# Using a delay-adjusted case fatality ratio to estimate under-reporting

**This study has not yet been peer reviewed.**

## 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.

## Data availability

The under-reporting estimates for all countries can be downloaded as a single .csv file here.

Similarly, the prevalence estimates can be downloaded as a single .csv file here.

## How to cite this work

If you wish to cite this work, please do cite the associated preprint [1]).

## Methods Summary

The associated preprint[1], specifically the corresponding supplementary material contains a full description of the methods and limitations used to arrive at the estimates presented here.

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.Â 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 [2â€“5]. Large studies in China and South Korea estimating the CFR at 1.38% (95% CrI: 1.23â€“1.53%)[3] and 1.4% (95% CrI: 1.2-1.7%)[5] respectively. Based on these studies, and for simplicity, we assume a baseline CFR of 1.4% for our analysis.

If a country has an adjusted CFR that is higher (e.g.Â 20%), it suggests that only a fraction of cases have been reported (in this case, \(\frac{1.4}{20}=7.0\%\) cases reported approximately).

We then go on to use these under-reporting estimates to adjust the confirmed case curves to arrive at adjusted new cases per day curves and prevalence estimates

The prevalence estimates are calculated by tallying up over the last 10 days of adjusted incidence, which serves as a crude proxy for prevalence