The missing Coronavirus cases

One of these things is true, and perhaps both of them are true:

1. The case fatality rate (CFR) for the novel Coronavirus is much greater than the 1% number often cited, and/or
2. We are missing hundreds of thousands of Coronavirus cases in the U.S. due to inadequate testing.

These two options work in opposition to one another. The lower you think the CFR is, the more undetected cases we must have. This is vitally important, because it is the undetected cases that likely contribute most to the continued spread of the virus.

This thesis is pretty easy to demonstrate with the graph below:

The bottom gray line of this graph shows reported deaths as a percentage of reported cases over the last two weeks. This number has been varying between 1.2% and 1.8%. However, we know that there is a lag between when cases are reported and when the reported ill person dies. That average has had several varying estimates published, so the rest of the lines compare the deaths reported on any given day to cases reported one, two, three, and more days prior, in order to get a handle on the effect of that lag.

For instance, the middle brown line compares total deaths on any given day to total reported cases five days earlier. This death rate has ranged from about 4.7% up to 6.8% over the last two weeks and is now around the low end. Because both reported cases and reported deaths have been on steep exponential growth curves, the farther back you go trying to correlate deaths to cases, the higher the death rate appears to be.

The missing cases

We have to at least hope that the true CFR is NOT in the 5% range for this virus. That number is a very scary one. Many reports claim that instead this number is closer to 1% in the long term. However, IF the 1% number is accurate, AND there is just a five-day average lag in reports to the day of death, THEN there must be anywhere from 5 times to 7 times as many cases out there than have been reported. That level of undetected virus infections is perhaps even scarier.

The reality here is still unknown, but you can propose your own reality pretty easily:

1. Pick a line that you think represents the true average lag between reported cases and reported deaths.
2. Select a CFR (death rate) from the graph that you think is realistic.
3. Divide the percentage from #1 by #2. This will be your proposed ball-park ratio for the number of actual cases to reported cases.
4. Subtract out the current reported case numbers. See this link for daily counts.
5. You now have an estimate for how many undetected, yet infected, folks are roaming the streets or, hopefully, self-quarantining.

For example, let’s start with a high 2% CFR (this will give us a low-end conservative case count). The death ratio from the “minus five days” line on the graph is running about 5%. These two assumptions say that there are 2.5 times as many actual cases than are reported cases. As of March 30, about 162,000 cases have been reported, so according to those assumptions, there are about 243,000 current or self-recovered cases out there in America.

If I insist on that often-cited 1% CFR, my multiplier jumps to 5 times, and so my unreported count jumps to almost 650,000 people. That’s a lot, but it is not an unreasonable guess.

This is the kind of uncertainty that gives statisticians fits. People want “accurate” numbers, but I think this is as close as you can get right now. And if we move to a seven-day lag assumption, the estimated multiplier could be as much as 7, which calculates to 970,000 unreported cases.

In order to get this bug under control, testing on a massive scale still needs to be done. Still here in Florida, and many other places such as Montana, according to that state’s governor, it is difficult to even get a test unless you can get a doctor to approve it, and even then you had better be pretty sick.

Entire NBA teams have gotten tested when tests were as scarce as hen’s teeth. Entire communities now need to be tested to get a better handle on the “map” of this virus, and the emerging antibody tests, indicating recovered (and possibly immune) individuals, will be required to get people confident that the economy can begin running again.

2 thoughts on “The missing Coronavirus cases”

1. Jeri Cooper Marshall

I always enjoy reading your blog but I read this one over twice. I guess I can not say I enjoyed it because it was like an eerie prediction of what is to come. Of course his Easter peak date is out of the question, and now I can see a June 1st peak is out of the question also. Just following the numbers. Thank you Rich for your insight.

1. @rklindgren Post author

Jeri, if the current break in the “reported case” growth continues, then we should see much slower growth by the third week in April, although deaths just keep climbing at over 27% per day. Over here in Manatee County (Bradenton), the health department publicized a drive-thru station, but only had 200 tests available, so restricted access and quickly exhausted their supply. Also we are still hearing of 6-day waits for test results, which, at these growth rates, cannot be good. I see Governor DeSantis has finally issued a “stay at home” order for the whole state, which is good.

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