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How to calculate the mortality rate during an outbreak
At present, it is tempting to estimate the case fatality rate by dividing the number of known deaths by the number of confirmed cases. The resulting number, however, does not represent the true case fatality rate and might be off by orders of magnitude [...]
A precise estimate of the case fatality rate is therefore impossible at present.
2019-Novel Coronavirus (2019-nCoV): estimating the case fatality rate – a word of caution - Battegay Manue et al., Swiss Med Wkly, February 7, 2020
The case fatality rate (CFR) represents the proportion of cases who eventually die from a disease.
Once an epidemic has ended, it is calculated with the formula: deaths / cases.
But while an epidemic is still ongoing, as it is the case with the current novel coronavirus outbreak, this formula is, at the very least, "naïve" and can be "misleading if, at the time of analysis, the outcome is unknown for a non negligible proportion of patients." [
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(
Methods for Estimating the Case Fatality Ratio for a Novel, Emerging Infectious Disease - Ghani et al, American Journal of Epidemiology).
In other words, current deaths belong to a total case figure of the past, not to the current case figure in which the outcome (recovery or death) of a proportion (the most recent cases) hasn't yet been determined.
The correct formula, therefore, would appear to be:
CFR = deaths at day.x / cases at day.x-{T}
(where T = average time period from case confirmation to death)
This would constitute a fair attempt to use values for cases and deaths belonging to the same group of patients.
One issue can be that of determining whether there is enough data to estimate T with any precision, but it is certainly not T = 0 (what is implicitly used when applying the formula current deaths / current cases to determine CFR during an ongoing outbreak).
Let's take, for example, the data at the end of February 8, 2020: 813 deaths (cumulative total) and 37,552 cases (cumulative total) worldwide.
If we use the formula (deaths / cases) we get:
813 / 37,552 = 2.2% CFR (flawed formula).
With a conservative estimate of T = 7 days as the average period from case confirmation to death, we would correct the above formula by using February 1 cumulative cases, which were 14,381, in the denominator:
Feb. 8 deaths / Feb. 1 cases = 813 / 14,381 = 5.7% CFR (correct formula, and estimating T=7).
T could be estimated by simply looking at the value of (current total deaths + current total recovered) and pair it with a case total in the past that has the same value. For the above formula, the matching dates would be January 26/27, providing an estimate for T of 12 to 13 days. This method of estimating T uses the same logic of the following method, and therefore will yield the same result.
An alternative method, which has the advantage of not having to estimate a variable, and that is mentioned in the
American Journal of Epidemiology study cited previously as a simple method that nevertheless could work reasonably well if the hazards of death and recovery at any time
t measured from admission to the hospital, conditional on an event occurring at time
t, are proportional, would be to use the formula:
CFR = deaths / (deaths + recovered)
which, with
the latest data available, would be equal to:
16,490 / (16,490 + 101,584) = 14% CFR (worldwide)
If we now exclude cases in mainland China, using
current data on deaths and recovered cases, we get:
13,220 / (13,220 + 28,881) = 31.4% CFR (outside of mainland China)
The sample size above is limited, and the data could be inaccurate (for example, the number of recoveries in countries outside of China could be lagging in our collection of data from numerous sources, whereas the number of cases and deaths is more readily available and therefore generally more up to par).
There was a discrepancy in mortality rates (with a much higher mortality rate in China) which however is not being confirmed as the sample of cases outside of China is growing in size. On the contrary, it is now higher outside of China than within.
That initial discrepancy was generally explained with ahigher case detection rate outside of Chinaespecially with respect to Wuhan, where priority had to be initially placed on severe and critical cases, given the ongoing emergency.
Unreported cases would have the effect of decreasing the denominator and inflating the CFRabove its real value. For example, assuming 10,000 total unreported cases in Wuhan and adding them back to the formula, we would get a CFR of 12.9% (quite different from the CFR of 14% based strictly on confirmed cases).
Neil Ferguson, a public health expert at Imperial College in the UK, said his “best guess” was that there were 100,000 affected by the virus even though there were only 2,000 confirmed cases at the time. [
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Without going that far, the possibility of a non negligible number of unreported cases in the initial stages of the crisis should be taken into account when trying to calculate the case fatally rate.
As the days go by and the city organized its efforts and built the infrastructure, the ability to detect and confirm cases improved. As of February 3, for example, the novel coronavirus nucleic acid testing capability of Wuhan had increased to 4,196 samples per day from an initial 200 samples.[
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A significant discrepancy in case mortality rate can also be observed when comparing mortality rates as calculated and
reported by China NHC: a CFR of 3.1% in the Hubei province (where Wuhan, with the vast majority of deaths is situated), and a CFR of 0.16% in other provinces (19 times less).
Finally, we shall remember that while the 2003 SARS epidemic was still ongoing, the World Health Organization (WHO)
reported a fatality rate of 4% (or as low as 3%), whereas the final
case fatality rate ended up being 9.6%.
