Signature
M = AR * CFR
| Inputs | Definition | Unit |
|---|---|---|
AR | Attack rate, cases divided by the population at risk over the outbreak, on the same case definition as CFR | proportion |
CFR | Case fatality rate among the cases counted in AR, over the same period | proportion |
M | Proportion of the population at risk that dies of the disease over the outbreak | proportion with no time unit, often reported per 1,000 people |
|---|
Function
Case fatality rate estimation, outbreak bias and population mortality function
Maps counts of deaths, recoveries and cases to the case fatality rate (CFR), the proportion of cases meeting a case definition who die of the disease over a stated period, and relates it to the delay bias of crude estimates during exponential growth and to population mortality through the attack rate. The records follow the notation of the Case Fatality Rate article. Matching the period of a CFR to a model cycle uses HE-FM-TP-003, and the attack rate itself is HE-FM-ATR-001.
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Implementations
Excel
Outbreak mortality from attack rate and case fatality rate
Excel multiplies the named cells holding the attack rate and the case fatality rate.
=AttackRate*CaseFatality
Assumptions
Same cases, period and population in both measures
AR and CFR use the same case definition and period, and the attack rate's denominator is the population at risk to which M refers.
All disease deaths occur among the counted cases
Every death from the disease counted in M occurs among the counted cases. Deaths among infections never ascertained as cases, or deaths after the counting window, break the identity.
Worked examples
Attack rate of 0.20 with a case fatality rate of 0.03
With the article's illustrative figures, an attack rate of 0.20 and a case fatality rate of 0.03 give a mortality of 0.006, or 6 deaths per 1,000 people over the outbreak.
AR = 0.2; CFR = 0.03; M = 0.006
Rare disease with a high case fatality rate
An attack rate of 0.001 with a case fatality rate of 0.5 gives a mortality of 0.0005, or 1 death per 2,000 people, low despite the high case fatality rate (computed here for illustration).
AR = 0.001; CFR = 0.5; M = 0.0005
Common errors
Pairing an infection fatality ratio with a confirmed-case attack rate
With five infections per confirmed case, as in the article's example, a confirmed-case attack rate of 0.20 multiplied by an infection fatality ratio of 0.006 gives 0.0012, one fifth of the 0.006 obtained with the matching case fatality rate of 0.03 (computed here for illustration). Applying an infection fatality ratio to confirmed cases understates deaths.
Sources
CDC mortality rate and case-fatality rate denominators
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 3, Mortality frequency measures. The mortality rate divides deaths by the size of the population among which they occurred, while the case-fatality rate divides deaths by cases. The product identity M = AR × CFR is derived here from these two definitions, for the same cases and population; the CDC text does not state it.
CDC attack rate as an incidence proportion
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. The attack rate, or incidence proportion, divides new cases during a specified interval by the population at the start of the interval.
Canonical Identity
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