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On August 2, bio-statistician Steven Salzberg argued that We Should Consider Starting Covid-19 Vaccinations Now. But, under immense pushback, including an article by another bio-statistician Natalie Dean writing in the NYTimes, he changed his mind and reversed course. I was frustrated by both sides of the debate since neither “biostatistician” presented any numbers to justify their arguments! So let’s do this better.

Suppose you take a vaccine now as opposed to (optimistically) on Dec. 1, 2020. From May 1 to August 5 we averaged 1001 deaths a day. There are 117 days between now and Dec 1 so at that rate there will be ~117,000 additional deaths by Dec. 1. Let’s call it 100,000. There are 324 million people living in the United States so the probability of dying from COVID in the next 117 days is 1/3240 or .03%.

Now what are the risks of dying from a vaccine? We don’t know these risks but suppose the vaccine is given to 100 million people in the United States then in order for there to be an equal number of deaths the probability of death from the vaccine would have to be 1/1000. That’s unlikely but not impossible!

Furthermore, phase three trials are the acid test for efficacy. Results from many phase II trials look good but we will learn more in a larger, more varied population actually at risk for the disease. We will also will learn which vaccines are better, e.g. Novavax’s protein based vaccine looks much better than others in early trials and that will become clearer with larger trials.

Overall, the numbers here do not make a strong case for vaccinating early. I’ve long argued that the FDA is much too risk averse in approving new drugs but vaccines are meant to be given to large numbers of healthy people which makes risk aversion more reasonable.

Note, however, that these numbers are for a randomly chosen member of the population but the people choosing to vaccinate early will not be randomly chosen. If you are an African-American or Latino, for example, your risks are higher. Your risks are higher still if you are an older, male, African-American or Latino physician, nurse, taxi driver or nursing home resident. In these cases, my judgment is that the benefits swing towards early vaccination. The benefits would be larger still if we assume that a vaccine won’t be available until 2021.

I’ve focused on deaths. Clearly, there are also other health risks but they fall on both sides of the equation.

A mass vaccination campaign in advance of phase three clinical trials would be unwarranted. Vaccinating large numbers of healthy people has real risks. Nevertheless, in my view it would not be unreasonable for someone at high-risk of COVID to choose to be vaccinated before waiting for longer clinical trials and such early vaccination, as Tyler noted, would also provide valuable information for everyone else.

Addendum: The Open Source RADVAC vaccine is one option for those with the requisite medical expertise.

As I said in my post Frequent, Fast, and Cheap is Better than Sensitive we shouldn’t be comparing virus tests head-to-head, as if all tests serve the same purpose. Instead, we should recognize that tests have comparative advantages and a cheap, fast, frequent testing regime can be better in some respects than a slow, infrequent but more sensitive testing regime. Both regimes can be useful when used appropriately and especially when they are used in combination.

Eric Topol has a good graphic.

As Topol also notes:

In order to get this done, we need a reboot at @US_FDA, which currently requires rapid tests to perform like PCR tests. That’s wrong. This is a new diagnostic category for the *infectious* endpoint, requiring new standards and prospective validation.

The FDA has sort-of indicated that they might be open to this.

Much, much too slow, of course. Matching a virus that grows exponentially against a risk-averse, overly-cautious FDA has been a recipe for disaster.

A number of firms have developed cheap, paper-strip tests for coronavirus that report results at-home in about 15 minutes but they have yet to be approved for use by the FDA because the FDA appears to be demanding that all tests reach accuracy levels similar to the PCR test. This is another deadly FDA mistake.

NPR: Highly accurate at-home tests are probably many months away. But Mina argues they could be here sooner if the FDA would not demand that tests for the coronavirus meet really high accuracy standards of 80 percent or better.

A Massachusetts-based startup called E25Bio has developed this sort of rapid test. Founder and Chief Technology Officer Irene Bosch says her firm has field-tested it in hospitals. “What we learned is that the test is able to be very efficient for people who have a lot of virus,” she says.

The PCR tests can discover virus at significantly lower concentration levels than the cheap tests but that extra sensitivity doesn’t matter much in practice. Why not? First, at the lowest levels that the PCR test can detect, the person tested probably isn’t infectious. The cheap test is better at telling whether you are infectious than whether you are infected but the former is what we need to know to open schools and workplaces. Second, the virus grows so quickly that the time period in which the PCR tests outperforms the cheap test is as little as a day or two. Third, the PCR tests are taking days or even a week or more to report which means the results are significantly outdated and less actionable by the time they are reported.

The fundamental issue is this: if a test is cheap and fast we shouldn’t compare it head to head against the PCR test. Instead, we should compare test regimes. A strip test could cost $5 which means you can do one per day for the same price as a PCR test (say $35). Thus, the right comparison is seven cheap tests with one PCR test. So considered a stylized example. If a person gets infected on Sunday and is tested on Sunday then both tests will likely show negative. With the PCR test the infected person then goes to work, infecting other people throughout the week before being the person is tested again next Sunday. With the cheap test the person gets tested again on Monday and again comes up negative and they go to work but probably aren’t infectious. They are then tested again on Tuesday and this time there is enough virus in the person’s system to show positive so on Tuesday the infected person stops going to work and doesn’t infect anyone else. Score one for cheap tests. Now consider what happens if the person gets tested on another day, say Tuesday? In this case, both tests will show positive but the person doesn’t get the results of the PCR test until next Tuesday and so again goes to work and infects other people throughout the week. With the cheap test the infected person learns they are infected and again stops going to work and infecting other people. Score two for cheap tests.

Indeed, when you compare testing regimes it’s hard to come up with a scenario in which infrequent, slow, and expensive but very sensitive is better than frequent, fast, and cheap but less sensitive.

More details in this paper.

1. Ross Douthat on meritocracy (NYT).  And Caleb Watney on American innovation slowing (Atlantic).

2. Superspreading events.  Very good piece.

3. “In 15 years, Guth has helped his 18 breeder members obtain near-monopolies on the world’s rarest parrots.”

4. What about single-strip testing yourself every day?

5. Parrondo’s paradox: how a combination of losing strategies (sometimes) can help you win.  And an application to pandemics.

6. Too few low-wage jobs after Covid?  And rolling 7-day averages for Covid deaths, worth checking that page regularly and don’t forget Sweden.

7. FDA approves pooled testing.

Tyler and I have been pushing pooled testing for months. The primary benefit of pooled testing is obvious. If 1% are infected and we test 100 people individually we need 100 tests. If we split the group into five pools of twenty then if we’re lucky, we only need five tests. Of course, chances are that there will be some positives in at least one group and taking this into account we will require 23.2 tests on average (5 + (1 – (1 – .01)^20)*20*5). Thus, pooled testing reduces the number of needed tests by a factor of 4. Or to put it the other way, under these assumptions, pooled testing increases our effective test capacity by a factor of 4. That’s a big gain and well understood.

An important new paper from Augenblick, Kolstad, Obermeyer and Wang shows that the benefits of pooled testing go well beyond this primary benefit. Pooled testing works best when the prevalence rate is low. If 10% are infected, for example, then it’s quite likely that all five pools will have at least one positive test and thus you will still need nearly 100 tests (92.8 expected). But the reverse is also true. The lower the prevalence rate the fewer tests are needed. But this means that pooled testing is highly complementary to frequent testing. If you test frequently then the prevalence rate must be low because the people who tested negative yesterday are very likely to test negative today. Thus from the logic given above, the expected number of tests falls as you tests more frequently (per test-cohort).

Suppose instead that people are tested ten times as frequently. Testing individually at this frequency requires ten times the number of tests, for 1000 total tests. It is therefore natural think that group testing also requires ten times the number of tests, for more than 200 total tests. However, this estimation ignores the fact that testing ten times as frequently reduces the probability of infection at the point of each test (conditional on not being positive at previous test) from 1% to only around .1%. This drop in prevalence reduces the number of expected tests – given groups of 20 – to 6.9 at each of the ten testing points, such that the total number is only 69. That is, testing people 10 times as frequently only requires slightly more than three times the number of tests. Or, put in a different way, there is a “quantity discount” of around 65% by increasing frequency.

Peter Frazier, Yujia Zhang and Massey Cashore also point out that you could also do an array-protocol in which each person is tested twice but in two different groups–this doubles the number of initial tests but limits the number of false-positives (both tests must be positive) and the number of needed retests. (See figure.).

Moreover, we haven’t yet taken into account the point of testing which is to reduce the prevalence rate. If we test frequently we can reduce the prevalence rate by quickly isolating the infected population and by reducing the prevalence rate we reduce the number of needed tests. Indeed, under some parameters it’s possible to increase the frequency of testing and at the same time reduce the total number of tests!

We can do better yet if we group individuals whose risks are likely to be correlated. Consider an office building with five floors and 100 employees, 20 per floor. If the prevalence rate is 1% and we test people at random then we will need 23.2 tests on average, as before. But suppose that the virus is more likely to transmit to people who work on the same floor and now suppose that we pool each floor. Holding the total prevalence rate constant, we are now likely to have a zero prevalence rate on four floors and a 5% prevalence rate on one floor. We don’t know which floor but it doesn’t matter–the expected number of tests required now falls to 17.8.

The authors suggest using machine learning techniques to uncover correlations which is a good idea but much can be done simply by pooling families, co-workers, and so forth.

The government has failed miserably at controlling the pandemic. Tens of thousands of people have died who would have lived under a more competent government. The FDA only recently said they might allow pooled testing, if people ask nicely. Unbelievably, after telling us we don’t need masks (supposedly a noble lie to help limit shortages), the CDC is still disparaging testing of asymptomatic people (another noble lie?) which is absolutely disastrous. Paul Romer is correct, testing capacity won’t increase until we put soft drink money behind advance market commitments and start using techniques such as pooled testing. Fortunately or sadly, depending on how you look at it, it’s not too late to do better. Some universities are now proposing rapid, frequent testing using pooling. Harvard will test every three days. Cornell will test frequently. Delaware State will test weekly. Lets hope the idea spreads from the ivory tower.

The common element to our twin crises is that many of the government agencies we thought were keeping us safe and secure—the CDC, the FDA, the Police–have either failed or, worse, have been revealed to be active creators of danger and insecurity. Alex Tabarrok.

Derek Thompson writing at The Atlantic uses my quote as a jumping off point for a good piece on the failure of American institutions. He does a good job of covering the failures of the CDC, the FDA and the police but most interestingly asks why the FED has acted very differently.

While too many American police are escalating encounters like it’s 1990, and the FDA is slow-playing regulatory approval as if these are normal times, and the CDC is somehow still using fax machines, the Federal Reserve has junked old shibboleths about inflation and deficit spending and embraced a policy that might have scandalized mainstream economists in the 1990s. Rejecting the status-quo bias that plagues so many institutions, this 106-year-old is still changing with the world.

Why haven’t other American institutions done the same? Perhaps America’s dependency on old leadership makes our institutions exquisitely responsive to the anxieties and illusions of old Americans. Perhaps the nature of large bureaucracies is to become lost in the labyrinth of mission-creeping path dependency. Perhaps years of political polarization and right-wing anti-science, anti-expertise sentiments have wrung all of the fast-twitch smarts out of the government. Or perhaps we should just blame Trump, that sub-institutional creature summoned from the bilious id of an electorate that lost faith in elites when elites lost their grip on reality.

Whatever the true cause for our failure, when I look at the twin catastrophes of this annus horribilis, the plague and the police protests, what strikes me is that America’s safekeeping institutions have forgotten how to properly see the threats of the 21st century and move quickly to respond to them. Those who deny history may be doomed to repeat it. But those who deny the present are just doomed.

I see three reasons why the FED may have been different. First, the FED is one of the most independent agencies which may help to explain its faster and more adaptive behavior ala Garett Jones’s 10% Less Democracy. Second, and relatedly, the FED pulls a lot of leadership and staff from academia. That gives FED staff an affiliation goal and clique outside of politics which creates mental independence as well as political independence. Third, the FED was also tested in the last crisis and experience with crises helps as we have also seen in Asia tested by H1N1, SARS and MERS more than the US was.

I am not sure which, if any, of these explanations is the most important but I do think that we have a lot more to learn from comparative institutional analysis not just within the US but across countries as well.

LATimes: Los Angeles Unified school police officials said Tuesday that the department will relinquish some of the military weaponry it acquired through a federal program that furnishes local law enforcement with surplus equipment. The move comes as education and civil rights groups have called on the U.S. Department of Defense to halt the practice for schools.

The Los Angeles School Police Department, which serves the nation’s second-largest school system, will return three grenade launchers but intends to keep 61 rifles and a Mine Resistant Ambush Protected armored vehicle it received through the program.

A school police department with grenade launchers and a Mine Resistant Ambush Protected armored vehicle! Only in America.

The article is from 2014 but relevant to current discussions of militarized police.

Hat tip: Noah Smith.

1. The Sahara was once the most dangerous place on earth, and why were there so many carnivorous relative to plant-eating dinosaurs and was that a paradox (Correct link here).

2. This guy documents product placement.

3. Good John Cochrane post about university finances and endowments in particular.

4. Words from Holman Jenkins (WSJ): “Please, if you are a jour­nal­ist re­port­ing on these mat­ters and can’t un­der­stand “flat­ten the curve” as a mul­ti­vari­ate propo­si­tion, leave the pro­fession. You are what econ­o­mists call a “neg­a­tive mar­ginal prod­uct” em­ployee. Your non­par­tic­i­pa­tion would add value. Your par­tic­i­pa­tion sub­tracts it.”

5. Large clusters with low R.

6. Netflix will make another season of Borgen.

7. Swedish public opinion.  And Swedes deter park visitors with horse manure.

8. What can we learn from other coronaviruses?

9. Why so many asymptomatic cases in prison?  And more heterogeneities: why are eastern European death rates so low?

10. How they do things in Iceland.

1. MIE: “This Man Owns The World’s Most Advanced Private Air Force After Buying 46 F/A-18 Hornets.”

2. Romer tweet storm states his plan.

3. What did Kerala get right?

4. Is American innovation speeding up? (WSJ)

5. Icelandic volcanoes yikes?

6. Non-exemplary lives (ouch).  And what do the humanities do in a crisis?

7. Instagram strippers (NYT).  And Bret Stephens: our regulatory state is failing us (NYT).

8. “Believe women,” selectively.

9. BloombergQuint on Alex and Shruti.

10. A proposal for releasing British young people (ever listen to early Clash?).

11. Arnold Kling annotates (and likes) my Princeton talk.

12. A Swede explains Sweden to an Israeli: “Some maintain that the Swedish policy can succeed only in Sweden, because of its distinctive characteristics – a country where population density is low, where a high percentage of the citizenry live in one-person households and very few households include people over 70 cohabiting with young people and children. Those are mitigating circumstances which the Swedes hope will work to their advantage.”