Common Misinterpretations Leading to Inaccurate Coronavirus Mortality Rates

Many smart people are making coronavirus projections and writing convincing social media posts and articles about it. I think it’s great for people to think for themselves, and I want to encourage people to do their own math. However, the key points I see people missing over and over is the difference between confirmed cases versus actual cases, concept of the denominator, and lag time to death.

We all know by now that we are short on testing for the novel coronavirus in the US. Three weeks ago, the CDC finally sent out working test kits, which ran out almost immediately. Two weeks ago, the FDA decided to start approving more labs to do testing. As of last week, we still only had enough lab capacity to test hospitalized cases. If you had significant exposure to a confirmed case but were not sick enough to require oxygen in a hospital bed, most of the time, you were sent home to self-isolate without a test. This week, we have started to test a bit more, some in emergency rooms and some at drive-through sites. In this coming week, we will be able to start testing healthcare workers who need to know to be able to return to work after an exposure. So our testing infrastructure is improving! We are finally testing more, and as a result we’re finding more confirmed cases.

A lot of people are trying to draw epidemiological conclusions from our confirmed cases. In a private Facebook forum for doctors, this Vox chart was being touted as evidence that we were at pace with Italy but now our rate of spread is surpassing Italy.

A New York Times article also uses confirmed cases to say that we are two weeks behind Italy. It incorrectly deduces that the number of cases doubles every 3 days.

Even a well-meaning-chemical-engineer-major entrepreneur who’s good at math is using these confirmed cases to say that the doubling rate is every 3 days and that we are all doomed unless we all stay at home.

We have no idea how many actual cases we have. Cases become confirmed when we test. There are many more actual cases than confirmed cases. As we test more, we will find more. Our confirmed case numbers are more representative of how much we are testing, not how many cases we actually have.

Our major cities may be at pace with Italy, or they may lag or surpass Italy. We don’t really know because our confirmed case numbers reflect testing, not actual cases. We can’t say that we are 14 days behind Italy for when our ICUs will be overwhelmed based on how many cases we are able to test. Our actual case doubling rate is not every 3 days. Our confirmed cases are doubling every 3 days, which again, reflects how our testing capability is increasing. We cannot draw R0, doubling rate, or case count conclusions based on confirmed case numbers.

The next important concept to understand is how the denominator impacts percentages. Here is what I mean.

• 0 deaths / 0 cases = undefined mortality rate
• 1 death / 15 hospitalizations = 6.7% mortality rate if you only test hospitalized cases
• 1 death / 55 people who decide to be tested = 1.8% mortality rate if you test people who go to a drive-thru or other free testing site
• 1 death / 80 people with a fever = 1.3% mortality rate if you test everyone who has a fever. China ended up doing this.
• 1 death / 100 people who caught it, with or without symptoms = 1% mortality rate if you went back months later and tested the blood of everyone (including children) for antibodies.

In late February, doctors at University of California Davis hospital finally convinced the CDC to test a woman with no travel history for the novel coronavirus. At that time, the CDC criteria for testing required travel to a country with known cases of the virus. If you didn’t travel, then you didn’t get tested. In other words, we were not looking at all for community spread COVID-19. If we don’t test for it, we have no cases.

If we test only hospitalized people, we will find a much higher mortality rate than if we tested everyone with symptoms. This is the concept of the denominator. The bigger the denominator, the lower the mortality rate. On March 3, 2020, the CDC reported 2 deaths out of 43 cases, a mortality rate of 4.7%. On March 22, 2020, our mortality rate is 1%. The more cases we find by testing more, the lower the mortality rate.

I mentioned China’s testing method above. To get their outbreak under control, they mobilized, repurposed, and trained many many administrative workers. I own a small business selling headphones for sleeping, and I speak Mandarin. I talk with my factories on a weekly basis. Our friends in Shenzhen joked that they knew their temperature hour to hour because they were being tested when they left their housing complex, at traffic stops, at the entrance of their business park, at the entrance of their factory, between floors of the factory, and during spot-checks. The restrictions have loosened significantly since the initial effort, but you can get a sense of how China screened intensively for fevers. Even now, we have to rely on China’s epidemiological numbers because they are the only country to be finishing their outbreak. Every other country still reports new cases.

When there are new cases, we have to track the case until the final outcome: either death or recovery. This takes time. From the time a person is infected to when they exhibit symptoms is about five to six days. Then they are pretty sick with fever and cough (and a variety of other symptoms) for about a week. From there, they either slowly recover over the next 1–2 weeks or they make a turn for the worse and need to be hospitalized. Some can get by with supplemental oxygen, and some need a machine to breath (a ventilator). The supplemental oxygen group is in for 1–2 weeks, and the ventilated group is generally hospitalized for at least 2 weeks or until death. Final outcomes take 3–6 weeks, sometimes longer.

When a country is at the start of an outbreak, like Germany is currently, the mortality rate will be low because people haven’t died yet. As of March 22, Germany reports 24,806 confirmed cases, 93 deaths (0.4% mortality rate), and 266 recoveries (1%), where 1.4% of cases have reached an outcome of either death or recovery. The Germany situation is more complex because a higher proportion of the sick are younger, so less likely to die, but since only 1.4% of their cases have reached an outcome, their outbreak is just starting. Compare that with China’s 81,054 confirmed cases, 3,261 deaths (4% mortality rate), and 72,440 recoveries (89%), where 93% of cases have reached an outcome.

In the US on March 22, we have 38,167 confirmed cases, 396 deaths (1%), and 178 recoveries (0.4%), where only 1.4% of cases have reached an outcome of either death or recovery. We are just starting out too. We cannot simply divide 396 by 38,167 and say that our mortality rate is 1%. The people who would die in a month haven’t died yet. The lag time to death skews mortality rate down.

25 years ago when I graduated from high school, I wanted to join the CDC as an epidemic intelligence officer. About 15 years ago, after summer stints in six labs, majoring in cellular molecular biology, graduating from medical school, and becoming a board-certified family doctor, I was offered the job. For various reasons, I didn’t join, and it remains the hardest decision I’ve ever made. Now, I’ve become an entrepreneur with a tiny bit of spare time. With every infectious disease outbreak, I wonder how I could contribute. Everyone is impacted by COVID-19, and many of us want to share our thoughts and contribute our talents, particularly with math. I wholly encourage thinking for yourself and crunching numbers. I’m doing the same thing. But since most of us are just armchair epidemiologists, we need to be more careful with how we interpret and extrapolate incomplete data.