The gap between confirmed COVID-19 cases and the actual number of infections, which is crucial in estimating the prevalence and lethality of the virus that causes the disease, may be far larger than most epidemiologists have assumed. According to a recent analysis by two German researchers, the official numbers published by 40 national governments at the end of March represented just 6 percent of infections on average, meaning that "the true number of infected people worldwide may already have reached several tens of millions," as opposed to the current global tally of fewer than 2 million.

"Case fatality rates may only be a very poor proxy for the true infection fatality rate if a high number of infections remain undetected," observe University of Gottingen economist Sebastian Vollmer and research associate Christian Bommer. That is especially true when most carriers experience no symptoms or have symptoms so mild that they never seek treatment or testing, as appears to be the case with the COVID-19 virus. The crude case fatality rate for COVID-19—reported deaths as a percentage of confirmed cases—varies widely by country, which suggests "vast differences in the quality of countries' case records," Vollmer and Bommer note. "Despite such uncertainties, policy makers rely heavily on the extrapolation of past trends when planning responses to the pandemic."

To figure out how many infections might be missing from the official numbers, Vollmer and Bommer applied estimates from a Lancet Infectious Diseases study published on March 30. That study, based on 24 COVID-19 deaths in China and 165 recoveries among citizens of other countries who returned from Wuhan after the outbreak there, estimated that the fatality rate was 1.4 percent among people who developed symptoms and 0.66 percent among everyone infected by the virus in China. Both of those rates rose with age, and the average time from symptom onset to death was 18 days.

"As returning Wuhan expats have been subject to extensive testing, substantial underdiagnosing is unlikely, providing confidence in these numbers," Vollmer and Bommer write. "We therefore treat the reported infection fatality rates as benchmark[s] for other countries and calculate infection fatality rates for the 40 most affected countries using UN population data to correct for differences in age distributions."

As of March 31, Vollmer and Bommer calculate, confirmed cases represented just 3.5 percent of infections in Italy, 2.6 percent in France, 1.7 percent in Spain, 1.6 percent in the United States, and 1.2 percent in the U.K. In other words, the true number of infections was between 29 and 83 times as high as the official tallies in those countries. The countries with the highest estimated detection rates were South Korea (nearly 50 percent), Norway (38 percent), Japan (25 percent), and Germany (16 percent). With the exception of Japan, all of those countries have tested a relatively large percentage of their populations. The estimated prevalence of infection ranged from 0.1 percent in India and Japan to more than 13 percent in Turkey; it was 3.6 percent in the United States. [For the newly revised estimates, see the update at the end of this post.]

"The average detection rate is around six percent, making the number of cases that is reported in the news on a daily basis rather meaningless," Vollmer and Bommer conclude. Vollmer adds: "These results mean that governments and policy makers need to exercise extreme caution when interpreting case numbers for planning purposes. Such extreme differences in the amount and quality of testing carried out in different countries mean that official case records are largely uninformative and do not provide helpful information." Bommer notes that "major improvements in the ability of countries to detect new infections and contain the virus are urgently needed."

The country-specific infection fatality rates (IFRs) calculated by Vollmer and Bommer cover a wide range, from just 0.2 percent in Iraq to 1.6 percent in Japan. Their estimate for Germany is 1.3 percent, which is more than three times as high as the IFR calculated in a recent study based on antibody testing in Germany's Gangelt municipality. Those tests, which covered 80 percent of the local population, found that 15 percent of residents had been infected and put the IFR at 0.4 percent.

Vollmer and Bommer's estimated IFR for the United States is close to 1 percent, which is the high end of the range that federal public health officials consider reasonable and would make COVID-19 about 10 times as deadly as the seasonal flu. That IFR implies a U.S. death toll much higher than has been reported so far. Vollmer and Bommer estimated that nearly 12 million Americans were already infected by March 31. If the IFR is in fact about 1 percent, we would expect to see something like 100,000 deaths by now, nearly two weeks later, as opposed to the official tally of 22,000 or so. It seems unlikely that so many COVID-19 deaths have been overlooked.

Since Vollmer and Bommer are relying on the IFR estimates from the Lancet Infectious Diseases study, the accuracy of their numbers depends on the accuracy of that model. Furthermore, they adjusted only for age when they estimated the IFR for each country.

"Countries also differ in other important characteristics such as prevalence of pre-existing conditions, quality and capacity of the health system and phase of the epidemic they are in," they note. "The true infection fatality rates could therefore differ from our estimates. For instance, it is possible that countries with very good health systems are more successful in treating patients than China." But if the IFRs for some countries (such as Germany and the United States) are lower than Vollmer and Bommer assume, that would imply an even larger number of undetected infections.

Update, April 14: Vollmer and Bommer have revised their estimates based on more recent data. According to the new calculations, the detection rate in the United States as of March 30 was 6.6 percent, up from 3.6 percent in the earlier analysis. The new estimates are also higher for other countries, including Italy (6.9 percent vs. 3.5 percent), France (3.6 percent vs. 2.6 percent), Spain (6 percent vs. 1.7 percent), and the U.K. (2.2 percent vs. 1.2 percent).

"The calculation for the number of infected people was done under the hypothetical assumption that detection rates had stayed constant between March 17th and 31st," Vollmer writes in an email. "We mentioned that in some countries, including the United States, the detection will likely improve. It turns out that it did improve, and therefore the estimated number of infections is much lower than under the assumption of a constant detection rate. The share of undetected cases is still quite sizeable, above 90 percent across these countries."

The new estimate for the number of infections in the United States at the end of March is 2.5 million, which is much lower than the original estimate of 11.9 million, although still 15 times the number of confirmed cases at the time and four times the current tally. Based on the "expected infection fatality rate" of 0.96 percent, that implies roughly the same number of deaths that have been reported so far. Since the calculation of the detection rate is based on the expected IFR combined with the death toll and the estimated time to death, that is what you would expect. Whether that IFR estimate will prove to be in the right ballpark is another question.