Attack Rate

Definition

An attack rate is the proportion of the population at risk that got infected. Note that it's not a rate, it's a proportion! (Which, again, is extremely annoying and this shows up a lot in epidemiology.) TLDR: The cumulative incidence of disease during an outbreak.

Other aliases

1. Incident proportion
2. Cumulative incidence
3. Infection attack rate
4. Clinical attack rate
5. Final size

Formula

where we accumulate the total incidence (getting total infections) and dividing it over $N$, the population at risk.

We can also think of it as the probability or the average risk that an individual will develop the disease during the period: if 30% of people in a population develop a disease then each individual has a 30% chance of developing it themselves.

Note, that attack rate is calculated over some surveillance period.

Relation to

1. Reproductive number (From Kretzschmar and Wallinga 2009) :
   $$
   AR = (1- exp(-R\times AR)),
   $$
   where $R$ is the reproductive number.

Usage

• Needed for calculating Vaccine efficacy in Clinical Trials
• A way to do case projections and calculate Sample Size. Something I need to do for work.

Caution

Attack rate is poorly identified from case date alone (epidemiological time series), it’s confounded with reporting fraction and the initial susceptible fraction.

References

Kretzschmar, Mirjam, and Jacco Wallinga. "Mathematical models in infectious disease epidemiology." Modern infectious disease epidemiology: Concepts, methods, mathematical models, and public health. New York, NY: Springer New York, 2009. 209-221.

Billard, Marie-Noëlle, et al. "Year-to-year variation in attack rates could result in underpowered respiratory syncytial virus vaccine efficacy trials." Journal of Clinical Epidemiology 147 (2022): 11-20.

Nauta, Jozef. Statistics in Clinical Vaccine Trials. Springer