Friday, January 1, 2021

Nothing matters but reproduction rate R

The new strain and the need for speed by Alex Tabarrok on Marginal Revolution makes an excellent point. The new strain is more transmissible. That means the reproduction rate R is higher. For given behavior, the exponential growth is faster. If or where R was a bit below one and the virus contracting, now the virus is spreading exponentially again. 

 "a more transmissible variant is in some ways much more dangerous than a more severe variant. That’s because higher transmissibility subjects us to a more contagious virus spreading with exponential growth, whereas the risk from increased severity would have increased in a linear manner, affecting only those infected."

The recurring failure of our government response to this pandemic has been to get behind exponential growth. Here we go again. Wasted months when the vaccines were known to be safe. Wasted weeks to have thanksgiving dinner rather than  approve vaccine. Snafu after snafu in vaccine distribution. And CDC rationing that is designed to just about nothing to stop the spread. 

When I suggested free market vaccine allocation on top of government distribution, critics lambasted me. Only the government can artfully offset externalities and information problems, they say. Implicitly every single dose must be requisitioned to the government's majestic planning effort, not one may be sold letting willingness to pay guide the usefulness of the vaccine. Not even a hospital emergency room treating covid patients may spring money and butt the line.  

There is one big externality: infectious diseases are, well, infectious.  If you want to stop a pandemic that is growing exponentially there is one rule. Give it fast to the people most likely to get it and to spread it to others. Over and over Nothing Matters but the Reproduction rate.

This has been about the last criterion on the CDC's allocation scheme. First it goes to protect old folks in nursing homes. The UK gave its first dose to a 91 year old. Germany to a 101 year old. That's nice. Then to old people in general, even though most non-nursing home old people are retired and doing fine staying home. 

Well, it appears kind-hearted to protect those who are most likely to die if they get it. It is a purely private benefit, so one might ask why they aren't asked to pay anything for it. So it's really an income transfer to old people in the form of a vaccine. 

Then as widely reported, "equity" has become their mantra, explicitly racial but also geographical. 

OK, I like old people and social justice too. But if that same vaccine were given to a front line health care worker, or to a young partier who just can't seem to help themselves from giving it to 25 other people, including 3 grandparents, we solve the disease, we address the externality, and we protect old people, much more effectively.

This is a hard choice, but it is one that competent public health (and military) bureaucracies are supposed to know how to handle. It's a classic trolley problem with one person on the left and thousands on the right. Do you first give a vaccine to old people who are likely to die if they get it, freeing them to go out a bit and freeing nursing homes from having to implement stringent protection requirements? But in doing so you let the disease run rampant and the economy tank for another six months. Or do you give it in a way that stops the pandemic, to people who individually won't die but will thereby not spread the disease? The overall death rate is lower in the latter case, but only in secondary infections, which you, the CDC cannot claim to have saved. 

Public health knows how to do this. Or used to know how to do this. When eradicating smallpox, and when an outbreak was noticed, they ring-fenced the outbreak and vaccinated in order to contain the spread of the disease. They did not give it randomly to the whole population in a country, taking six moths to a year to get everyone, protecting people by age and demographic class, and meanwhile letting the disease spread exponentially. 

When combating exponential growth and heterogeneous spreaders, targeting matters and speed matters even more. Alex

"the FDA should have approved the Pfizer vaccine, on a revocable basis, as soon as the data on the safety and efficacy of its vaccine were made available around Nov. 20. But the FDA scheduled it’s meeting of experts for weeks later and didn’t approve until Dec. 11, even as thousands of people were dying daily. We could have been weeks ahead of where we are today. Now the epidemiologists are telling us that weeks are critical.

It's not really that "thousands were dying daily." It's that the disease was growing exponentially in this crucial 20 days, and thousands upon thousands will die in a few months as a result of delay. A lesson which should have been painfully obvious from the January-March delays in addressing travel, not allowing tests to be used, not ramping up tracing while it could do any good, and so on. 

In a year, our bureaucracies just have not wrapped their heads around a simple fact. The point is to stop the exponential spread of a disease, not (just) to protect individuals. Tests should be evaluated by their usefulness in stopping spread -- and there imperfect is far better than nothing -- not only by their usefulness in diagnosing a given patient for treatment. Vaccines, used right, can stop exponential spread of a disease, not just protect individuals -- or, more accurately, enable them greater social interactions. 

So what good has been achieved by banning a private market on top of government allocation? The government is basically not even thinking about the prime market failure -- the externality that if I get it I might give it to you.  In doing that it is mostly just achieving an income transfer to favored groups. 

Suppose there were a free market in vaccines. The only difference is, the government would have to buy at market prices. How would this look different? First, I think we would see much quicker allocation to health workers. Even if the government were not willing to buy and give it to them, hospitals would figure out they need to give it to their covid staffs immediately, and pay whatever it takes. They are forbidden from doing that now. Second, people and businesses that know they are host to spreading events could buy the vaccine. There is a lot of private incentive to combat an externality! Third,  the government could do exactly what it is doing now. It just might have to pay a bit more. If you are a huge fan of the CDCs allocation scheme, and its brilliant targeting of externalities, public goods, information problems and every other fable from econ 101, good for you. It can keep doing that. The treasury just might have to pay a bit more. 

So the ban on private sales comes down to one thing only. Money. The government is keeping down the price it has to pay by forbidding you and me and businesses that could hire back lots of employees from bidding for the vaccine. 

This is the same government that has borrowed $5 trillion dollars already, and is currently discussing $2,000 checks, far more than the free-market cost of a vaccine. Penny wise and pound foolish.  

I think we can summarize epidemiology by the one maxim: nothing matters but the reproduction rate. R<1 and it goes away. R>1 and it explodes. And given a reproduction rate, nothing matters but how quickly you get on top of exponential growth. Time is exponentially valuable. 




 



48 comments:

  1. "OK, I like old people and social justice too."

    Your entire post demonstrates how the ideology of the social justice left is a leading cause in a grave misallocation of vaccines which will result in thousands of unnecessary deaths, as well as massive waste in production capacity...

    Just tell it like it is, professor: they're killing people because they are focused on maintaining the APPEARANCE of compassion.

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  2. It all makes sense, provided people vaccinated won't spread the disease to susceptibles. Afaik this hasn't been demonstrated yet, but more data should come as vaccines are being administered.

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  3. John’s right. The case against allowing markets to direct the allocation of the vaccine comes down to a claim that vaccinations benefit others besides the vaccinated. That’s obviously true but it completely ignores the lesson Coase taught 60 years ago: these so-called externalities are really a consequence of incomplete markets. If you want to internalize these external costs, you need to encourage markets, not choke them off.

    This is not some abstract libertarian daydream. Ask yourself who would buy vaccines if they could. Frontline health care facilities and nursing homes? Of course. The cost of vaccinating their staff and patients is trivial compared with the costs of becoming a super spreader. What about those meat packing plants we’ve heard so much about? Certainly. Shutting down because of a labor shortage is many times more expensive than the cost of few hundred vaccinations. Schools? Absolutely. Any parent who’s struggled with homeschooling would gladly chip in a few bucks to pay for the teacher’s shots.

    Externalities are the last refuge of the scoundrel!

    (Oh, and if you care about inequality and are worried that creating a market for vaccines will price disadvantaged people out of the market, don’t. There are simple ways to subsidize people who don’t have the cash to buy a shot.)

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    1. More to the point even when an externality is clear and simple, our government has shown itself completely incompetent to address it. Plus, over and over -- the issue is not against government allocation. The issue is the government ban on private allocation!

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    2. And yet, they've had years to prepare for a pandemic, and still they keep shooting themselves in the foot like Barney Fife trying to pull his gun out of the holster. It's a wonder that any government learns. Just like World War II, after the war broke out, guess what? We were woefully unprepared for it. And just like that, we were woefully unprepared for this as well. Cause no one learns a damn thing from history, and yet, they keep repeating the same damn mistakes. And not learn from a single one. However, I will say this: with war, if one reads the intelligence correctly, we'll be prepared; but with disease, one never knows when it'll happen, or where it'll come from. Hopefully this time around lessons will be learned. We can only hope. That is if we elected the right people!

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    3. Not ANY government, this particular government has proven incapable of distributing vaccines at the required pace. Self-fulfilling truth: decrying the inefficiency of governments and simultaneously appointing incapable administrators and 'experts' (= lobbyists) will make it so. Abolishing the White House task force on pandemics was such a brilliant step. Externalities: the government being so incapable. The FDA approval process was started as soon as the test data needed to judge the efficacy were available (required part of the application). Why the delay to examine the data of the 3 stages of the test? So the public trusts the process of verification and actually accepts vaccination as comparatively safe, and hence reduce R due to high willingness to get vaccinated. The super spreaders in old-age homes are the staff taking care of old people (who go home to their families and are often poorly paid), and thus you need to vaccinate them and their customers (old people) to reduce R. -- The CDC seems to have reducing R very much in focus, and not all the factors line up with 'willingness", or may I say "ability" to pay. Minorities (African Americans, Latin American descent) have higher incidences, because in many cases are living in tighter spaces and are working in essential jobs with lots of interaction: higher vaccination of population with higher incidence AND interaction reduces R. Public health is about externalities, hence the term public (epidemiology is an essential part of that). I am not denying efficiency problems within the government, but externalities and public goods are a particularly bad example to invoke the free market. Does anybody recall the air and water pollution of the 70s? Coase's side-payments to restore efficiency as you may recall require perfect enforcement of contracts - by itself a public good. Private militia or the Mafia to enforce fulfillment of bribery contracts?

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    4. John, I'm not sure that this is only or even mainly government incompetence and not self- interested political behavior in response to myopic voters. That's my own twist to your very interesting pos. I elaborated here.

      https://econominecraft.blogspot.com/2021/01/is-government-intervention-appropriate.html?spref=fb&fbclid=IwAR2V7ARQRkpG00TMjNyeb45EqadT1GdJAbh5tSjqRvvUIVQwieN7LGCYvNQ&m=1

      I hope you won't mind the extensive quoting.

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    5. agreed. Makes one think, "If this was Obama all over again, would he even fair better?"

      Answer: No.

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    6. > these so-called externalities are really a consequence of incomplete markets. If you want to internalize these external costs, you need to encourage markets, not choke them off.

      Are you denying externalities in principle? Brian Simpson, in _Markets Dont Fail_, says externalities is an invalid concept,a contradictory package-deal of property rights and arbitrarily selected effects that dont violate rights. And a rationalization of altruist sacrifice. Every action in society has many direct effects and a virtual infinity of indirect effects. Only those which violate property rights are of political interest. The alternative is complete stagnation as everbody sues everybody for negatives and govt forces everybody to pay for positives. Externalities is a rationalization for powerlust. You are benefiting from my knowledge without paying! You will hear from the govt. And I am suffering from your vagueness. You will hear from my attorney!

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  4. Do these vaccines prevent transmission? The efficacy results I know are only for symptoms, which moots your main point if it's the whole story.

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    1. These are really a sort of neo or pseudo vaccine. And you are right that his premise is undermined by the fact that they are carefully avoiding the claim that these mRNA vaccines will reduce spread or even infection. They are functionally a treatment.

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  5. > to a young partier who just can't seem to help themselves from giving it to 25 other people, including 3 grandparents, we solve the disease

    Note that this is likely but we don't know this-- most vaccines interrupt transmission, but many are much more effective at suppressing severe illness than preventing transmission. There's a real risk that targeting crucial transmission links will not be as effective in reducing mortality as giving it to the most likely to have severe illness.

    > Even if the government were not willing to buy and give it to them, hospitals would figure out they need to give it to their covid staffs immediately, and pay whatever it takes.

    Where I am, the hospitals seem to be being allocated and shipped vaccine but unable to administer it quickly to their staff and affiliated practitioners.

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    1. Hospitals are govt-controlled. They were refused permission to increase preperation for pandemics because of alleged sufficient capacity.

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    2. > government incompetence and not self- interested political behavior

      Plato's philosopher-king is alive and well (as a mystical ideal, not as an abstraction from concretes). Totalitarianism will solve the "problem" of alleged self-interest. See the Declaration Of Independence and the US Constitution for an alternative, profoundly realistic politics.

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  6. This comment has been removed by the author.

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  7. that must be why I liked Limitless, a film that works in the other direction. Oh, and I just watched TeneT

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  8. John,

    I left this comment at marginal revolution, but I thought you might be interested as well.

    "That’s because higher transmissibility subjects us to a more contagious virus spreading with exponential growth, whereas the risk from increased severity would have increased in a linear manner, affecting only those infected."

    Both propositions in this quote, upon which Alex's argument is based, aren't true.

    Transmissibility is not just a property of the virus; it's also a function of the precautions people take as well as government mandates to wear masks, social distance, etc. As we've seen since March, the transmissibility of the virus, captured by Rt, is endogenous and time-varying. As cases and deaths rise, Rt falls, choking off the exponential growth of the pandemic. As cases and deaths fall, Rt then goes back up as people and governments relax, sparking a new boom and bust cycle. Thus, the pandemic doesn't really grow exponentially but rather in cycles. If the coronavirus suddenly became more transmissible (as some evidence now suggests), it's not clear at all that the growth rate of the virus will change, since people and governments will change their behavior to accommodate the new circumstances.

    It's also not true that the risk, i.e. the infection fatality rate (IFR), would necessarily be cut linearly by a vaccination policy. The current policy of vaccinating the elderly will cut the IFR non-linearly, since the IFR grows very rapidly with age. For example, taking the IFR estimates by age from "Age-specific mortality and immunity patterns of SARS-CoV-2," (Nature Nov 2) and adjusting them for the 2010 age-specific demographics in the US, the overall IFR turns out to be 0.37%. However, if we vaccinated everyone over 65 with a 95% efficacy, which is 13% of the population, then the overall IFR would decline to 0.11%.

    Thus, if the characteristics of the growth of the pandemic don't change very much, given endogenous behavioral changes, and the IFR declines non-linearly if we vaccinate everyone over 65 first, it seems to me that the the policy of vaccinating the elderly first and then working down the age spectrum makes the most sense, assuming that our goal is to minimize the number of deaths. Where the vaccine is going is more important than speed.

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    1. Second sentence, "for given behavior." I'm an early and vocal proponent of the fact that the reproduction rate depends on behavior as much as if not more than biology. See "a behavioral SIR model" from last spring. Yes, vaccinating the elderly is great for reducing the IFR ratio. But if you want to reduce fatalities, it's just as effective to reduce I, infections! If we work on vaccines, behavior, and testing testing testing to reduce R, then we avoid exponential growth in I, and you get far fewer fatalities F.

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    2. Pierangelo and Michael Hopper get it.

      "Or do you give it in a way that stops the pandemic, to people who individually won't die but will thereby not spread the disease?"

      No evidence thus far that this is true, but hard science has never been the forte of this blog. If only life followed math, but as any engineer can tell you, reality never follows the mathematical models.

      A private market for vaccines? Sure, let the former university professors with fat pensions and ongoing large consulting fees outbid the ICU nurses, the medical staff, receptionists, custodial workers and everyone else on the health care front line while they work from home doing Zoom meetings. The protection of supermarket checkout workers outweighs the protection of armchair quarterbacks.

      We need doctors and nurses more than economist with blogs right now. The tangible benefits of economic theory and policy since the inception of this pseudoscience wouldn't fill a single vial of polio vaccine.

      The hospitals are overloaded not just because of the volume of patients but because the staff are out sick with covid.

      I've been exposed to 4 people who were covid positive (3 patients and one colleague). The day I was exposed none of them had fever other symptoms, yet within 24 hrs they all notified me that they were sick and tested positive. Heaven only knows how many times I've been exposed to infectious people. I can't socially distance while doing a physical exam. I can't sit in my house and write op-ed pieces for the WSJ. I'm risking my life every week and you want this vaccine to go to the highest bidder? My only response would be filled with four letter words.

      I have strong libertarian and free market beliefs, but I have yet to see any single philosophy that can answer all questions. Yes there have been glitches but free market principles totally fail in this situation. You can nitpick at the government's response but as you seem to be unaware they have broken a lot of rules to fast track these vaccines. Vaccine testing and development usually takes years and you're fussing about a month or two.

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    3. “Our society must make it right and possible for old people not to fear the young or be deserted by them, for the test of a civilization is the way that it cares for its helpless members.” -- Pearl Buck

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    4. That's exactly the point. From what we know so far, vaccines prevent the disease, not necessarily the infection.

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    5. Greg Hopper is exactly right. The nonlinear dependence of IFR on age is absolutely critical. In fact, this dependence is exponential. That is why targeting transmission in the young is a mistake. You will just end up killing people unnecessarily. There are several epidemiology papers on this and ALL show that targeting age is the right approach. This is especially true when vaccine supply is limited.

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  9. My sense is that lowering the transmission rate is a strategy rather than a goal. I’ve heard a number of goals expressed, such as ‘minimize lives lost to COVID,’ ‘minimize person-years lost to COVID,’ ‘minimize GDP lost to COVID,’ ‘minimize employment lost to COVID,’ and ‘minimize above-capacity demand for ICU beds.’ Each goal would require a somewhat different vaccination strategy. If the democratic process results in a national goal such as ‘minimize lives lost to COVID,’ what role is to be played by ‘the market?’

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    1. The most reliably democratic of processes is daily market behavior by individuals. Any national goals should be seen with suspicion.

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  10. Hi John,

    To give a bit more detail about why I favour age-based government distribution.

    In the UK, 80% of covid deaths are people 65+, and a large proportion (can't find exact stat) are 80+.

    There are 11m people 65+, and 3m over 80.

    Therefore, the policy that minimises excess deaths is one where we vaccinate health workers and the oldest first.

    We might be weeks away from vaccinating most 80+, and a few months away from vaccinating most 65+.

    The age skew is much steeper than qualys lost, so 80 year olds are losing more qualys to Covid than the young because so few young people are dying.

    I'm really frustrated this isn't moving faster, and think we should put moral pressure on vaccinators to work around the clock and ignore or solve bureaucratic hurdles.

    I also don't endorse what seems to be happening in America, with a complicated mix of age and profession for vaccine allocation.

    I don't see how vaccinating the young and middle aged, using market based system, will reduce the number of deaths.

    Maybe you can create a model, or fill in some of the gaps in your argument. How much faster does the vaccine have to be allocated, and how much higher does the R have to be for the vaccine buyers, before deaths are lower than for an age targeted rollout.

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  11. What is the evidence that this new strain is actually more transmissible? Considering the misinformation about the virus, testing, and mitigation techniques that has been spread over the past 10 months (by both media and government officials), why should I believe this latest claim about a new mutant strain?

    In how many people is the virus's genetic makeup even tested? Are such tests more reliable than PCR tests? I don't know the answers to these two questions (and others that arise with this new claim), but my initial response is a large dose of skepticism.

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  12. I feel like a lot of epi-types are biased towards the “planning” model instead of the “market” model here since it’s unlikely the vaccine is sterilizing, so the argument is we need to get it to the most vulnerable - like the very elderly - to reduce disease since it’s not solving the externality problem of transmission much. I think this reasoning is somewhat correct but also is too confident. I agree these vaccines are probably not sterilizing - the very poor CD8+ response coupled with detectable RNA on challenge in rhesus already strongly suggest this (and performance may be worse in humans). We won’t know for sure until (if?) anti-NP data is published on trial participants but they aren’t likely sterilizing. But I feel like this ignores the data that while it did replicate fine in rhesus monkeys on challenge, clearance was much faster suggesting a substantially shorter period of infectivity. I guess my point is the mantra of we're going to save more lives by restricting to the very elderly first actually doesn't seem as sound when you look at the entirety of the data and work off some logical reasoning rather than forcing every fraught decision to be RCTed before doing anything.

    I’m unconvinced the planning is even targeting the correct group of elderly anyway on a purely moral calculus ignoring any economic benefits. Median life expectancy of nursing homes/long-term care homes is less than a year, some as low as 5 months. It seems cruel but it honestly seems more cruel to kill a 75 year old not in a facility who has another 10 years in him or her with much higher quality of life.

    I guess my point is even if you ran the "planning" model most efficiently I'm not sure it's even rationally designed compared to a market alternative that's just highest bidder.

    In case anybody reading this cares - we actually might not be that far from a sterilizing candidate. You likely need IgA - mucosal antibodies - to get sterilizing immunity for an upper respiratory tract infection and these are hard to induce intramuscularly, instead a nasal candidate is probably the best route and there is a promising one in trials.

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  13. FWIW I think using the price system to distribute vaccines to higher valued users is a good idea, but I also think even the current system (aside from the delays involved in governments managing distribution) isn't terrible.

    Somewhat ironically, this is because I believe that the costs of government restrictions (large at the margin given their inability to adjust) far exceed their benefits (small at the margin given significant spread even under harsh restrictions). So whatever plan gets restrictions lifted the fastest seems just fine. By vaccinating the small portion of the population likely to die from COVID first, you bring down the deaths statistic and make it politically feasible/imperative to end significantly scale back such restrictions sooner rather than later.

    As you suggest, you might do this by getting the vaccine to superspreaders, but I'm not sure even now (and even taking advantage of local knowledge opened up by market pricing) we would know how to do that. I have greater confidence in prioritizing vaccines for those at risk of death.

    As I allude to above, the bigger issue with the current distribution system is it seems to be doing a subpar job of actually getting vaccinations does. The current poor results suggest we should abandon the current priority system (at least in part) if it got more vaccinations done sooner.

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  14. There seems to be some confusion about the three vaccine candidates given emergency authorization so far. The Pfizer-BioNTech vaccine prevents COVID-19 in those inoculated with the vaccine. The Moderna vaccine also prevents COVID-19 in those inoculated with that vaccine. But, apparently, neither of these two vaccines acts to prevent the onward transmission of the novel coronavirus SARS-CoV-19 by those who are vaccinated with either one of those two vaccines who become infected with the novel coronavirus. In other words, the vaccinated patients can be carriers of the virus but not become sick from the virus. As carriers they can transmit it onward to other susceptibles. In consequence, the basic reproduction number is unchanged by these two vaccines.

    This may be one reason why those two vaccines are currently targeted to older cohorts and nursing home staff--i.e., to prevent development of COVID-19 in those sub-populations and thereby to reduce the loading on the hospital systems.

    The AstraZeneca-Oxford vaccine prevents the development of COVID-19 in vaccinated individuals and apparently also prevents those individuals from transmitting the virus to others. But the AZ-O vaccine is only 70% effective in two full doses; 90% effective (perhaps) in 1-1/2 doses in a small test sample.

    The AZ-O vaccine is the vaccine you want in order to reduce the basic reproduction number through vaccination. The AZ-O vaccine is also easier to handle and store (5 deg.C vs. -70 deg.C and -20 deg.C for Pfizer-BNT and Moderna resp.)

    A rural village or parish can be vaccinated with the AZ-O vaccine at a rate of 100% and achieve an effective 70% immunization rate with the benefit being that the basic reproduction rate drops significantly. For example, if R0 = 2.6 when 100% of the population is susceptible, then upon administration of the AZ-O vaccine to 100% of the population the basic reproduction number drops to 0.3 x 2.6 = 0.78 which is less than 1 and the pandemic is effectively at an end. This would not be so for either the Pfizer-BNT or Moderna vaccines, according to the information in the Reuters online report found at the URL below.

    Further information here: https://graphics.reuters.com/HEALTH-CORONAVIRUS/VACCINE/nmovabblmpa/

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    1. "But, apparently, neither of these two vaccines acts to prevent the onward transmission of the novel coronavirus SARS-CoV-19 by those who are vaccinated with either one of those two vaccines who become infected with the novel coronavirus.": It is possible that those 2 vaccines reduce the risk of transmission, but this was not yet investigated. I've heard Pfizer/BioNTech would probably study this for their vaccine, but it would take some time.

      "This may be one reason why those two vaccines are currently targeted to older cohorts and nursing home staff": it may also be related to the high reproductive rate and limited vaccine supply.
      See A Comparative Analysis of Influenza Vaccination Programs, Shweta Bansal, Babak Pourbohloul, Lauren Ancel Meyers, Plos Medicine, 2006 (https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0030387) and the preprint Prioritising COVID-19 vaccination in changing social and epidemiological landscapes, Peter Jentsch, Madhur Anand, Chris T Bauch, medRxiv, 2020 (https://www.medrxiv.org/content/10.1101/2020.09.25.20201889v2.full.pdf)

      "The AstraZeneca-Oxford vaccine ... apparently also prevents those individuals from transmitting the virus to others.": For the AstraZeneca-Oxford vaccine, the efficacy for asymptomatic infections was studied and found to be positive, but the confidence intervals were very large.
      "Asymptomatic infections or those with unreported symptoms were detected in 69 participants (table 2). Vaccine efficacy in the 24 LD/SD recipients was 58·9% (95% CI 1·0 to 82·9), whereas it was 3·8% (−72·4 to 46·3) in the 45 participants receiving SD/SD (table 2)." and "However, the wide CIs around our estimates show that further data are needed to confirm these preliminary findings, which will be done in future analyses of the data accruing in these ongoing trials."
      from Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK, Merryn Voysey, Sue Ann Costa Clemens, Shabir A Madhi, Lily Y Weckx, Pedro M Folegatti, Parvinder K Aley et al., The Lancet, 2020 (https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)32661-1/fulltext)

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    2. "But, apparently, neither of these two vaccines acts to prevent the onward transmission of the novel coronavirus SARS-CoV-19 by those who are vaccinated with either one of those two vaccines who become infected with the novel coronavirus.": It is possible that those 2 vaccines reduce the risk of transmission, but this was not yet investigated. I've heard Pfizer/BioNTech would probably study this for their vaccine, but it would take some time.

      "This may be one reason why those two vaccines are currently targeted to older cohorts and nursing home staff": it may also be related to the high reproductive rate and limited vaccine supply.
      See A Comparative Analysis of Influenza Vaccination Programs, Shweta Bansal, Babak Pourbohloul, Lauren Ancel Meyers, Plos Medicine, 2006 (https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0030387) and the preprint Prioritising COVID-19 vaccination in changing social and epidemiological landscapes, Peter Jentsch, Madhur Anand, Chris T Bauch, medRxiv, 2020 (https://www.medrxiv.org/content/10.1101/2020.09.25.20201889v2.full.pdf)

      "The AstraZeneca-Oxford vaccine ... apparently also prevents those individuals from transmitting the virus to others.": For the AstraZeneca-Oxford vaccine, the efficacy for asymptomatic infections was studied and found to be positive, but the confidence intervals were very large.
      "Asymptomatic infections or those with unreported symptoms were detected in 69 participants (table 2). Vaccine efficacy in the 24 LD/SD recipients was 58·9% (95% CI 1·0 to 82·9), whereas it was 3·8% (−72·4 to 46·3) in the 45 participants receiving SD/SD (table 2)." and "However, the wide CIs around our estimates show that further data are needed to confirm these preliminary findings, which will be done in future analyses of the data accruing in these ongoing trials."
      from Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK, Merryn Voysey, Sue Ann Costa Clemens, Shabir A Madhi, Lily Y Weckx, Pedro M Folegatti, Parvinder K Aley et al., The Lancet, 2020 (https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)32661-1/fulltext)

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    3. "But, apparently, neither of these two vaccines acts to prevent the onward transmission of the novel coronavirus SARS-CoV-19 by those who are vaccinated with either one of those two vaccines who become infected with the novel coronavirus. In other words, the vaccinated patients can be carriers of the virus but not become sick from the virus."

      That's speculative. Neither is *proven* to prevent the onward transmission of COVID because neither study was designed to assess that outcome.

      The most likely scenario, however, is that they do impede onward transmission, though efficacy at doing so could be less than efficacy at preventing symptomatic COVID.

      One key point to consider is that transmission of SARS-CoV-2 appears to be far lower from asymptomatic carriers than from those with symptoms. A recent JAMA meta-analysis looks at secondary household attack rate - i.e., other members of the same household as someone with a positive SARS-CoV-2 test also testing positive for SARS-CoV-2. The meta-analysis indicates an 18.0% secondary attack rate in households with a symptomatic index case versus 0.7% in households with an asymptomatic index case. https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2774102

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  15. If one or two vaccines prevent the development of COVID-19, but do not affect the basic reproduction number (i.e., the vaccinated individual can be infected by the novel coronavirus and pass the virus along to another susceptible person but not themselves develop the disease referred to as COVID-19) then the public good that vaccination produces is the reduction in the number of and seriousness of hospitalizations during the pandemic but only to the extent that the vaccine in administered to those sub-populations that are vulnerable to developing the disease COVID-19.

    While, arguably, there is an undoubted private benefit in vaccination (for why else would one be vaccinated?), the public benefit is greater. It is known now that the response by state and local governments to an upswing in confirmed infections ("confirmed cases") is to curtail private economic activity and public schooling when the number of "confirmed cases" exceeds a certain threshold corresponding to hospitalizations and ICU capacity utilized. A vaccine that reduces or prevents the development of the disease COVID-19 and thereby reduces hospitalizations related to COVID-19 will allow the state and local governments to ease or eliminate restrictions on private activity and private business activity in particular, and allow the economy to recover sooner. This is the public benefit of vaccination of nursing home staff and residents, and the elderly rather than vaccinating younger sub-populations such as university students, or grocery store clerks.

    On the other hand, if the vaccine is available only to the highest bidder, and not to nursing home populations (the majority of which are not wealthy enough to qualify) then there is the likelihood that the only benefit to accrue from the available vaccine quantity is the private benefit which is cornered by the most well-to-do and wealthiest cohorts in the population with little or no public benefit delivered (i.e., hospitalizations remain high and concerning and ICU utilization approaches and may exceed full capacity). Alternatively, the highest bidder might be a private hospital system for the sole benefit of its clientel while other hospitals and clinics and nursing homes go begging.

    Contrary to your assertions in the blog that a free market in vaccine procurement will deliver public benefits from pursuit of private benefits, a 'free market' in the vaccine does not guarantee that the public benefit is obtainable let alone maximized.

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    1. You appear to have fallen foul of the fixed supply fallacy.

      And forgotten that brevity is a virtue.

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    2. Mr. Coker, supply is fixed in the short run. It is the short run that determines what measures our politicians take in response to the pandemic.

      As to 'brevity', if the post is too long for you then skip it.

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  16. The US federal government has reputedly spent $12 billions on development and manufacturing bounties to pharmaceutical firms (source: https://time.com/5921360/operation-warp-speed-vaccine-spending/ ).

    The private pharmaceutical firms entered into voluntary contracts with the federal government for the provision of specific quantities of vaccine doses in exchange for payments totalling $12 billions (+/-). This free contracting between two or more parties acting at arms-length is characteristic of a 'free market'. The vaccines in question, and other pharmaceuticals, were not then available to the general market at the time the parties entered into the contracts. None were offered for sale through normal market channels.

    A time-line of the federal government's contracting activities is summarized here: https://www.hhs.gov/coronavirus/explaining-operation-warp-speed/index.html --for those who are interested in such things.

    The blog post focuses on the distribution of the vaccines and the administration of the vaccine to 'susceptibles', after the manufacturing facilities have been built and are operating and FDA approval has been obtained. The blog argues that private interests (a.k.a., the 'free market') can do it better, cheaper, faster, etc. Details are missing: who?, where?, what?, etc.

    Suppose McKesson Corporation ($230 billions annual revenues in 2020) is granted a monopoly to distribute and sell the vaccines with no constraints imposed on pricing or geographic coverage. It would sell the first allotment to the highest bidder(s) in a Dutch auction setting, say, at $10,000 per dose. It would sell the second and larger allotment to the highest bidder at $5,000 per dose, and so on until all 300 million doses are allotted to qualified bidders. Social welfare would be minimized, and net private benefit maximized thereby. The 'free market' mantra would be adhered to.

    Suppose the Biden Administration on day 2 enrolls the U.S. military to distribute the vaccines, pre-empting the private sector, on the presumption that the government can do better, faster, cheaper than the 'free market'. Suppose that it is true. Using the McKesson Corporation scenario as a backdrop, in the Biden-US Military scenario social welfare is maximized while private benefit is minimized. Furthermore, under the Biden-US Military scenario, private interests cannot 'corner' the vaccine supply to drive the price up by restricting access to that supply. Additionally, vaccine supplies can be delivered wherever the government decides the public interest (as it defines that interest to be) is best served. The 'free market' mantra is ignored.

    The choice criterion is maximizing net public benefit, or maximizing net social welfare. That alternative which achieves maximum net social welfare is the alternative to choose.

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    1. Only individuals are real. The public is an abstraction, from real individuals,ie, a method of knowing reality, a method of considering all individuals at the same time. Eg, the US has 300M people. Only individuals, not abstractions or methods, face life or death, can have welfare. There is no real public which is healthy or sick. This is mysticism, the claim of a supernatural entity or realm. There is no real God, no real public. Acting to defend God or the public is fantasy whose real effect is destroying real individuals. There is no general welfare, except as it refers to the welfare of each individual as individual. Real individuals, _considered_ as isolated individuals or as a group, think, act, produce and trade. There is no mystic economy above and beyond real individuals. There is no mystic race, ethnic group or economic class above and beyond the individual prisoners in labor/death camps. Such is the necessary effect of rejecting individualism.



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    2. "public" [adjective]
      1. "of or concerning the people as a whole."

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    3. > the people as a whole."

      As a whole of real individuals or as a mystical ideal above and beyond real individuals and to which real individuals should be forcibly sacrificed. Some words have both distributive (individualist) and collective meanings, eg, "general welfare."

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    4. people (noun), plural of person (noun).

      Language is based on concepts -- a people, the people, a person, some person, "a person or persons unknown", etc. "General welfare" is interchangeable with "public welfare" = "of or concerning the welfare of the people as a whole."

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  17. If vaccines A and B immunize the vaccinated individual against the disease COVID-19, but have no effect on the transmissibility of the virus from host to susceptible, then it would make little sense to vaccinate the young and middle-age that are not at risk of developing COVID-19 if infected with the novel coronavirus as there would be no benefit to those sub-populations.

    The greatest benefit of vaccines A and B (described in the prior paragraph) are to those most susceptible of developing critical and acute infections of the virus that result in hospitalization for COVID-19. The purpose of vaccinating those sectors of the population using vaccines A and B is to reduce the demand placed on hospitals and intensive care units in hospitalsd, for it has been amply demonstrated this year that social 'lockdowns' of businesses are driven the by rate of change in hospital utilization and ICU capacity constraints. If vaccines A and B reduce the prevalence of COVID-19 in vulnerable segments of the population, then to the extent that hospitalization and ICU demand are reduced, there is a public benefit to be gained by vaccination of those susceptible population segments (elderly and nursing home residents, etc.)

    The 'private benefit' aspect of such a policy is the motivating factor for the individual, and in this sense, 'free' is correct price to apply to the vaccination process to encourage the individual to agree to be vaccinated.

    The converse to "willingness to pay" is "willingness to accept". Any positive price applied to access the vaccine will impede acceptance of vaccination. Think, for example, of the oral polio vaccine administered on sugar cubes to school children. Suppose, in 1960, the vaccine cost $2 per dose and the administering of the dosages cost a further $0.50 per dose, for a total of $2.50 per dose administered. Suppose the government or a private actor sought to recoup the $2.50 and earn $0.25 in profit before tax by charging $2.75 per dose administered. How many doses would be taken up at $2.75 versus the number of doses taken up a no cost in the next health district? "Willingness to accept" has to be considered when developing policy for a broad immunization program to curtail a pandemic or local epidemic.

    Likewise, the characteristics of a vaccine have to be considered when determining the policy to be put into effect to achieve the greatest social benefit. Vaccines A and B (see above) are best deployed to reduce the incidence of critical COVID-19 symptoms requiring hospitalization and potential ICU demand because politicians gauge the need for restrictions on business and private activities based on hospitalization rates and ICU demand--higher hospitalization rates and ICU demand trigger more draconian restrictions on business and private activities and cause greater damage to economic activity and employment. Vaccines A and B deliver positive social welfare improvement by reducing demand for hospitalization and ICU capacity in elderly and nursing home populations, and that social welfare improvement exceeds the private benefit to individuals in those susceptible populations. That effect needs to be recognized and acknowledged.

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  18. With all due respect, your argument is intellectually disingenuous insofar as it doesn't even address the empirical finding that the vaccines are likely much more effective at preventing illness and death than at preventing transmission. There is plenty of empirical debate to be had about this issue, but your arguments don't even address it even though I struggle to believe. It's a little dishonest.

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  19. Cochrane: "[Hospitals] are forbidden from [purchasing Covid vaccine] now."

    Forbidden how, exactly? Under penalty of law? (This seems to be Cochrane's innuendo here.)

    Is there really a de jure prohibition against a private party today entering the market to purchase certified Covid vaccine doses, should they wish to do so?

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    1. Likely so, though I think the particulars are a combination of (1) the federal contracts with Pfizer and Moderna to acquire vaccine doses and (2) the terms and conditions attached as those doses are then distributed (with states also part of that chain).

      I haven't readily been able to find the full text of the federal contracts with Pfizer and Moderna, but the OWS summary page ( https://www.hhs.gov/coronavirus/explaining-operation-warp-speed/index.html ) links to various HHS press releases as those agreements were executed. There's a degree of supposition on my part, but it wouldn't surprise me if the supply contracts with Pfizer and Moderna (and also R&D/clinical trial contracts with Moderna) require those companies to fill the federal government orders before selling to any other party in the U.S.

      The "exclusivity" or "first priority" terms (for vaccine doses in the U.S.) are where I'm making a supposition. It's abundantly clear, however, from press releases about the agreement with Pfizer (in July 2020) and Moderna (in August 2020) that the federal government has supply agreements with each under which the feds own the vaccine doses.

      It's also clear that the doses come with conditions as they're shipped to providers to administer. Quoting from the HHS August 2020 press release about its agreement with Moderna: "If these doses are used in a COVID-19 vaccination campaign, the vaccine would be available to the American people at no cost. As is customary with government-purchased vaccines, healthcare professionals could charge for the cost of administering the vaccine." That doesn't 100% address the topic of resale to the highest bidder, but I'd be absolutely shocked if that's not covered in the terms under which providers accept federally-purchased vaccine doses. That process goes via allocation/prioritization procedures set by state governments, so that's also a link in the chain where legally-binding terms could be formalized.

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    2. Realist, thank you for the helpful reply. I was unable to answer via my own digging. Cochrane himself doesn't say.

      I suspect that Cochrane believes the mechanism of government interference here is "crowding out", not prohibition by law. And that a private marketplace for the vaccine exists today, he'd concede, even if at present only governments are large enough to enter.

      If so, we are left to clean up some rather loose and misleading right-wing polemics here.

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    3. You get free speech, but I don't answer insults. Call up a hospital and ask them to buy some doses for you. Let us know how it works.

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    4. It seems that to debate on social media is to risk insult, both incoming and outgoing, unfortunately. Some remarks judged insulting can simultaneously be germane, however. It's not strictly one or the other, I believe.

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  20. A pre-print paper "Prioritising COVID-19 vaccination in changing social and epidemiological landscapes" [medRxiv, Sept. 27, 2020, online, Jentsch, P., et al.] presents a model-based analysis of several vaccination priority strategies to determine an 'optimal' programme to minimize mortalities arising from the SARS-CoV-2 novel coronalvirus pandemic. The authors base their analysis on an age-cohort segmented Susceptible-Exposed-Infective-Recovered ("SEIR") compartment model.

    Navigate to: medrivx.org/content/10.1101/2020.09.25.202021889v2

    No paywall for the pre-print version of the paper. Links to supplementary material and data/code are provided. The supplementary material includes a description of the mathematical model used by the authors.

    Results presented are in summary form of the output of computer simulations. When the vaccine is made available early in the pandemic, vaccination of the age cohort 60 years and over is optimal. When the vaccine is made available later in the pandemic contact-specific vaccination is optimal. The threshold for enforcing lock-downs of the economy influences the age-cohort selection for the optimal vaccination program. The paper discusses the effect of the basic reproduction number (R0) on the choice of vaccination programme to minimize mortalities.

    The usefulness of the paper is limited by the assumptions chosen by the authors. For example, the economic cost of the lock-downs is not modelled; and, the effect of cases on hospital utilization is not considered. The lock-down threshold is an exogenous variable. Despite these limitations, the paper presents a behavioural-SEIR model that endogenously selects one out of many possible vaccination programme strategies to minimize mortality. The mathematical details of the model will be of interest to those prepared to delve more deeply into the details.

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