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COVID-19: The Dilemma in Pictures
We’d all like this to go away so we can get back to normal life. This is an attempt to show what’s involved graphically. Here’s a chart of what lets the virus expand its human footprint, or causes it to shrink:
The horizontal axis is the famous ‘R’ – the replication number, which is how many other people a COVID-19 victim will infect, on average.
The vertical axis is the percentage of immunity in the population. The line is the critical frontier. Any combinations of R and immunity that plot downright means the virus is winning. To the top left, the famous ‘herd immunity’ has been reached and the virus will lose ground with each generation.
The logic is pretty easy. Take a look at the R = 2 hash line. Follow it up to the critical line and read over to the Immunity level: 50%. If a COVID victim would ordinarily infect two others, but on average one of them is immune, then the virus won’t grow. The actual formula is Critical Immunity = 1 – (1/R)
To start heading back to normal, we need to be in the upper left of the chart. Where are we, actually, and what might it take to get to the promised land? Let’s start with R. Next slide, please…
Here we’re looking at R-sub-t, that is, the probable R at a specific time. I’ve rolled time back to mid-March, and I’m taking estimates from this paper. There are a few dozen countries in their list. I’m using only those that had an infection count of 1000 or more at the time, which are Western democracies. That gives more confidence in the data and some cultural similarity to the US.
It’s quite a range. Spain is on the high end. The virus got into retirement homes there early, and this data was taken the day a lock-down was finally enforced. Italy is on the low end – by the time of this data, parts of northern Italy had been locked down for three weeks, and a national quarantine had been in effect for almost a week. Remember, this is an effective R at the time.
The US estimate is towards the middle. At the time, school closings had begun, but there was no national lock-down effort as yet. It’s probable that the US would have a somewhat lower beginning R anyway since its population density is considerably lower than European countries. So it makes sense that we’d be in about this spot.
How about immunity levels? Now I’ll use more current data. As of this writing, approximately .2% of the US population has been tested positive for COVID-19. Since there has been rationing of tests, we can assume the vast majority of these patients had notable symptoms of their infection.
What about those that didn’t get tested? It’s now well known that many, probably most, who get the virus never display symptoms, or have cases mild enough that they don’t bother to enter the healthcare system. Before going any further, I need to note a major assumption here: That a mild or asymptomatic case of COVID-19 will confer effective immunity once the virus has been cleared from the victim’s system. If that’s false, or only partially true (resistance, not immunity) then the discussion below on the costs of immunity will be worse.
To get from positive tested cases to total infections, we need an estimate of the ratio of unreported (asymptomatic + mild) infections to reported positive cases. What do we know about that? Appallingly little, at this point.
So little that I’m not going to put down a marker for the US, but instead show a range. As the bottom, I’m taking data from the Diamond Princess cruise ship that was struck by the virus. All of the passengers were tested, and of those testing positive for the virus, about half were asymptomatic. I’m taking this as a worst case, as the passengers were generally elderly and more likely to develop symptoms.
At the other end, I’m taking the recently concluded Stanford study by Bendavid and Bhattacharya, of 3300 subjects recruited in Silicon Valley. They reported a range of 50 to 85 times (!) more non-reporting virus carriers than positive tests. As to why I am taking this as the upper limit, I refer you to the able discussion by @mendel starting here.
Wow, a range of 2x to 85x, we’ve got this nailed, right? (More testing, more testing!) Applied to the known positive test rate, it suggests the actual infection level in the US is currently somewhere between .4% and 17%. On the chart, you can see it’s still a long way from beating the virus, even at the high end.
Now I put the two together, so you can see the rather large range of possibilities for our situation. While the range on the Immunity axis seems large, remember that the R-value is an exponent, not a multiplier.
Getting from there to the upper left, beating the virus, is the problem at hand. Here is the dilemma in stark terms:
Since there is no vaccine, we get immunity by having more people infected. Since some fraction of the infected will die, we pay in blood. How much? This is why the ratio just above is so important:
As of right now, we’ve endured 38,244 deaths to get to the current immunity level, whatever it is. If the 2x ratio above is true, and we’ve only achieved .4% immunity, then we’re going to pay about 95,000 deaths for each 1% increase in average immunity. If the 85x is true, then we pay 2250 deaths per 1%. We need to know that number, badly.
Beyond the human cost, there’s a dollar-cost on this axis as well. While some abhor the idea of assigning dollar values to life, we do it all the time. The US government assigns a cost between $7 and 9 million to premature death. I’m going to discount that heavily, since the victims of COVID average older, and because Federal regulators have an incentive to inflate that number to justify their meddling. I’ll use $2m per death. So we have a range of $190 billion on the bad end, to $4.5 billion on the good end, to achieve a one percent increase in immunity, plus the costs of healthcare for the sick and dying.
How about the other axis, R? While the virulence of the coronavirus can’t be changed directly, R can be affected by reducing the number of potential contacts per victim, and the chance of transmission per contact. Hence quarantines, distancing, masking and all the rest. The initial R values above showed that effect, it’s real. But how much does it cost? No one really knows, but there’s a gross figure in the news: About $2 trillion on the Federal tab for the COVID stimulus package, to cover one month of Full Monty lock-down. That probably doesn’t cover it all, but it was undoubtedly stuffed with pork, so call it a wash.
How effective are the individual ‘non-pharmaceutical intervention’ measures at reducing R for the coronavirus? We don’t know. And because of that, we don’t how cost-effective they are. Masking and hand washing are undoubtedly cheaper than shutting down whole industries, but what’s the relative benefit? Putting on all these measures at once may have made sense once, but it’s stopping us doing that evaluation.
If there’s a silver lining in the pictures above, it’s that they are averages for the point of the illustration. The pandemic does not deal in averages. On one hand, you have New York City, which has lost about 1 in 1000 inhabitants to COVID in a month. On the other, you have Adams County here in Idaho, with one case who is resting at home. Applying the same policies to them is ridiculous, but they offer an opportunity to reduce the ignorance of our actual state of affairs. The less impacted areas are a laboratory to test backing off on social control and measuring the effects, New York and others heavily infected are the logical places to nail to down the infection levels and death rates. Let’s be about it.
Published in Healthcare
I wouldn’t put a lot of credence in this study. They didn’t show that their test was specific enough to be making the claims they are making.
Can you expand on that? What do you mean by a lack of specificity?
It’s not certain to be a bell curve at all. There’s no guarantee of that. It could end up being a long fat tail that goes on for months or even a new peak, like they are seeing in Japan, especially if we enter this phase of staged re-opening too soon.
I wonder if opening up right now would change much. The virus is still out there, the count of active cases is still rising, the opportunity to catch the virus is greater than ever if one tries to resume normal activities. I don’t think that people are going to come out just because the government says it’s time.
Can’t like that enough.
The IHME model was being used to estimate things it was never designed for. Every answer to a public policy question has to followed by the question, “Then what?” If you don’t do that at least once, you are setting yourself up for an epic fail. Some other modeling issues are summarized here.
Well, I think it’s eventually going to be a bell curve. But it could take a long time to get there, given that at most a few percent of the population is likely to be infected thus far.
When you say you don’t think the people will come out just because the government says it’s time, I think you may have the motivation backwards: I think the pressure will come from the grass roots at least as fast as it comes from the government.
No trying to be an a****** about it, but what are your qualifications to make a judgement on it? @mendel seems to know his way around virology. And his issues with the statistical treatment seemed valid to me.
Or, a better question: what is your reasoning for making such a statement?
If people were treating IHME as cost/benefit analysis, it certainly was not. There was and is no economics in it at all, other than a poor attempt to be a demand forecast for hospital resources. After northern Italy turned bad, I think the political response was simply to shut things down regardless, and work it out later. Still necessary for NYC and a few other places, but not for most of the country.
Agreed. I think a turning point will be reached the day the onus of proof shifts, so that those who say we should continue to stay home, and not those who say it’s time to get back to work, will be asked to justify their position.
I expect that will occur about April 31, in most places. If not before.
[ Or, if this April happens to have fewer than 31 day, perhaps a little sooner. ]
That’s why I also expect some of the shutdown supporters try to elevate COVID-19 to smallpox/polio status, where if there’s a small bump up in cases due to reopening, that will justify claiming the reopening was a failure and blood is on the politicians’ hands.
I agree with this philosophy and it is why I’ve previously concluded that all the western states not including CO and NM can relax government social distancing orders. On reviewing today’s data, I think it is safe now to include NM and CO as well. There is another rationale I will use based on the topic of this post. A highly contagious virus is like a double edged sword – it carries the seeds of its own destruction. The level of immunity for a given community is like a ratchet, it only can increase. In some communities like Stanford, immunity (or you could say resistance at least) had been spreading in the background with few confirmed cases compared to actual, and over a period presumably prior to implementation of social distancing mandates. Turning the argument on its head, one could argue that rigorous and effective social distancing is also self defeating because it inhibits the background spread of immunity/resistance. I would argue that IHME or others ought to be modeling the spread of immunity using the same tools they are using to predict cases and deaths to evaluate resource capacities. These numbers had to be forecast prior to actuals but constrained somewhat by starting and adjusted empiricals. They should be able to do this now. Stanford is one reference but there are several now, and we are past most peaks now, so we have plenty of empirical data to use for reference. We shouldn’t need to wait for widespread implementation of the antibody test.
I can’t agree with that at our current state of affairs. To the extent that IHME succeeded, it’s because it used previous data that was fairly unambiguous – dead is dead, comorbidity quibbles aside. Right now we don’t have a clear handle on background infections compared to official cases, even as point estimates as opposed to time series. The numbers are all over the place. We’re going to need not only more tests, but some longitudinal data sets before the IHME trick will work — you have to have something to bootstrap from. And we’re going to have to deploy antibody tests to get that data.
(continued from #41)
The task force emphasis of relying on increasing testing has multiple disadvantages. They (Birx said) are looking for a severe drop off in % positive testing. This makes many of the tests wasted. In WA, we have seen multiple days of positive outcome percents in single digits, one day even zero percent. If only 1% tested positive, 99 out of 100 tests were wasted. If on the other hand, the emphasis were placed on determining immunity — and if we could rely on the antibody testing — we could eliminate testing most people for COVID-19 who already are showing presence of antibodies, except to confirm for admission to a hospital for segregation purposes if there were strong symptoms requiring hospitalization.
Increasing testing will at some point be limited by the continued availability of supply. In other news today, China’s new export restrictions are preventing or will delay shipping of respirator masks and 1.4 million test kits, ostensibly to ensure the quality of exported medical products. Not that there hasn’t been some cases of quality problems. But this illustrates an obvious drawback of the strategy of relying on the COVID-19 test itself to diagnose indirectly readiness for resumption of normal activities, and to me seems to be a strategy for prolonging the ill effects of the shutdown. Prolonging the shutdown also indirectly delays the natural development of herd immunity. With individuals and businesses freed to practice safe distancing on our own and make our own choices to practice good personal hygiene and on what risks to avoid in our own cases, and especially now that the resources are available and mobilized, we will get through this sooner if we open now instead of waiting. I don’t want to let the government make its case for showing how dependent we are on their pretended wisdom.
I’ve previously recommended deployment of the antibody testing randomly to determine background immunity, but at that time there were a number of tests being tested to determine which test was most reliable before mass usage. I surmise we have gotten closer, but are not ready to pull the trigger. Soon it is I hope. But the actuals we have to date should be some indication of where background immunity/resistance is being acquired. Modeling employed for immunity could help bridge the gaps in our knowledge.
The studies in Santa Clara County (CA) — which has a certain amount of baked-in self-selection — and Chelsea (MA) — much more of random sample, but occurring in a tremendously more crowded locale and using in absolute numerical terms a smaller sample and local population — both merely provide us with snapshots as to the likely extent of the spread of the Wuhan Virus.
That is all they provide.
I range this against the fact that the WIV/Wuhan Institute of Virology, in tandem with the China CDC Wuhan branch lab, spent the past several years frenetically amassing/cataloging new bat coronavirus strains — chiefly from within caves in the PRC but also from a number of other locations globally. The CDC lab under Tian Jun-Hua, for instance, is estimated to have begun its research initiative with approximately 2,000 coronavirus strains on the books as a baseline — and to date has collected/identified a further 2,000 (in what apparently is record time).
My pet theory is that the cover story for both labs might have been advancing the frontiers of coronavirus research in order to combat successfully any next SARS variant and accompanying pandemic risk — but that the real mandate was selecting the most efficacious and plausibly-deniable tool (because naturally occurring) for deployment in the Uyghur re-education facilities in Xinjiang.
If I’m ballpark correct, that could:
1) explain why the CCP/PLA regime has so far not conducted even a Modified Limited Hangout with regard to the virus’s origins;
2) explain why no vaccines (even for “adjacent” coronavirus strains, potentially serving as some kind of guidance) have been forthcoming from our vaunted PRC “counterparts” in the virology research field — not even plausibly efficacious palliatives (by all means, please correct me if I’m wrong here);
3) underline that the US “in-the-wild” antibody/infection studies only provide us with snapshots of the virus’s spread.
I have no doubt that the release of the virus into Wuhan’s general populace was strictly an accident; I also find it difficult to dispel the very strong likelihood that this virus was conscientiously and meticulously *selected* (notwithstanding the lack of meticulousness in its handling).
So if indeed the virus is not a randomly-occurring assault (even if not originally intended for use against *us*), the risks of misinterpreting the US “in-the-wild” antibody/infection studies really need to be guarded against with vigilance.
There appears to be a very wide range in quality of ‘antibody tests’. (That’s the NYT, so salt to taste.) Quick and dirty finger prick tests won’t get what we need, both due to quality issues and because we need numerical antibody titer levels to correlate with outcomes, to figure what confers immunity or resistance to reinfection. The ELISA platform being used by Stanford among others seems to be sort of a ‘gold standard’, but it’s not a market that I know much about.
For any clinical pathology test like this the false positive rate has to be determined. They said they tested their assay against 30 negative controls. If the results of that were perfect then all they could say is that the false positive rate of that test was less than 18%. So most likely the 1.5% was random variation. In order to make the claim they did they’d have to have a negative control group of about 5000 samples.
The problem with using an antibody test like that is that the false positive rate is usually about 3-5%. If you get a 5% positive rate in the target population what it really means is that asymptomatic cases were not detected. It may be true that they are out there, but the test is not specific enough to detect them. Maybe they will come up with an assay that’s specific enough.
Thank you. I won’t pretend to understand that other than in outline, but I’m wondering why these presumably bright people didn’t take that into account, if what you’re saying is correct. I will be interested to see how the study is received and critiqued.
Point well taken, from the statistical point of view. They will have to run more known negatives to narrow the confidence interval. Hopefully they’ve been saving negative specimens from the RNA tests run at Stanford.
The issue of the false positives is addressed in the paper, and especially the appendix, using something called the “delta method.” I may have been sufficiently competent in these statistics 30 years ago to have evaluated it, but no longer. I think that it is important to understand that this is not something that Bendavid and Bhattacharya just forgot to address. They did address it, though perhaps there is something wrong with their methodology for doing so.
I’m not sure how important antibody titer levels are. By that, I mean exactly what I say — I’m not sure.
As I understand it, antibodies confer protection, but you don’t necessarily need to have a certain level of antibodies in your blood in order to be immune. I’m far from an expert on this. I think that there are things called T-cells, which can be “activated” or “sensitized” to a particular pathogen (a virus, in this case). The T-cells essentially “remember” how to rapidly create the antibody to a particular virus that they have encountered before.
Having a certain level of antibodies in the blood will probably help in the initial stages of a new infection, and perhaps this is where the “titer level” that you reference may be important. But, I think, as long as you have those activated or sensitized T-cells, your body is going to be able to produce the proper antibodies very rapidly.
I get the impression that this is a very complicated issue, and my understanding is quite limited. I’d appreciate any correction, confirmation, or elaboration. Or put another way, Mendel, where art thou?
#52 Jerry Giordano
Just FYI — your mileage may vary.
https://legalinsurrection.com/2020/04/researchers-report-wuhan-coronavirus-could-attack-immune-system-like-hiv-by-targeting-protective-cells/
I was encouraged that Cuomo today was talking about randomized antibody testing of 1000 people to attempt to get a handle on how much immunity in their state. I didn’t think they were thinking like that yet. That’s what I was hoping they do in WA.
I take the point about the samples not being representative, likely leading to an overestimate of the actual infected population. The WSJ article put a resulting range of CFR at .2% to a low of .12%. I think you can arrive at a lower estimate by looking at where the projected deaths per million is highest in the world (not counting San Marino), i.e., the numbers for NY state, and get the lowball figure using assumptions of perfect contagion, ignore over counting and using 19,612,004 for NY population (derived from current 933 deaths per million and deaths of 18,298 on 4/19 for NY), and for projected deaths out to Aug 1 of 21,812, I get .00111 or .11% for min CFR and the projection seems in the ballpark to me. To get the highball figure, I would need to make an assumption on the minimum level of contagion including the whole state. If it were 20%, the upper estimate goes to .55%.
Anyone still following this would probably like this post.
Great article. I particularly liked this Venn diagram from an earlier post on the blog.