Estimating case fatality rates of COVID-19
Authors: Piotr Spychalski, Agata Błażyńska-Spychalska, Jarek Kobiela
Journal: The Lancet Infectious Diseases (2020)

We congratulate David Baud and colleagues1Baud D Qi X Nielsen-Saines K Musso D Pomar L Favre G Real estimates of mortality following COVID-19 infection.Lancet Infect Dis. 2020; (published online March 12.)https://doi.org/10.1016/S1473-3099(20)30195-XSummary Full Text Full Text PDF Scopus (825) Google Scholar 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".2Porta M A dictionary of epidemiology.5th edn. Oxford University Press, Oxford2008Crossref Google Scholar 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".2Porta M A dictionary of epidemiology.5th edn. Oxford University Press, Oxford2008Crossref Google Scholar 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,3Pueyo T Coronavirus: why you must act now.Available from: https://medium.com/@tomaspueyo/coronavirus-act-today-or-people-will-die-f4d3d9cd99caDate accessed: March 18, 2020Google Scholar 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,4Wu Z McGoogan JM Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: summary of a report of 72 314 cases from the Chinese Center for Disease Control and Prevention.JAMA. 2020; (published online February 24.)DOI:10.1001/jama.2020.2648.FUECrossref Scopus (12695) Google Scholar 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.2Porta M A dictionary of epidemiology.5th edn. Oxford University Press, Oxford2008Crossref Google Scholar 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. All calculations were based on data acquired from worldometer.info/coronavirus and are available in the appendix. We declare no competing interests. Download .xlsx (.02 MB) Help with xlsx files Supplementary appendix Real estimates of mortality following COVID-19 infectionAs of March 1, 2020, 79 968 patients in China and 7169 outside of China had tested positive for coronavirus disease 2019 (COVID-19).1 Among Chinese patients, 2873 deaths had occurred, equivalent to a mortality rate of 3·6% (95% CI 3·5–3·7), while 104 deaths from COVID-19 had been reported outside of China (1·5% [1·2–1·7]). However, these mortality rate estimates are based on the number of deaths relative to the number of confirmed cases of infection, which is not representative of the actual death rate; patients who die on any given day were infected much earlier, and thus the denominator of the mortality rate should be the total number of patients infected at the same time as those who died. Full-Text PDF Authors' replyWe thank David Dongkyung Kim and Akash Goel,1 Piotr Spychalski and colleagues,2 and Marc Lipsitch3 for their critical reading of our Correspondence.4 In response to the points raised regarding our statistical methods, we agree that our model might not be appropriate for the early epidemic period because of the rapid increase in the number of cases in the 14 days preceding reported deaths. During this period, many patients were certainly diagnosed with coronavirus disease 2019 (COVID-19) at the time they developed critical illness or even at the time of death. Full-Text PDF Estimating case fatality rates of COVID-19In their model, David Baud and colleagues1 exclude individuals who die within 14 days of testing positive for severe acute respiratory syndrome coronavirus 2. If an individual contracts symptoms on March 1, tests positive on March 10, and dies on March 11, they would not be included in the denominator for case fatality rate (CFR) on March 11. In addition, patients might test positive up to 13 days after recovery.2 As testing is expanded, an asymptomatic patient infected 1 week before testing positive on March 3 should, but will not, be included in calculations for March 16. Full-Text PDF Estimating case fatality rates of COVID-19In their Correspondence, David Baud and colleagues1 suggest that case fatality rates (CFRs) for coronavirus disease 2019 have been underestimated and propose to divide deaths at time t by cases at time t minus 14 days to correct this underestimation and provide so-called real estimates. Many biases in both directions afflict CFR estimates during outbreaks,2 and experts have spent 2 decades (since the outbreak of severe acute respiratory syndrome coronavirus) finding ways to overcome these.3 The delay problem highlighted by Baud and colleagues produces falsely low estimates, whereas the under-ascertainment of mild cases produces falsely high estimates. Full-Text PDF