Balaji Srinivasan gave what I call a micro critique of the Santa Clara study. I am going to provide a macro critique, and in the process I will articulate the significance of the 3DDRR, the ratio of cumulative deaths in a given day to the cumulative deaths as of three days earlier.
Suppose that we have 10 deaths in a population of 20,000. How deadly is the virus, and how widely has it spread? We face the problem of the Unknown Denominator. If 100 people have had the virus,then the death rate is 10 percent, and it has not spread widely (yet). If 1000 people have it, then the death rate is 1 percent, and it has spread modestly. If 10,000 people have had the virus, then the death rate is 0.1 percent, and it has already spread so far that it will not spread much farther.
The Santa Clara study suggests a high spread rate and a low death rate. The authors report their results as indicating that at least 50 times as many people have had the virus as have been reported positive in tests conducted by County medical officials. This suggests that in calculating the true fatality rate for the virus, we should divide the reported case fatality rate by 50, giving a result of something like 1 in a thousand, or 0.1 percent. With 35,000 deaths in the United States, that would imply that 35 million people have had the virus.
Commenters on this blog have pointed to studies in other countries that seem to give similar results. But there are other studies in various parts of the United States and in other countries that suggest that far less than 10 percent of the population has had the virus.
Srinivasan argues that the Santa Clara results are likely distorted by a test that can produce a high number of false positive results when applied to a population that is mostly negative for the virus, that the study sample probably includes a high proportion of positive individuals relative to the population, and that the implied high spread rate exceeds that of similar past epidemics.
My own skepticism comes from the dynamic of the disease as we have observed so far. My intuition comes from my family’s annual vacations on the Delaware seashore.
I am one of those people who is mesmerized by ocean waves coming ashore. I can stand for long periods at a spot where some of the waves wash over my feet and others stop just short of reaching me. I like to guess which waves will get to me, and which waves won’t.
One phenomenon I noticed I call heavy in, heavy out. When a heavy wave comes in over my ankles, the next wave gets diminished. This is because the heavy wave recedes quickly, and in the process it pushes back against the subsequent wave.
My intuition is that the spread of the virus would operate the same way. If it spreads really rapidly, it will also recede rapidly. Because the virus will have a hard time finding new targets, we will see heavy in, heavy out.
It was to spot a heavy in, heavy out pattern that I chose to track the 3DDRR. I decided that reported cases were too much affected by ever-changing testing criteria to be useful in identifying trends in the wave. Although deaths are a lagging indicator, I decided that they would work better for providing a more reliable picture of how quickly the wave was receding.
So far, the wave is receding slowly. Because it is receding slowly, I infer that we are not experiencing heavy in, heavy out. Therefore, I doubt that the virus has a miniscule death rate and a spectacularly high spread rate.
Of course, my thinking could be wrong. As more studies come in, if they are consistent with the Santa Clara study, my estimates of the death rate and the spread rate will move in the direction of the Santa Clara study. But from the macro perspective of the 3DDRR, I am skeptical.
I’d like to pause and think about the idea of heavy. Some of my thinking was formed while we were still in the ‘contact trace and quarantine’ phase; at that time, the issue was ‘exposure’ and the hope was it could be kept out of the country, vanquished overseas, more or less, like SARS1 or MERS. My argument at the time was that on the course we were following, 100% of the world would be exposed. Not necessarily progress to infected, or to being a spreader, or symptomatic, or in the hospital, or in the ICU… but exposed. If that was the case, then preventing exposure wasn’t going to be a sound strategy; we would need things to protect from infection or remedy the consequences.
But this brings to mind an interesting rhetorical twist with the ‘Sensitive-Infected-Recovered’ model. In the most primitive conception of disease, the bad people are the sick people and the good people are healthy. Bad people pose a hazard to good people of contamination. In a SIR model, the sensitive people are no longer virtuous, they are a liability, because Infected is on the path to Recovery, which is the real happy place. Herd immunity is the ultimate cult of Recovery, the product of a virtuous population.
Returning to the question of exposure – while we are trying to prevent exposure, contamination, the leaven in the dough – the exposed people are the unseen hazard, contamination, contagion. Later, it’s the sensitive people who are at risk of exposure. As our terminology changes, so do perceptions.
Just something to consider.
No links on test issues, yet, but wife & ministry of health discuss tests:
It seems that there is one gene (“E”), which tests positive for this Wuhan virus — but also many other coronaviruses, having that same gene.
So many “positives” are false positives for this Wuhan virus.
This could be the case in the homeless shelter in Boston – such info is not yet usually reported. Perhaps this is the Santa Clara case, as well.
The better tests use 2 genes. But the second gene is so long that some primers can’t use it. So some private labs (in Slovakia) are only using the E gene test, finding “positive”, sending the patient to the hospital, where it is found they are not Wuhan virus positive.
There are other tests that use other genes.
Because the tests are not fully compatible, the numbers of false positives and false negatives can and will be quite different.
Good testing is expensive, and lots of already done testing is so inconsistent that using the test data introduces test errors as yet another “known unknown” into the long list of unknowns we have. Plus it casts doubt on whether any of our “known knowns” are actually accurate.
Usually when one of our “known knowns” is actually wrong is when we make the worst policy. (Like “knowing” Hillary will win?)
Even “deaths” are not great data, since so many occur with multiple co-morbidities. Not great, but we have nothing better.
There is far too little standardization in tests so as to allow more “test calibration”.
One thing I’ve been seeing around a bit lately is the hypothesis that the deaths are undercounted because we’re not able to test them all (think of NY adding 3,000 deaths recently). Graphically, imagine a bell shaped curve of true deaths but we’re sort of clipping that bell and so it looks like deaths are flattening for a longer period.
This might mean that both views are somewhat correct – we are experiencing heavy in/heavy out and a larger percentage of the population has been infected. But also the death rate is quite high (or at least not 0.1%). Eg if there really are say 10m infected (15x not 50x) and the death rate is 0.5%, then it means we missed 1/3 of the deaths. So our death numbers peaked much higher than we thought but also might be falling much faster.
I’m not sure it’s a valid theory but the NY revisions should at least make us question whether the death numbers are as accurate as we’d been assuming.
We also have an unknown numerator, as we don’t know how many of those who test positive will ultimately die of the virus (it can take three weeks or more for a fatal case to resolve).
And as xkcd reminds us, doing math with unreliable numbers is generally pointless.
https://fox4kc.com/tracking-coronavirus/johnson-county-reveals-3-8-test-positive-in-random-coronavirus-testing/
Here’s a random COVID-19 virus test (not antibody test) in the Kansas City area (Johnson County, Kansas) that had a 3.8% positive rate. So this could be a indication of the current incidence of the infection in the population, not the total % that has had it and recovered.
I heard they selected participant to represent population, but we all know how that goes. I know people who tried to get in and that’s what they told them. They are inviting people for a rep sample.
Also, almost all who tested positive had symptoms, as well. So, they were not asymptomatic at the time of the test. But, it’s unclear of the severity of their symptoms.
Rough math: If that is representative of the KC metro population, that would mean about ~80,000 current infections vs. the 1,000 confirmed cases we have in surrounding Mo and Ks counties. KC metro has 2.1 million population with most of that in 3 Mo counties: Jackson, Clay and Platte and 2 Ks counties: Johnson and Wyandotte.
Poke holes.
I don’t see why the “heavy-in heavy-out” model would generalize to this instance. Heavy-in heavy-out is about waves on the shore, not new infectious pathogens in pristine populations.
My crude notion of the Black Death is that it kept coming back. It didn’t kill up to 1 in 3 Europeans ca. 1347 and then go away–it kept coming back for generations.
Maybe I’m not understanding your perspective.
= – = – = – =
I’m not certain we fully understand why the Black Death went away again.
1. Different rat populations (Norway vs. Black Rat)
2. Different building materials (less thatch)
3. Better hygiene and nutrition
4. ????
= – = – = – =
DISCLAIMER
I used to read on this topic decades ago. I don’t know the current literature and I only know it from casual interest.
Wikipedia makes it look like the Bubonic Plague mostly vanished from Western Europe after 1738.
Perhaps you could give an end-date of 1666 for the Great Plague of London. or after Marseilles 1720.
The 3DDRR for Colorado is now at 1.1884 and has been trending down from April 1 when it was at 1.9020. The 5day moving avg of daily deaths has been trending down since April 10. The peak of actual cases was probably sometime in mid to late March.
I think you are falling into a fallacy here, Arnold, in that you think you know what is heavy/fast in this case. You don’t know, and neither do I.
+1.
What is this is merely a “dress rehearsal?”
Let me try that again.
What if this is merely a “dress rehearsal?”
Belgium is not far from a fatality rate of one in a thousand of its entire adult population. I find it pretty implausible that most adult Belgians were already infected a few weeks ago. San Marino already has a fatality rate more than in in a thousand of its entire population. I think there is plenty of evidence that the fatality rate is quite high.
Due to the various issues of defining/recording deaths from COVID, I think it is much better to use excess deaths. Use TOTAL deaths last three days minus TOTAL deaths same dates a year ago multiplied by change in population. It sounds noisy but in countries with a lot of COVID deaths unfortunately these deaths are such a large fraction of total deaths that I personally think it is less noisy than reported COVID deaths.
Good points, for sure. Of course, all of this just returns us to the uncertainly we face — all the more reason we need an antibody test so that we can better approximate the true number of cases. Now, deaths is about the only reliable data we have. Yet even here, as your daily reports remind us, reporting may be belated or otherwise skewed and deaths also appear only after a natural delay.
In the meantime, what policy differences do you see implied according to whether the Santa Clara study is correct or incorrect?
If you build a sensor sensitive enough, everybody has the virus. If you have a sensitivity dial on your test, you essentially choose the percentage of infected in a population. It’s not useless information because it is a warning.
If the percentage infected is a property of a population that you can just choose, may be we should consider that the ability of the mucous membrane to protect people might be a variable that we can choose. Avoid feeling physically taxed. Avoid being in the cold or heat. Eat to promote the health of the mucous membrane.
It’s interesting to think of this in light of the new autopsy results.
https://www.sccgov.org/sites/covid19/Pages/press-release-04-21-20-early.aspx
It may have been circulating there well before what we knew.
Wow. First one died 10 weeks ago, probably contagious as far back as late January. Didn’t have whatever travel history and symptoms necessary to qualify for testing either, so it’s plausible he or she picked it up domestically. That nudges me slightly in the direction of “more people infected than usually estimated”.