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How to correctly calculate the mortality rate during an outbreak
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." [8]
(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 flawed formula (deaths / cases) we get:
813 / 37,552 = 2.2% CFR (flawed formula).
Instead, even 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).
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:
910 / (910 + 3,466) = 21% CFR (worldwide)
If we now exclude cases in mainland China, using current data on deaths and recovered cases, we get:
2 / (2 + 44) = 4.3% CFR (outside of mainland China)
The sample size above is extremely limited, but this initial discrepancy in mortality rates, if confirmed as the sample grows in size, could be explained with a higher case detection rate outside of China, especially with respect to Wuhan, where priority had to be initially placed on severe and critical cases, given the ongoing emergency.
As the days go by and the city organizes its efforts and builds the infrastructure, the ability to detect and confirm cases should improve. 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.[10]
A similar discrepancy in case mortality rate can 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).