Comparing Coronavirus Attack Rates

I’ve been plotting cases per capita (I’ve been calling that a “case rate” but learned today the correct term is “attack rate”) in US states compared to Italy (as a bad benchmark) and South Korea (as a good benchmark). Some people have noted, fairly, that the testing in those countries is very different. I’m skeptical this would have much of an impact on apparent growth rates. Italy started with and still has limited testing. I don’t start the lines at the first case, I start when each area crosses 2 cases per million people. Although Korea had poor test coverage in the very early days, just like every other country, by the time they reached 100 cases (their population is ~50 million people) their testing was probably almost as good as it is now. If the testing coverage improved by less than a factor of two, the impact on the growth rate when cases grow through a factor of over 100 would be almost negligible.

However, when we compare absolute attack rates, and not the growth rate, it’s probably worth it to make a crude adjustment for testing differences. In the future, I’m sure many groups of scientists will take blood samples from a lot of people to estimate what fraction of the population was ever infected. In the meantime, I believe we can use age-adjusted case fatality rates to estimate what fraction of infections have been identified.

In two cases – one city in South Korea and one cruise ship – every person in a contained area was tested for coronavirus, whether they showed symptoms or not. From there, we can estimate the infection fatality rate – the number of people who die per number of people infected – instead of the case fatality rate – the number of people who die per number of people we know are infected. Both studies gave similar results. The results are also similar to the overall case fatality rate in South Korea. Based on that comparison and South Korea’s well known and extremely thorough testing, I think it’s safe to estimate that South Korea identifies approximately 100% of infections. From there, if we compare people in the same age bracket, if another country has twice the case fatality rate, we can guess that that country is identifying approximately half its infections.

Here are case fatality rates for China, Italy, South Korea, and Spain pulled from Wikipedia.

With a CFR of 0 in South Korea below 30, we can only use data for people 30+. Here are the multiples of South Korea’s case fatality rate in each of the other age brackets:

The final column is a simple average of the others. From these data, my rough guess for the fraction of known cases in each country is:

China – 43%

Italy – 29%

Spain – 65%

Earlier today, based on logic I’ll block quote below, I estimate that in the US we’re currently identifying about 2/3rd of cases. So, if we want to get a more accurate international comparison of true infection rates, we should probably multiply Italy’s infections by 3.4 and America’s infections by 1.5. Both of these numbers are rough, but the value of 1.5 for the US is much more rough.

Based on the few areas where 100% of people were tested, we know the fatality rate is around 1%. The British simulation flying around for the last week makes an educated guess that the fatality rate in the ICU is 50%. NYT says “13 percent of people who have tested positive were hospitalized with nearly a quarter of those hospitalized in intensive care.” 13% by 25%, round down is 3%. So 3% of known cases are in ICU. That could extrapolate to about 1.5% fatality rate. So if the infection fatality rate is 1% and NY’s case fatality rate is 1.5%, they have identified about 2/3rds of the infections. Obviously, this is all very rough.