# Coronavirus Fatality Rate or Death Percentage: Puzzling Estimates

If you are looking for the new coronavirus’ fatality rate or the percentage of infected people who will die, this is the most accurate estimate you will find on the internet. I did a Google search and none of the answer I found on the first page were accurate enough. Some articles claim that coronavirus’ fatality rate is between 2% and 4% which is based on the case fatality rate in China’s Hubei province. I will explain what case fatality rate is later in the article, but you should know that actual fatality rate is lower than 2% or 4%.

We are estimating coronavirus fatality rate in order to estimate the potential damage this new coronavirus may inflict on our lives and economies. The last time we had a pandemic in the United States was in 2009 (H1N1 swine flu) and it infected around 50 million Americans within 12 months. If this coronavirus infects 50 million Americans and its fatality rate is 4%, then it will kill 2 million Americans. I am 100% confident that it won’t infect 50 million Americans and its fatality rate is much less than 4%. I will provide an estimate at the end of this article. Let’s start with some of the basics.

In order to calculate an accurate estimate for COVID-19’s fatality rate we need a big enough sample, an accurate count of the number of deaths, and an accurate count of the number of infections.

In this case, we usually have pretty accurate data about the number of deaths caused by the new coronavirus disease, though I read several stories about undercounting the number of deaths caused by lack of hospital beds and test kits, and communication problems between hospital staff and local/national health officials who tally the numbers.

The second problem with the actual number of deaths is that there is a long lag between the identification of an infection and the resolution of that infection (either death or recovery). So, this is something we need to pay attention to.

We don’t know much about the new coronavirus and we don’t have accurate counts of the number of infected people. Sure, we have identified more than 700,000 cases worldwide at this point in time, but the actual number of infections could be 2 million or 20 million. Some countries test only the people who show symptoms, other countries test only the people who are hospitalized, but there might be millions of people who show no symptoms, yet are infected with the new coronavirus.

So, the real problem we are trying to solve here is the true number of coronavirus infections.

As of March 27th (morning), Iran reported 32332 “confirmed” cases and 2378 deaths due to the new coronavirus. If we rely on these numbers, we can estimate that coronavirus’ fatality rate as 7.35% (2378 divided by 32332). Are there really 2378 deaths in Iran due to COVID-19? Are there really a total of only 32332 people who are infected with the coronavirus in Iran? We don’t think so. Iran is an authoritarian country with a poor healthcare system. They don’t have the resources, organizational capabilities to identify, to test, and to track all potential coronavirus patients. They probably tested mostly infected people who are hospitalized. They also don’t have any incentives to truly report the actual number of deaths. The only thing we can assume about the numbers reported by Iran is that the correct numbers are greater than what is reported.

In our analysis we are going to use the numbers reported by Iceland, South Korea and the Diamond Princess cruise ship. We especially like the data from the cruise ship because all passengers were tested for COVID-19, so we have a near perfect count of all infections (there is still the small possibility that the tests yielded some false negatives and we missed a few infections). The problem we have with the Diamond Princess data is that its sample size is small and the average age of the passengers is much higher than the average age we normally see in any country. Also, nearly 100 of the cases haven’t resolved yet.

There were a total of 3711 people on board when the Diamond Princess was quarantined on February 5th. Passengers were allowed the leave the ship after 14 days only if they spent 14 days in quarantine without being near a confirmed case (i.e. they didn’t share their cabin with a person who was infected), they have a negative test result for COVID-19 by PCR in the final days of their quarantine, and they didn’t show any symptoms on the 14th day of their quarantine.

A total of 712 passengers and crew tested positive. More importantly, 331 of these infections were asymptomatic at the time of testing. So far, 603 of the patients recovered and 10 of them died. There are still 99 unresolved cases. This puts Diamond Princess’ infection fatality rate at 1.63% (10 divided by 613 total resolved cases). However, around two thirds of the infected people are over the age of 60. Unfortunately I don’t have the entire age distribution of the Diamond Princess passengers and crew, so I can’t calculate the age adjusted infection fatality rate. A rough estimate will probably be around 0.5%.

As of March 29th (evening), Iceland is the #1 country in terms of testing a large percentage of its population. What is great about our Iceland data is that most of the sample is randomly drawn. If you aren’t familiar with statistics, I can tell you that this is amazing. This is amazing because we can make generalizations using this random sample.

Iceland tested nearly 5% of its entire population. It is a very small country. There were 1020 confirmed infections as of March 29th. More interestingly, around half of the infected people were asymptomatic. This figure matches the percent of asymptomatic cases on the Diamond Princess cruise ship. Most of the infected people in Iceland were identified over the last 2 weeks and their cases haven’t resolved yet. Iceland reported only 2 deaths so far (Iceland’s case fatality rate is currently 0.2%), but that may also be because of its relatively younger population (see the graph below).

We can’t use Iceland’s data to calculate the new coronavirus’ fatality rate, but we are going to use its findings about the percent of asymptomatic cases.

As of March 29th, South Korea is the #2 country in terms of deploying more resources and testing a higher percentage of its population for coronavirus. South Korea reported 152 deaths, 9583 infections, and tested nearly 370 thousand people. This is a huge number. This means South Koreans tested 1 out of every 140 people in the country. This is equivalent to 2.25 million people in the United States.

That’s why we believe using South Korea’s case fatality rate will help us calculate the most accurate estimate for coronavirus’ fatality rate.

The problem with the South Korean data is that so far only 5033 of the infected people recovered and nearly half of the cases haven’t resolved yet.

South Koreans calculated that around 20% of the infected people didn’t show any symptoms while they were under observation. Considering that nearly half of the Diamond Princess COVID-19 patients didn’t show any symptoms and around half of the Iceland’s sample didn’t show any symptoms, we can safely infer that South Koreans weren’t able to identify all of the asymptomatic cases.

Overall, South Korea had a total of 5185 resolved cases (5033 recoveries and 152 deaths). Assuming that 20% of these cases were asymptomatic (as calculated by the South Korean authorities), there were a total of 1037 identified asymptomatic cases, and 4148 symptomatic cases. Since we know that around half of all cases are asymptomatic, we can estimate that South Korea also had 3111 unidentified asymptomatic infections. This brings our total cases count to 8296 infections. Since we had 152 deaths in South Korea, this implies an infection fatality rate of 1.8%. You should keep in mind that if a patient dies in his third week of infection, the case will resolve as a “death” whereas if he is still alive we will have to wait at least a couple of more weeks before it counts as a “recovery”. That’s why we expect South Korea’s infection fatality rate to go down as more South Korean COVID-19 patients recover.

Conclusion

These results are a bit puzzling. Diamond Princess data tell us that COVID-19’s infection fatality rate should be around 0.5% whereas South Korean data tell us it should be around 1.8%. When we have divergent estimates from different sources and we are certain about the data integrity of each source, the best estimate is usually somewhere in between.

That’s what we are going to do in this case and calculate the average of both estimates. This gives us an infection fatality rate of approximately 1.2%. We will be able to calculate a more accurate estimate as more cases resolve over the next couple of weeks and we have access to more data.