The Covid-19 case fatality rate in the UK is one of the highest in the world. This note explains that the large under-reporting of cases is one possible reason behind it and highlights that the number of plausible cases is at least 8-fold higher than the current known cases. Increasing the number of tests conducted daily, allowing for detection of asymptomatic or mildly symptomatic patients, would likely result in a lower fatality rate.

The case fatality rate (CFR), the ratio between the number of deaths and the number of cases of Covid-19, has reached the level of 10.3 percent on April 6th, meaning that around 10 people die out of 100 infected. This number has been constantly increasing over time, as Figure 1 shows.

Figure 1. SARS-CoV-2 Case fatality rate in the United Kingdom

Data: Public Health England. Author’s elaboration.

Compared to other countries that recorded at least 100 deaths the case fatality rate in the United Kingdom is among the highest. Only Italy, Algeria and France have higher fatality rates (Figure 2). Strikingly, countries like Germany, Austria and South Korea – similar to the UK along a number of different dimensions (economy, demography, etc.) – register considerably lower CFRs, at levels around 1.5-1.8 percent.

Figure 2. Case fatality rates in countries with at least 100 deaths as of 6 April

Data: ECDC. Downloaded 6 April 2020. Author’s elaborations.

What explains the difference between the United Kingdom and other countries? The same question was asked when the Italian fatality rate skyrocketed in the first weeks of the epidemic. Researchers hypothesise that the difference between the Italian fatality rate and that of other developed economies is due to social and demographic factors. Bayer and Kuhn (2020) argue that the share of young people living with their parents is correlated with the fatality rate of the virus, providing evidence that countries with more social interactions between age groups have higher death rates. The idea is simple: elderly people are more likely to be infected and therefore killed if they live under the same roof with their sons and daughters. This idea has been widely criticised and proved to be not robust to falsification tests using different samples or data (Belloc et al., 2020). Moreover, it is very unlikely that this mechanism could explain the higher fatality rate in the UK. Indeed, although the UK is not among the countries analysed by Bayer and Kuhn (2020), data by the Office for National Statistics provide suggestive evidence that this explanation is unimportant in the British case: only 9 percent of individuals aged 30-34 live with their parents in 2019 (and this percentage declines as older age groups are considered), whereas the share of middle-age Italians living with their parents is above 20 percent.

The second explanation put forward to reconcile the higher fatality rate in Italy is demography. Italy has a high share of old population compared to other countries. Dowd et al. (2020) focus specifically on the age structure as one key determinant of differences in fatality rates across countries. In the UK, the share of individuals older than 65 years old is 19% (source: UN World Population Prospects), higher than South Korea (15%), but lower than Germany (22%). Therefore, differences in age structures between countries would not help explain why the UK has a higher fatality rate than Germany.

Both the social and the demographic explanations do not seem to explain why the UK has such a high fatality rate. A third possible (and probably simpler) explanation is the under-reporting of cases.

In fact, we can think of the prevalence of the virus among the population as an iceberg. What we see is just the tip of it. If only people showing symptoms are being tested, there is a higher chance of detecting more severe cases. Therefore, the denominator of the CFR is biased downward, and the ratio is biased upward just because *symptomatic* cases are detected. However, a large number of asymptomatic (or paucisymptomatic) cases may still be present and transmit the virus: a study in the small town of Vo’ Euganeo in the Italian region of Veneto shows that 70 percent of infected individuals are asymptomatic.

There are reasons to believe that only symptomatic individuals are being tested in the UK, therefore considerably under-estimating the true number of cases. A suggestive evidence of this point is provided in Figure 3, which reports the fraction of individuals who test positive over time. The graph shows that the percentage of tests resulting in positive cases went from approximately 1.4% on March 10th to 24.7% on April 6th. If this number represents the true prevalence rate of the virus it would mean that 1 out of 4 individuals is infected. Although we cannot exclude that, at some point, the majority of the population ends up contracting the infection, it seems implausible that, already at this early stage, the prevalence is so high. It is more likely, instead, that tests are being conducted only on patients showing symptoms, therefore under-estimating the true number of infected individuals.

Figure 3. Fraction of positive tests

Data: Public Health England and @DHSCgovuk. Author’s elaboration.

At this point, we still have an unanswered question: what is the *plausible* number of infected individuals in the UK? Ferguson et al. (2020) estimate a *plausible* case fatality rate (the so-called infection fatality rate, IFR) of 0.9 percent (95 percent confidence interval: 0.4-1.4 percent).^{1} With these estimates at hand, we can compute the number of *plausible* cases in the UK. It suffices to divide the total number of deaths by the IFR. Following Villa (2020), an additional correction is made by subtracting the number of recovered patients from the number of plausible cases. Since neither Public Health England nor the Office for National Statistics provide up to date information on the number of recovered patients, I estimate a time-varying proportion of recoveries from Italian data.^{2} Figure 4 reports the results. The graph shows the number of currently active cases (*known cases*, computed as the number of cumulative cases minus deaths and estimated recovered patients) and the number of estimated plausible cases. The results suggest that, as of April 6th, there are approximately 525,000 total cases of Covid-19 among the British population, with a 95% confidence interval that ranges between 337,500 and 1.18 million cases. Given that the number of currently active cases (total cases net of deaths and recovered patients) is around 40,000, the estimate suggests that the plausible number of cases is at least 8-fold higher than the number of known cases. This is still a conservative estimate compared to Flaxman et al. (2020), who calculate that 2.7 percent (95 percent confidence interval: 1.2-5.4) of the British population was infected on 28 March (hence, around 1.8 million individuals).^{3}

Figure 4. Known and plausible cases of SARS-CoV-2 in the UK

Data: Public Health England. Author’s Elaboration

Therefore, we conclude that the large number of undetected cases might be the main reason explaining the high case fatality rate in the UK. Other social or demographic explanations seem to play a smaller role in the British case, although we cannot formally reject them.

The large number of undetected cases is a threat to the effectiveness of the strategy to suppress the virus. Italy is, again, an interesting case study. The under-estimation of the virus in the first days of the epidemic led the number of cases to increase exponentially. However, contrarily to the indications of the World Health Organization, many Italian regions did not conduct enough tests, losing contact with the true diffusion of the epidemic. The United Kingdom seems to be performing a low number of tests, too. A strategy which could prove harmful.

**References**

Bayer, C. and Kuhn, M. Intergenerational ties and case fatality rates: A cross-country analysis. *VoxEu.org*, 20 March 2020

BBC News. Coronavirus: Up to 70% of Germany could become infected – Merkel. 11 March 2020.

BBC News. WHO head: ‘Our key message is: test, test, test’. 16 March 2020

Belloc, M., Buonanno, P., Drago, F., Galbiati, R., and Pinotti, P. Cross-country correlation analysis for research on COVID-19. *voxeu.org*, 28 March 2020

Dowd, J. B. et al. Demographic science aids in understanding the spread and fatality rates of COVID-19. medRXiv, March 2020.

Ferguson, N. et al. Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand (Report 9). Imperial College report, 16 March 2020.

Flaxman, S. et al. Estimating the number of infections and the impact of non- pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College report, 30 March 2020.

Office for National Statistics. Young adults living with their parents. 2019.

The Guardian. In one Italian town, we showed mass testing could eradicate the coronavirus. 20 March 2020

United Nations. World Population Prospects 2019.

Verity et al. Estimates of the severity of COVID-19 disease medRXiv, 13 March 2020.

Villa, M. Coronavirus: la letalità in Italia, tra apparenza e realtà. ISPI report. 27 March 2020.

^{1} The IFR in Ferguson et al. (2020) builds upon the estimate for China provided by Verity et al. (2020), but taking into account and correcting for the different age structure of the British population compared to the China. A similar exercise is conducted in Villa (2020), who estimates an IFR for Italy of 1.14%.

^{2} Specifically, I run an OLS regression of the share of daily recovered patients in Italy on a linear time trend. The regression has an R2 of 0.84. I then compute the fitted values, which I use as an estimate of the share of recovered patients in the UK.

^{3}My approach to estimating the plausible number of cases is more naïve. However, Flaxman et al. (2020) base their estimates on some assumptions that could explain why they get a higher number of plausible cases (for example, they assume a very high basic reproduction rate of around 4). Moreover, the simple estimate presented in this note does not correct for the right censoring of deaths, the numerator of the CFR, caused by the delay between the disease onset and death (however, given this would represent an under-estimation of deaths, the estimate of plausible cases can be interpreted as a lower bound).

*About the author*

Salvatore Lattanzio is a PhD student at the Faculty of Economics, University of Cambridge. His research interests are Labour economics, Inequality, Gender wage gap.