Estimating case fatality rates of COVID-19

We congratulate David Baud and colleagues¹ for their apt observations regarding the burden of the coronavirus disease 2019 (COVID-19) epidemic and the possibly higher than expected proportion of cases that are fatal. Precision, however, is as necessary in calculations as in semantics.

According to the Dictionary of Epidemiology, the mortality rate is an “estimate of the portion of a population that dies during a specified period”.² In the case of this outbreak, the mortality rate over a period of 1 year per 100 000 Chinese citizens would be around 0·23 (as of March 16, 2020). Therefore, precisely speaking, neither older estimates nor Baud and colleagues' new calculation can be referred to as the mortality rate.

In both trade press and newspapers, the case fatality rate (CFR) is often used to describe the situation pertaining to COVID-19, as well as to any other epidemic. The definition of the CFR in the Dictionary of Epidemiology states that it is “the proportion of cases of a specified condition that are fatal within a specified time”.² On the one hand, as accurately pointed out by Baud and colleagues, the CFR might be underestimated because of a type of time-lag bias associated with diagnosing and reporting cases. Furthermore, calculations are based on the questionable assumption that all cases are being tested. On the other hand, as Pueyo suggests,³ the CFR might be overestimated due to the definition of a case. During an epidemic, cases might be defined either as total cases (ie, every confirmed case) or as closed cases (ie, only those who have recovered or died). Hence, the denominator for the CFR might be either of these numbers. In the initial phase of the epidemic, the number of closed cases is relatively small, and so the CFR calculated per closed cases is an overestimate. By contrast, when the CFR is calculated per total cases, the numerator is underestimated, and thus the whole calculation becomes an underestimate.

Baud and colleagues' calculation, although interesting, is biased as well. As shown in the figure, it vastly overestimates the fatality of COVID-19 if one uses data from the initial phase of the outbreak. This overestimation is obviously due to undertesting and a time-lag bias, which is more pronounced in the beginning of an outbreak. As demonstrated in the figure, irrespective of the method used, all calculations are biased, especially in the initial part of an outbreak, and converge once all cases are closed. Nevertheless, it seems that the CFR calculated per total cases is the least affected by reporting biases.

As of March 16, the CFR per total cases in China is 4·00%, per closed cases is 4·44%, and as calculated with Baud and colleagues' method is 4·03%. However, despite the downturn of the outbreak in China, 8043 cases are still open, of which 2622 are serious or critical. According to Wu and McGoogan's estimates based on 72 314 cases from Wuhan,⁴ 81% of patients are classified as mild, 14% as severe, and 5% as critical. CFRs in these subgroups are 0%, 0%, and 49%, respectively. Based on these estimates, of 8043 open cases in China, about 377 are in a critical condition and of those 184 will die. Therefore, once all active cases are closed, we might expect the CFR in China to be around 3·85%.

On a technical note, Baud and colleagues' calculation seems to be an attempt at reporting the cumulative death rate, which is defined as “the proportion of a group that dies over a specified time”, rather than the mortality rate.²

In summary, the CFR calculated per total cases seems to remain the best tool to express the fatality of the disease, even though it might underestimate this figure in the initial phase of an outbreak.