Signature
CFR_r = D / (D + R)
| Inputs | Definition | Unit |
|---|---|---|
D | Deaths from the disease among detected cases up to the time of estimation | count of people |
R | Recoveries among detected cases up to the same time | count of people |
CFR_r | Proportion of the resolved cases (those who have died or recovered) who died | proportion with no time unit |
|---|
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
Resolved-case fatality rate in one cell
Excel divides the named cell holding deaths by the sum of the named cells holding deaths and recoveries among detected cases.
=Deaths/(Deaths+Recoveries)
Assumptions
Deaths and recoveries resolve at similar speeds
The estimate is unbiased only if cases that will die and cases that will recover leave the unresolved pool at similar times. If people who die typically do so sooner than others recover, the estimate is too high; if the reverse holds, it is too low.
Recoveries recorded as completely as deaths
Detection of cases, deaths and recoveries stays consistent over the outbreak and recoveries are recorded as fully as deaths. Missing recoveries shrink the denominator and raise the estimate.
Worked examples
Resolved-case estimate at week 8 of the illustrative outbreak
At week 8 the article's illustrative outbreak has 40 deaths and 1,000 recoveries, so 40 / 1,040 gives about 0.0385. It is too high, because deaths occur sooner than recoveries in this outbreak and the final value is 0.030.
D = 40; R = 1000; CFR_r = 0.0385
Resolved-case estimate once every case has resolved
When all 2,000 cases have resolved, with 60 deaths and 1,940 recoveries, the resolved-case estimate equals the final crude value of 0.030 (computed here for illustration).
D = 60; R = 1940; CFR_r = 0.03
Common errors
Treating the resolved-case estimate as unbiased
At week 8 the resolved-case estimate of about 0.0385 exceeds the final 0.030 because deaths come sooner than recoveries. In the article's cost-effectiveness example it gives about £8,667 per QALY, below an illustrative threshold of £10,000, against about £11,111 with the final estimate, so a model using it reaches the wrong decision.
Sources
WHO resolved-case approach to case fatality during an epidemic
World Health Organization. Estimating mortality from COVID-19: scientific brief, 4 August 2020. WHO/2019-nCoV/Sci_Brief/Mortality/2020.1. Geneva: WHO; 2020. Section on calculating CFR during an ongoing epidemic: restricting the analysis to resolved cases, and the warning that the estimate is too high if people die quicker than they recover and too low in the reverse case.
Canonical Identity
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