Signature
SAR = S / (H - P)
| Inputs | Definition | Unit |
|---|---|---|
S | Number of cases among contacts that arise after the primary cases, for example within one incubation period | count of people |
H | Total number of people in the households of the primary cases, including the primary cases | count of people |
P | Number of primary cases in those households | count of people |
SAR | Proportion of contacts of the primary cases who became secondary cases | proportion, often reported as a percentage |
|---|
Function
Attack rate, secondary attack rate and final epidemic size function
Maps counts of new cases and of people at risk over a stated period to an attack rate, a risk expressed as a proportion rather than a rate per unit of time. The same structure gives the secondary attack rate among contacts of primary cases, and comparing attack rates between groups gives the attack rate ratio and vaccine efficacy or effectiveness. Under the assumptions of the simple susceptible, infectious and recovered model, the final attack rate of a completed epidemic is linked to the basic reproduction number R_0 through the final size relation. In an economic evaluation the attack rate is either a fixed input probability of infection, as in a static model, or an output that changes with the intervention, as in a dynamic transmission model.
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Implementations
Excel
Secondary attack rate from household counts
Excel subtracts the primary cases from the household members to give the contacts, then divides the secondary cases by that number.
=SecondaryCases/(HouseholdMembers-PrimaryCases)
Assumptions
Secondary cases counted in a stated window after the primary cases
S counts cases among contacts that arise after the primary cases, within a stated window such as one incubation period, and the window is reported with the rate.
Household members minus primary cases as the contacts at risk
H minus P stands for the contacts at risk. Where some household members are known to be immune, or contacts outside the household are traced, the denominator is the number of contacts actually at risk.
Worked examples
Illustrative secondary attack rate of 20% in 20 households
In the article's illustrative figures, 20 primary cases live in 20 households with 80 members, leaving 60 contacts. If 12 contacts become ill, the secondary attack rate is 0.20.
S = 12; H = 80; P = 20; SAR = 0.20
Secondary attack rate in the CDC shigellosis outbreak
In the CDC example, 17 people in the households of 18 primary cases developed shigellosis one incubation period later. The households held 86 people, so there were 68 contacts and the secondary attack rate is 0.25, against an overall attack rate of 1.8% in the community.
S = 17; H = 86; P = 18; SAR = 0.25
Common errors
Leaving the primary cases in the secondary attack rate denominator
Dividing the 17 secondary cases in the CDC shigellosis example by all 86 household members gives about 0.198 instead of 0.25, understating spread within households.
Reading a secondary attack rate as a reproduction number
A secondary attack rate of 25% among household contacts is a proportion of contacts infected, not a number of cases per case. It converts into R_0 only under the assumptions of a specific model.
Sources
CDC definition and example of the secondary attack rate
Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice. 3rd ed. Atlanta: CDC; 2006, page last reviewed 2012. Lesson 3: Measures of Risk, section 2: Morbidity frequency measures. Secondary attack rate as cases among contacts of primary cases divided by the number of contacts, often the household population of the primary cases minus the primary cases, and the shigellosis example.
Canonical Identity
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