Using a delay-adjusted case fatality ratio to estimate under-reporting of COVID-19 infections

Authors: Timothy W Russell, Joel Hellewell, Sam Abbott, Christopher I Jarvis, Kevin van Zandvoort, CMMID nCov working group, Stefan Flasche, Rosalind Eggo, W John Edmunds & Adam J Kucharski.
Partial extract.

Aim

To estimate the percentage of symptomatic COVID-19 cases reported in different countries using case fatality ratio estimates based on data from the ECDC, correcting for delays between confirmation-and-death.

Methods Summary

• In real-time, dividing deaths-to-date by cases-to-date leads to a biased estimate of the case fatality ratio (CFR), because this calculation does not account for delays from confirmation of a case to death, and under-reporting of cases.
• Using the distribution of the delay from hospitalisation-to-death for cases that are fatal, we can estimate how many cases so far are expected to have known outcomes (i.e. death or recovery), and hence adjust the naive estimates of CFR to account for these delays.
• The adjusted CFR does not account for under-reporting. However, the best available estimates of CFR (adjusting or controlling for under-reporting) are in the 1% - 1.5% range. We assume a baseline CFR, taken from a large study in China, of 1.38% (95% crI: 1.23–1.53%)[1]. If a country has an adjusted CFR that is higher (e.g. 20%), it suggests that only a fraction of cases have been reported (in this case, 1.3820=6.9%$\frac{1.38}{20}=6.9\mathrm{\%}$ cases reported approximately).

Approximating the proportion of symptomatic cases reported

At this stage, raw estimates of the CFR of COVID-19 correcting for delay to outcome, but not under-reporting, have been calculated. These estimates range between 1% and 1.5% [1,4,6]. We assume a CFR of 1.38% (95% crI 1.23% - 1.53%), taken from a recent large study [1], as a baseline CFR. We use it to approximate the potential level of under-reporting in each country. Specifically, we perform the calculation 1.38%cCFR$\frac{1.38\mathrm{\%}}{\text{cCFR}}$ of each country to estimate an approximate fraction of cases reported.

Figure from report:

Comment by the Pundit:

The epidemic curve trajectories of highlighted countries have instructive features: