Authors' reply

We 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. By contrast, asymptomatic patients and those with mild disease remained untested. These two factors probably explain the overestimates of mortality at the beginning of the curve (Feb 12–24 in our model,⁴ as exemplified in the appendix).

As mentioned by Spychalski and colleagues, “irrespective of the method used, all calculations are biased, especially in the initial part of an outbreak, and converge once all cases are closed”. During and after the epidemic peak, patient denominators correspond to the best estimates of people presenting with clinical COVID-19 because of access to diagnostic testing and stabilisation of the number of new daily cases. At that time, we consider that patients were screened close to symptom onset. According to reports from WHO,⁵ the time from symptom onset to death ranges from 2 to 8 weeks. In our estimates, we chose to use the minimum time between symptom onset and death so not to overestimate mortality rates. Another factor that is still unknown and could bias the model is the number of asymptomatic cases, as acknowledged in our Correspondence. Most asymptomatic patients are not captured by screening, leading to underestimates in the denominator. We presented our model as a mortality rate estimate among people presenting with clinical COVID-19—that is, symptomatic cases. In our experience, patients are mostly interested in knowing mortality rates when symptomatic, and less so of asymptomatic carriers.

There are other limitations that would apply to any statistical method, such as the possible change in testing frequency due to a shortage of tests. In some places, patients might even die before being tested. In the extreme, the mortality rate would reach 100% if only patients who had died were tested, whereas mortality rates would significantly drop if the entire population was to be tested. Thus, ideally, estimates should be adjusted according to test availability. Another consideration is that mortality in this epidemic is highly age-dependent, and so will vary according to the number of older individuals in the population. In high-income countries, the demographic pyramid is such that there are higher proportions of older individuals in the population. With larger numbers of vulnerable individuals exposed, one will observe higher overall mortality rates. In addition, mortality will vary across communities depending on access to tertiary medical centres and well equipped critical care units.

For the time being, in Europe, we are still in the early epidemic period, with a rapid increase in the number of cases; additional data are needed for the assessment of cumulative mortality rates due to confirmed COVID-19 cases over time.⁶ Thus, the goal of our publication was to share our vision of the potential impact of COVID-19 using a model that integrated the viral incubation period and the time to death following diagnosis. As with every model, estimates will improve as the number of cases increase.