Signature
CFR = D / N_c
| Inputs | Definition | Unit |
|---|---|---|
D | Deaths from the disease among the cases counted in N_c, over the stated period | count of people |
N_c | Number of cases meeting the case definition, for example laboratory-confirmed cases | count of people, above zero |
CFR | Proportion of the counted cases who died of the disease over the stated period | proportion with no time unit, often reported as a percentage |
|---|
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
Case fatality rate from named death and case counts
Excel divides the named cell holding the deaths among the counted cases by the named cell holding the number of cases.
=Deaths/Cases
Assumptions
Deaths restricted to the counted cases
Every death in D comes from a case in N_c. A death-to-case ratio, which divides deaths in a period by new cases in the same period, does not meet this condition and cannot be read as the probability that a newly diagnosed case dies.
Every counted case resolved and detection consistent
The crude ratio is reliable once every counted case has died or recovered and detection of cases and deaths has stayed consistent, as at the end of an outbreak. Part-way through, unresolved cases push it down and preferential ascertainment of severe cases pushes it up.
Worked examples
CDC hepatitis A outbreak with 555 cases and 3 deaths
The CDC teaching text works through a hepatitis A outbreak with 555 cases, 3 of whom died, a case fatality rate of about 0.0054, reported as 0.5%.
D = 3; N_c = 555; CFR = 0.0054
Final case fatality rate in the article's illustrative outbreak
Once every case has resolved, the article's illustrative outbreak has 60 deaths among 2,000 confirmed cases, a final case fatality rate of 0.030.
D = 60; N_c = 2000; CFR = 0.03
Crude case fatality rate at week 8 of the illustrative outbreak
At week 8 the same outbreak has 40 deaths among 2,000 confirmed cases, a crude estimate of 0.020. It is too low because 20 of the 960 cases still ill will die.
D = 40; N_c = 2000; CFR = 0.02
Common errors
Treating a four-week case fatality rate as annual
The article's 3% refers to deaths within four weeks of becoming a case. Rescaled with HE-FM-TP-003 to weekly cycles it gives about 0.0076 a week. Treated as an annual probability over 52 weekly cycles it gives about 0.00059 a week, and a four-week illness then carries a death risk of about 0.23%, roughly one thirteenth of the intended value.
Reading a mid-outbreak crude case fatality rate as final
At week 8 of the article's illustrative outbreak the crude estimate is 0.020 against a final 0.030. In its cost-effectiveness example the crude figure gives about £16,667 per QALY instead of about £11,111, because it counts too few deaths averted.
Applying a confirmed-case fatality rate to all infections
A CFR among confirmed cases goes with confirmed cases. In the article's example five infections per confirmed case give an infection fatality ratio of 0.006 against a CFR of 0.030, so applying the CFR to all infections multiplies deaths by five, and applying the infection fatality ratio to confirmed cases divides them by five.
Sources
CDC definition of the case-fatality rate as a 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 3, Mortality frequency measures. Defines the case-fatality rate as the proportion of persons with a particular condition who die from that condition, restricts the numerator to deaths among the cases in the denominator, works the hepatitis A example and distinguishes the death-to-case ratio.
Risk period in a precise case fatality definition
Lipsitch M, Donnelly CA, Fraser C, Blake IM, Cori A, Dorigatti I, et al. Potential biases in estimating absolute and relative case-fatality risks during outbreaks. PLoS Neglected Tropical Diseases. 2015;9(7):e0003846. Box 1: the period over which deaths are counted for the CFR is rarely explicit, and a precise definition would include it, for example the one-month CFR.
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