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Attack rate

In epidemiology, the attack rate, also known as the incidence proportion, is the proportion of an initially disease-free population that develops illness, injury, or death during a specified period, serving as a measure of the risk or probability of disease occurrence.^[1] It is particularly useful in outbreak investigations to quantify the impact of an infectious agent or exposure within a defined group.^[2] The attack rate is calculated by dividing the number of new cases occurring during the specified period by the size of the population at risk at the start of that period, then multiplying by a power of 10 (often 100) to express it as a percentage.^[1] For example, if 30 cases of gastroenteritis occur among 99 exposed individuals at a picnic, the attack rate is (30 / 99) × 100 = 30.3%.^[1] Although termed a "rate," it is technically a proportion because it does not incorporate a time interval in the denominator beyond the specified period.^[2] Several types of attack rates are commonly distinguished based on context. The overall attack rate reflects the total new cases divided by the total population at risk, providing a broad measure of outbreak severity, such as 18 cases per 1,000 individuals yielding 1.8%.^[1] Food-specific attack rates, used in foodborne outbreak analyses, are computed as cases among those who consumed a particular item divided by the total who consumed it, helping identify potential sources.^[1] The secondary attack rate measures transmission within close contacts, calculated as new cases among contacts divided by the total number of contacts, for instance, 17 cases among 68 susceptible household members resulting in 25.0%.^[1] Attack rates facilitate comparisons across populations, exposures, or locations during outbreaks, aiding in hypothesis generation about causative factors and informing public health responses.^[2] They are especially valuable in acute scenarios where rapid assessment is needed, though they assume a closed population without ongoing entries or exits.^[1]

Fundamentals

Definition

In epidemiology, the attack rate is defined as the proportion of an at-risk population that develops a specific health event, such as illness or infection, following exposure to a hazard or pathogen within a defined, short time interval.^[2] This measure captures the immediate impact of exposure in a targeted group, serving as a snapshot of disease occurrence rather than a long-term trend.^[3] The at-risk population for calculating an attack rate comprises individuals who are susceptible or exposed within a closed cohort during the specified period, excluding those already immune, previously affected, or not subject to the exposure.^[4] This denominator focuses on the defined group under observation, ensuring the rate reflects the potential for new cases among those genuinely vulnerable.^[5] Attack rates are particularly suited to acute, point-source outbreaks, where the health event arises from a single or brief exposure, as opposed to continuous monitoring in endemic settings.^[1] As a cumulative incidence measure over short durations, it provides a practical tool for evaluating outbreak dynamics in such scenarios.^[3]

Key Characteristics

The attack rate is inherently time-limited, typically applied to acute events or outbreaks spanning days to weeks, rather than extended periods spanning months or years. This short-term focus makes it particularly suitable for assessing rapid-onset health events but renders it inappropriate for studying chronic diseases, where incidence accumulates over prolonged durations.^[2] A core assumption underlying the attack rate is that of a closed population, wherein the group under observation remains fixed with no significant migration in or out during the defined period. This static denominator allows for a snapshot of risk within a bounded cohort, aligning with scenarios where exposure occurs in identifiable, contained settings such as gatherings or facilities.^[1] The metric is conventionally expressed as a percentage or proportion, representing the cumulative incidence of illness among the at-risk population over the observation interval. This formulation emphasizes the overall proportion affected rather than time-adjusted rates, providing a straightforward measure of outbreak impact.^[1] Beyond infectious diseases, the attack rate extends to non-infectious hazards, including foodborne illnesses from contaminated sources and acute chemical exposures in environmental incidents. Its versatility stems from applicability to any point-source event where a defined exposure leads to measurable health outcomes in a cohort.^[2]

Measurement

Calculation Methods

The attack rate in epidemiology is calculated using the standard formula: attack rate = (number of new cases / total population at risk) × 100, typically expressed as a percentage.^[1] This proportion measures the risk of disease occurrence following an exposure event within a defined population.^[6] The numerator consists of incident cases, defined as new diagnoses occurring after the exposure event and within an appropriate incubation or observation period, excluding any pre-existing cases.^[1] The denominator represents the initial population at risk, which includes all exposed or susceptible individuals at the start of the period, also excluding pre-existing cases to ensure the focus remains on new infections.^[1] Accurate data collection requires verifying exposure status, symptom onset timing, and population size through surveys, records, or cohort tracking.^[6] To compute the attack rate, first identify the specific exposure event or outbreak onset. Next, count the number of new cases that develop within the relevant time frame, such as the disease's incubation period. Then, determine the at-risk population size at the exposure's beginning. Finally, apply the formula to derive the percentage.^[6] For deeper analysis, attack rates can be adjusted by stratifying the population into subgroups, such as by age, sex, or exposure intensity, to calculate subgroup-specific rates and identify high-risk groups.^[6] This stratification involves applying the standard formula separately to each subgroup's numerator and denominator.^[7]

Primary and Secondary Attack Rates

In epidemiology, the overall attack rate quantifies the proportion of initially exposed individuals who develop illness following an exposure to a disease source, such as contaminated food or water during an outbreak.^[1] It is calculated using the formula:

\text{Overall attack rate} = \left( \frac{\text{New cases from source}}{\text{Total initially exposed}} \right) \times 100

^[1] The secondary attack rate measures the proportion of susceptible contacts of primary cases who subsequently become ill, reflecting person-to-person transmission after the initial exposure.^[3] Its formula is:

\text{Secondary attack rate} = \left( \frac{\text{Secondary cases}}{\text{Total susceptible contacts}} \right) \times 100

^[8] In outbreak investigations, the overall attack rate evaluates the strength of the initial source, while the secondary attack rate assesses transmissibility through subsequent chains of infection, aiding in sequencing the spread.^[1] Secondary attack rates are particularly focused on household or close-contact settings, where rates are often higher due to prolonged and intimate exposure compared to general community transmission.^[8]

Usage

In Outbreak Investigations

In outbreak investigations, attack rates play a central role in the descriptive epidemiology phase, where they help quantify the extent of disease spread within affected populations and facilitate the generation of hypotheses regarding transmission dynamics. Investigators typically calculate these rates early in the process to describe the epidemic curve, identify patterns by time, place, and person, and compare rates between exposed and unexposed groups to assess associations with potential risk factors.^[9]^[10] This integration into standard protocols, such as those outlined by the CDC, allows teams to prioritize resources and refine case definitions based on observed incidence proportions during the limited outbreak period.^[11] To identify sources of infection, outbreak teams stratify populations by relevant exposures and compute subgroup-specific attack rates, revealing disparities that point to likely vehicles or reservoirs. For example, in foodborne investigations, substantially higher attack rates among individuals who consumed specific items—such as certain salads or dishes—compared to those who did not can indicate contamination as the source, guiding further analytic studies like cohort analyses.^[10]^[11] Similarly, elevated rates in particular settings, like childcare centers in affected areas (e.g., 20% versus 2% in unaffected areas), highlight localized transmission risks and inform targeted tracing efforts.^[12] Attack rates also directly influence public health actions by providing thresholds that trigger interventions. For instance, in mumps outbreaks, a minimum attack rate of 5 cases per 1,000 population at risk prompts recommendations for a third dose of MMR vaccine to curb further spread, while in meningococcal disease scenarios, an attack rate exceeding 10 per 100,000 over a 3-month period (per previous CDC criteria) may necessitate reactive vaccination campaigns.^[13]^[14] These metrics enable rapid decision-making, such as product recalls, contact tracing, or quarantine measures, to mitigate ongoing transmission. In surveillance and reporting, attack rates are standard components of outbreak summaries disseminated by agencies like the CDC and WHO, serving as key indicators to evaluate containment efficacy and guide resource allocation across jurisdictions.^[15] By tracking changes in these rates over time, public health officials monitor intervention impacts and detect any resurgence, ensuring coordinated responses at national and international levels.^[12]

Real-World Examples

One notable application of attack rates occurred during the 1984 Rajneeshee bioterrorism attack in The Dalles, Oregon, where followers of the Bhagwan Shree Rajneesh cult intentionally contaminated salad bars at 10 restaurants with Salmonella Typhimurium to influence a local election. This incident resulted in 751 confirmed cases of salmonellosis in Wasco County (population approximately 22,000), yielding a primary attack rate of about 3.4%, though rates were markedly higher—up to 54%—among restaurant employees who consumed from the tainted salad bars.^[16]^[17] In the 2011 Escherichia coli O104:H4 outbreak centered in northern Germany, contaminated fenugreek sprouts served as the primary vehicle, leading to 3,816 confirmed cases nationwide and an overall attack rate of about 0.005% in Germany's population of roughly 80 million. However, in heavily affected regions like Hamburg and surrounding areas, attack rates reached up to 20% among individuals who consumed the sprouts, as evidenced by cohort studies at implicated farm stands and restaurants where exposure directly correlated with illness.^[18] A non-infectious foodborne example is the 1993 Jack in the Box E. coli O157:H7 outbreak across Washington, California, Idaho, and Nevada, triggered by undercooked hamburgers contaminated during processing. This event resulted in approximately 500 laboratory-confirmed cases.^[19] In these outbreaks, attack rate calculations played a key role in contact tracing by highlighting secondary transmission patterns, such as household spread where secondary attack rates for E. coli O157:H7 typically ranged from 15-20% among close contacts of primary cases, informing isolation protocols to curb further dissemination.^[20]

Comparisons and Limitations

Comparison to Other Epidemiological Measures

The attack rate, as a proportion of an at-risk population that develops illness following exposure during a specified interval, differs from the incidence rate primarily in its lack of a time denominator. While the incidence rate measures new cases per unit of person-time at risk, accounting for varying durations of observation and exposure, the attack rate treats the population as fixed and does not adjust for time, rendering it a crude cumulative measure suitable for brief, defined periods such as outbreaks.^[1]^[21] In contrast to prevalence, which captures the proportion of a population affected by a condition at a specific point in time (point prevalence) or over a period (period prevalence), including both new and preexisting cases, the attack rate focuses exclusively on new occurrences among an initially disease-free group post-exposure. This makes the attack rate a dynamic measure of event risk in response to a precipitating factor, whereas prevalence provides a static snapshot of disease burden, particularly useful for chronic conditions.^[1]^[22] The attack rate also contrasts with the case fatality rate (CFR), which quantifies the proportion of diagnosed cases that result in death, emphasizing lethality among those affected rather than the initial proportion attacked. For instance, in outbreak settings like cholera, the attack rate tracks cumulative cases relative to the exposed population, while the CFR monitors deaths relative to cases to assess severity and care quality.^[23] Attack rates are preferentially selected for point-source outbreaks or short-term events where the population and exposure period are well-defined, such as foodborne incidents, whereas incidence rates suit longitudinal studies with variable follow-up, prevalence applies to ongoing disease monitoring, and CFR evaluates outcomes among confirmed cases.^[1]^[22]

Limitations and Considerations

The attack rate relies on several key assumptions that, if violated, can lead to inflated or deflated estimates. In open populations, where individuals may enter or leave the at-risk group during the observation period—such as through migration or recovery— the denominator becomes inaccurate, potentially underestimating the true risk if new susceptibles are not accounted for.^[24] Underreporting of cases, common in infectious disease outbreaks due to mild or asymptomatic infections, typically results in underestimation of the attack rate, as the numerator fails to capture all incident cases.^[25] Additionally, the measure often does not adjust for pre-existing immunity levels within the population, leading to overestimation of risk in groups with partial herd immunity, where only susceptibles should ideally form the denominator.^[26] Unlike true incidence rates, the attack rate is not a genuine rate because it lacks a time dimension in its denominator, treating the observation period as a fixed point rather than incorporating person-time at risk. This absence limits its comparability to ongoing incidence measures, which account for varying exposure durations and allow for trend analysis over extended periods.^[21] As a result, attack rates are best suited for short-term, point-in-time assessments in outbreaks but can mislead when applied to scenarios requiring temporal adjustments. Several biases can further compromise the accuracy of attack rates. Denominator errors arise when non-respondents or hard-to-reach individuals are excluded, introducing selection bias that skews the population at risk and often inflates the rate among the observed subgroup.^[24] Similarly, using observation intervals shorter than the disease's incubation period misses emerging cases, leading to underestimation, as symptoms may not manifest within the defined timeframe.^[1] To mitigate these issues, best practices include calculating 95% confidence intervals around attack rates to quantify precision and uncertainty, particularly in small populations where estimates may be unstable.^[6] Attack rates should be used in conjunction with complementary metrics, such as risk ratios or incidence rates, to provide a more robust analysis of associations and transmissibility.^[6] Finally, the measure is inappropriate for chronic conditions with long latency periods, where cumulative incidence over time is more suitable, as attack rates are designed for acute events with clearly defined exposure windows.^[21]

References

[1]
Principles of Epidemiology | Lesson 3 - Section 2 - CDC Archive
Overall attack rate is the total number of new cases divided by the total population. A food-specific attack rate is the number of persons who ate a specified ...
[2]
Principles of Epidemiology | Lesson 3 - Section 1 - CDC Archive
Thus, an attack rate is the proportion of the population that develops illness during an outbreak.
[3]
Principles of Epidemiology: Glossary - CDC Archive
attack rate a form of incidence that measures the proportion of persons in a population who experience an acute health event during a limited period (e.g. ...
[4]
Estimating the Attack Ratio of Dengue Epidemics under Time ...
Calculating the attack ratio. The attack ratio of an epidemic is defined by the number of infections divided by the size of the population at risk.<|control11|><|separator|>
[5]
Epidemiology - Medical Microbiology - NCBI Bookshelf - NIH
The most commonly studied rate is the attack rate: the number of cases of the disease divided by the population among whom the cases have occurred.
[6]
The U.S. Military and the Influenza Pandemic of 1918–1919 - PMC
The war fostered influenza in the crowded conditions of military camps in the United States and in the trenches of the Western Front in Europe.
[7]
Analyzing and Interpreting Data | Field Epi Manual - CDC
Jan 6, 2025 · The RR, the preferred measure for cohort studies, is calculated as the attack rate (risk) among the exposed group divided by the attack rate ( ...
[8]
SARS-CoV-2 Variants and Age-Dependent Infection Rates ... - CDC
Jun 21, 2023 · According to a meta-analysis, the overall household secondary attack rates ... Second, we calculated infection rates stratified by the ...
[9]
Glossary - Epiville
Attack rate is really the proportion of exposed people that become ill. There are two types of attack rate: primary attack rate and secondary attack rate.
[10]
Estimating and interpreting secondary attack risk: Binomial ...
The household secondary attack risk (SAR), often called the secondary attack rate or secondary infection risk, is the probability of infectious contact from an ...<|separator|>
[11]
Section 2: Steps of an Outbreak Investigation - CDC Archive
When the attack rate for the exposed group is the same as the attack rate for the unexposed group, the relative risk is equal to 1.0, and the exposure is said ...
[12]
Designing and Conducting Analytic Studies in the Field - CDC
Aug 8, 2024 · In a cohort study, investigators can calculate the attack rate for botulism among potluck attendees who reported having eaten each food and for ...
[13]
[PDF] Steps of a Toxicological Outbreak Investigation | CDC
Calculate attack rates for each of the strata. If the attack rate increases with increasing exposure, then that suggest that it might be the implicated exposure ...
[14]
[PDF] Principles and steps of an outbreak investigation
• Childcare centres in affected areas: Attack rate: 20%. • Childcare centres in unaffected areas: Attack rate 2%. • Absences started to increase at the ...
[15]
[PDF] Summary and Discussion Third Dose of MMR Vaccine for Mumps ...
When should the intervention be conducted? ❑ Minimum attack rate. ▫ 5 cases/ 1000 population at risk. ❑ Number of generations.
[16]
[PDF] meningococcal-outbreak-guidance.pdf - CDC
Although an absolute outbreak threshold is no longer used, calculating an outbreak attack rate may still be useful in determining the magnitude of an ...
[17]
[PDF] Technical Guidelines for Integrated Disease Surveillance and ...
• Possible causes of the outbreak/ public health problem, laboratory results, source of infection, mode of transmission, attack rate, case fatality rate and.
[18]
German Outbreak of Escherichia coli O104:H4 Associated with ...
During the outbreak period, 884 main dishes containing sprouts were served to the guests of the restaurant. Applying the attack rate of 27% among sprout eaters, ...
[19]
Multistate Outbreak of Escherichia coli O157:H7 Infections ... - CDC
From November 15, 1992, through February 28, 1993, more than 500 laboratory-confirmed infections with E. coli O157:H7 and four associated deaths occurred in ...Missing: attack | Show results with:attack
[20]
Point-Counterpoint: Should All Stools Be Screened for Shiga Toxin ...
Jul 1, 2011 · The secondary attack rate for STEC is between 5 and 20%, with the ... Primary and secondary cases in Escherichia coli O157 outbreaks: a ...
[21]
[PDF] Common Measures and Statistics in Epidemiological Literature
The three most common measures of health outcome or frequency are risk, rate, and prevalence. Risk. Risk, also known as incidence, cumulative incidence, ...
[22]
12.5 Epidemiologic Measures - Population Health for Nurses
May 15, 2024 · The denominator is the population at risk during the same period. Incidence rates describe how quickly a disease or illness occurs in a ...
[23]
8.3 Key epidemiologic indicators - MSF Medical Guidelines
The two key epidemiologic indicators used during a cholera outbreak are the attack rate and the case fatality ratio or rate.
[24]
The Unknown Denominator Problem in Population Studies of ... - NIH
Problems related to unknown or imprecisely measured populations at risk are common in epidemiologic studies of disease frequency.
[25]
Measuring underreporting and under-ascertainment in infectious ...
An extensive literature review was conducted to identify studies that estimate ascertainment or reporting rates for salmonellosis and campylobacteriosis.Missing: flaws | Show results with:flaws
[26]
SARS-CoV-2 Attack Rate and Population Immunity in Southern New ...
May 26, 2022 · This case series analysis for Rhode Island, Massachusetts, and Connecticut revealed that two-thirds of residents were immune to SARS-CoV-2 by May 31, 2021.