Post #925: Has Tennessee turned the corner? The jackknife says yes.

Posted on December 24, 2020

Source:  Analysis of NY Times Github COVID-19 data reported through 12/23/2020.

Today’s question is, what’s likely to happen next, on the graph shown above?  And how on earth could you attempt to quantify that?

Today’s answer is, the odds overwhelmingly suggest that Tennessee has in fact peaked.  And that line will probably continue downward.

Why?  I’d like to go all science-y on you, but the simple fact is, we’ve seen something like this 12 times before.  And every time, it was a true peak in the rate.  So, chances are pretty good that this is number 13.

And I’d say that there’s a single underlying reason for this.  My best guess is that once states hit those high rate of infection, they simply start to run out of un-infected people.  I think that this is how herd immunity is playing out, in the U.S., right now, for the third wave of the pandemic.

To be clear, I’m not advocating herd immunity as a strategy.  Far from it.  I think that’s an appalling inefficient way to deal with a pandemic.  I’m just pointing out that it’s happening, regardless.

All good statistical analysis is easy to understand.

If you’ve been following along, you realize there really is no good theory for predicting what will happen next in the U.S. portion of the COVID-19 pandemic.  Most recently, for example, we were warned of a great post-Thanksgiving surge in cases.  And that simply did not happen.

But that doesn’t stop you from calculating your odds.  Not now, when we have lots of experience behind us, in this third U.S. pandemic wave.  It just means that you have to step away from your theory, and rely on purely data-driven methods.

In statistical analysis, approaches of that nature — “non-parametric methods” – are commonly called jackknife or bootstrap approachesAnd of those, by far the simplest is just to start counting how many times a certain event does or does not happen.  Yes or no, like a coin flip.  And from that simple exercise, you get an estimate of how likely something is to happen in the future.

This assumes that there’s something consistent about your data.  You don’t have to know what, or why.  You just have to observe that there’s some sort of underlying regularity to what’s happening.  The lines below don’t just kind of wander around, like a random walk.  Something seems to be creating the same shape over and over.

Source:  Analysis of NY Times Github COVID-19 data reported through 12/23/2020.

Now, I think I have a pretty good idea of what that “something” is.  It’s herd immunity, or something akin to it.  You can see my various posts on that, particular with regard to North Dakota.  Once you get sufficiently rapid spread, to a sufficiently large portion of the circulating population, I think you just start running out of infectable bodies.  (I note in passing that many of these peaks occurred well before any plausible impact of government policy.  By and large, policy has, if anything, lagged behind the infection rate, rather than led it.)

But calling the peak is not straightforward.  Because, in prospect, you can have something that looks like a peak, but in hindsight, is not.  Like so, for Rhode Island.

Source:  Analysis of NY Times Github COVID-19 data reported through 12/23/2020.

And so, at root, we’re trying to guess what the rules are, that generate these curves.  And then apply those rules to the case of Tennessee.  (In this sense, what we’re doing here is akin to a classic problem in artificial intelligence.  We’re looking at what happened, and trying to guess what the underlying rules are that caused it to happen.)


And so we come to the current case of Tennessee.  Pandemic out of control, hospitals filling up, people dying, nursing homes swept with disease.   Republican governor refusing to issue a mask mandate.

Same old same old, in other words.  That’s not intended to downplay the seriousness of it.  It’s just meant to convey that we’ve seen this before.  A lot of times before.   And so, given that, we can now ask how often has this occurred before, and what happened?

First we have to classify what “this” is.  There’s a danger of “over-fitting” this, but for Tennessee, I’d say it’s:

  1. A possible peak rate of 140 new cases/100,000/day or more,
  2. Followed by decline of 5 days or longer,
  3. Declining 20 cases/100,000/day or more.
  4. And never exceeding that prior peak by more than 10 cases/100,000/day.

How many states fit the first three criteria, and then also meet the 4th?  Here’s my tabulation, based on the graphs I’ve been presenting all along.  The top line is the base case — just as we have observed in Tennessee — and the subsequent lines lower the peak rate that we required to be observed.

The short answer is on the third line, boldfaced.  So far, we’ve seen 12 states exceed a daily new case rate of 100 cases/100,000/day, and have that rate turn downward for at least five days, and eventually fall at least 20 cases/100,000/day.  For all 12 of those, what we observed, at that moment, was, in hindsight, a true peak.

What happened this last week in Tennessee has happened to 12 other states during the U.S. third wave, and every time, that has signaled a true peak.

Only when we look at apparent peaks below 100 cases/100,000/day do we start to find some false peaks.  We had three states show what looked like a peak at the time, but in hindsight was not.  So, below 100 cases/100,000/day, this rule is not quite as reliable.  That’s a “weaker signal”, as it were.  But even then, the odds strongly favor that such an event is a true peak.

Now, I should be saying something like “short-run peak”.  But the pool of people remaining — those who could still get infected — shrinks pretty fast once states hit these high rates.  If the recent CDC estimate of the ratio of total cases to diagnosed cases is even roughly right (eight-to-one!), the majority of people in almost half of US states have already been infected with COVID-19.  (You can read the cartoon version of that analysis on this CDC webpage.)

I should caveat that by saying that the CDC estimate is a national average.  So I need to add the further wording ” … and the state-level ratios are all somewhere near the CDC’s national estimate … “.

In particular, if the CDC is right, (and caveat above), somewhere around two-thirds of Tennessee’s population has already been infected with COVID-19.

To put it crudely, there’s no way that North Dakota is ever again going to achieve 180 new cases/100,000/day.  Not because of anything they are doing, but because there simply aren’t enough un-infected individuals left in North Dakota to be able to achieve that rate of infection.

The broader take-away:  Self-limiting pandemic.

Let me make some final observations.

We’re seeing this basic arch-shaped peak, repeatedly, in this third wave.  To be completely obvious, these curves are the complete opposite of “random walk” curves like stock prices.  Unlike stock prices, the path here seems fairly predictable, once things get really out-of-hand.  Once the rate of new infections gets high enough, the same story seems to play out repeatedly.  Only the name of the state changes. 

All I have done, in the analysis above, is quantify that.  I counted the arches, so to speak.  True arches versus false arches.

This is not a result of uniform changes in state policy.  In many cases, there was no change in state policy.  In other cases, the peak occurred well before the effects of changes in state policy could have affected the numbers.

I think it’s a sign of a self-limiting pandemic.  If the CDC estimate cited above is anywhere near right, then at this point, more-or-less half the states have had the majority of their population infected with COVID-19 already.

This is how herd immunity works.  It’s doesn’t shut off the pandemic in a week.  But as the pool of uninfected persons shrinks, the pandemic ebbs.  The rates of transmission slow purely for lack of infectable people left.

I’ll make the further obvious prediction, that once states have been through ultra-high rates of infection (such as North Dakota), that will never happen in that state again.  It’s not that they wised up.  It’s not the hand of the Almighty granting them relief.  It’s simply due to a lack of fresh bodies.

And my conclusion is that Tennessee just hit that fresh-body limit.  At least, the odds strongly favor that.  And so, like all 12 states before it, who found themselves in that position, the rate of new infections per 100,000 per day will start to decline.

And so, if I’m right, it’s only the states toward the bottom of the list above that are in question.   As the weather turns colder, indoor air gets dryer, can we successfully prevent ourselves from going the way of North Dakota?  Or is North Dakota written in the stars, and that’s going to be our fate, regardless?

My guess — and it’s purely a guess — is that, based on what’s happened so far in New England, states with good COVID-19 hygiene may yet muddle through this.  (The huge exception to that is California, but as I’ve said in earlier posts, I think that’s due to a combination of exceptionally low humidity in Southern California combined with a high fraction of the population Latino.)  Because it’s already cold in New England, I think that’s a bellwether for the South.  Or, at least, I hope it is.