the attack rate is a key tool for quantifying and investigating outbreaks.
Source: Rothman, Greenland & Lash 2008
What is the difference between an attack rate and incidence?
An attack rate is a specific form of cumulative incidence applied to a defined outbreak over a limited period, measuring the proportion of an at-risk population that develops the disease during the outbreak, whereas incidence more generally measures the occurrence of new cases in a population over time, either as cumulative incidence, a proportion, or an incidence rate, per person-time. So the attack rate is essentially cumulative incidence in the context of an outbreak, focused on a particular event and time frame, while incidence is the broader concept of new-case occurrence used across epidemiology.
Source: Rothman, Greenland & Lash 2008
What is a secondary attack rate?
A secondary attack rate measures the proportion of susceptible contacts of an initial case who develop the disease within a defined period after exposure to that case, indicating how readily an infection spreads from person to person, for example within households. It is calculated as the number of secondary cases among contacts divided by the number of susceptible contacts. The secondary attack rate is useful for assessing transmissibility and the effect of measures to prevent spread. So it extends the attack rate concept to quantify person-to-person transmission from primary cases to their contacts.
Source: Rothman, Greenland & Lash 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 21 Nov 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/attack-rate
- Term code
- HE-ES-EP-002
Stable URI · Machine-readable · Resolvable · CC BY 4.0