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The Opportunity of Skewed Coronavirus Transmission

30 Monday Mar 2020

Posted by Nuetzel in economic growth, Pandemic

≈ 1 Comment

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Contagion, Coronavirus, Covid-19, Fat-Tailed Distribution, Heart Disease, Herd Immunity, John Cochrane, President Trump, Prophylaxis, Public Park Closures, Reproduction Rate, Restart Economy, Right Skew, Shelter In Place, Stay-at-Home, Suicide, Super-Spreaders, The Federalist, Transmission Rate

People talk about the transmission rate or reproduction rate (R0) of Covid-19 as if it’s a single number that applies to the entire population. John Cochrane emphasizes the huge implications of this misperception for how best to prevent the spread of the virus, and at lower cost, and for how best to “restart” the economy.

First, however, lets dispense with the absolutist position that there can be no compromise on virus mitigation in favor of economic activity. I am not opposed to the “lockdown” we are now living, but it will have significant and unnecessary costs if it goes on too long: the lost output is a huge blow not only to our current lifestyles but to our ability to grow in the future, or even to afford better health care in the future. Beyond that, the lockdown has immediate negative impacts of its own on public health: economic stress leads to all kinds of terrible health outcomes like heart disease and even suicide. About the latter, the President is absolutely correct: if you need research to prove it, see here, here, here, and here, all respected journals (the links all courtesy of The Federalist.) Economic stress and isolation is quite likely to promote poor dietary habits, lethargy, and possibly family dysfunction as well. Don’t pretend there aren’t real tradeoffs between the economy, virus interventions, and public health. The trick is to improve those tradeoffs. A balance can and must be struck, and depending on policy actions, the tradeoff can be made better or worse.

Back to the virus reproduction rate: the R0 values we see quoted are estimates of the average number of other people infected by each infected person. A value of three means that each person infected with the virus passes it on to three others, on average. If R0 is greater than one, an epidemic grows. If R0 is less than one, a contagion recedes. It becomes a “non-epidemic” if R0 remains less than one. It does not have to be zero (and probably cannot be zero).

But not everyone is the same: my R0 is different from your R0 if only because we have different occupational exposure to others and different levels of social engagement. We also differ physiologically, which probably leads to differences in our “personal” R0 values. And an individual’s R0 will differ by time and place, depending on random circumstances like which way the wind is blowing. But here is where it gets interesting. Cochrane describes an extreme version of the skewed distribution shown at the top of this post:

“Suppose there are 100 people with a 0.5 reproduction rate, and 1 super-spreader with a 100 replication rate. The average reproduction rate is 1.5. Clearly, locking everyone down is wildly inefficient. It’s much more important to find the 1 super-spreader and lock him or her down, or change the business or behavior that’s causing the super-spreading.

This is exaggerated, but not far off the mark. I have not seen numbers on the distribution of reproduction rates across people, but it is a fair bet that it has an extremely fat tail. Most of us are washing our hands, social distancing, work in businesses that are shut down or are taking great steps to limit contact. And a few people and activities contribute to most of the spread.

This wide and fat-tailed dispersion is ignored in a lot of simulations I’ve seen. They take the average reproduction rate as the same for everyone. That’s a big mistake.

The danger: we waste a huge amount of time and money moving you and me from a 0.5 reproduction rate to an 0.4 reproduction rate. …  The opportunity: focus on the super-spreaders, and the super-spreading activities, and you bring down the reproduction rate at much lower cost. “

There are many ways to reduce R0. Cochrane gets a little more specific about this and the policy implications of the skewed R0 distribution across individuals:

“All we need is to get the transmission rate under one. Activities with possible but very low transmission rates, and high economic benefits should go on. Don’t separate to ‘essential’ and ‘non-essential.’ Separate into ‘high likelihood of transmission’ and ‘low likelihood of transmission.’

Why are we not using masks everywhere? Sure, they’re not perfect. Sure, an old hankerchief might only cut the chance of transmission by half. We’re not all surgeons. Cutting by half is enough to stop the virus. 

Conversely, why did they close the state parks? Really? Just how dangerous is it to drive the dog to a hiking trail and stay 6 feet away from other people? Parks, ski areas, golf courses, all sorts of businesses that surely can be run with a reproduction rate far less than one are just shut down. I met a realtor on our dog walk yesterday. They’re totally shut down. Just how hard is it to run a realty business with a 0.5 reproduction rate? One family in the house at a time, don’t touch anything, an hour between showings, stay 6 feet from the realtor… But instead the whole business is just shut down.”

The beginning of that last paragraph echoes a point I made in my last post about public park closures and the health benefits of getting outside generally.

Cochrane goes on to discuss several other policy options, including the potential benefits of simple kinds of testing and the overemphasis on false negatives and positives in policy discussions. Imperfect tests should not be discouraged by these concerns. If you’re worried about that, you shouldn’t use a thermometer either!

“Stay-at-home” or “shelter-in-place” orders will increasingly be tested by private parties if they remain in effect too long. That will be encouraged by the seemingly arbitrary distinctions some orders make between “essential” and “non-essential” activities. If workers or small businessmen judge themselves to be at low risk, they will take matters into their own hands to the extent they can. I believe that’s already happening where the specifics of “lockdown” orders have gone too far.  Workers at the low end of the income spectrum are especially hard hit by these orders. One can hardly blame them for trying to earn what they can if they believe, and their customers believe, their activities and interactions are of low risk.

Ultimately, the entire distribution of R0s will slide to the left. That will occur even at low levels of “herd immunity” and anything that offers at least weak prophylaxis. Broadly speaking, the latter includes maintaining distance, refusing admittance to venues with a fever, avoiding handshakes, wearing masks, and potentially chloroquine, which is already in widespread use by physicians treating coronavirus patients. Ultimately, a vaccine will slide the distribution far to the left, but the economy need not be held hostage until that time. To paraphrase Cochrane, we can get the transmission rate below one and keep it there without stopping the world permanently. There are many options, and now is the time for business and government to start planning for that.

Statists Might Like To Vaccinate Against Many Things

25 Monday Nov 2019

Posted by Nuetzel in Vaccinations

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Anti-Vaxxers, Community Protection Threshold, Contagion, Contra-Indications, Externality, Federaalism, Herd Immunity, Immunization, Jeffrey Singer, Lancet, Measles, Mercury, Michigan Vaccine Law, Post Hoc Ergo Propter Hoc, Precautionary Principle, Price Discrimination, Private Governance, Vaccine Hesitancy, Vaccine Preservatives, Vaccine Resistors, Whooping Cough

The vaccine debate illustrates a widespread misunderstanding about the meaning of an “advanced society”. It does not mean that difficult social problems must be dealt with always and everywhere in a uniform way, as supporters of vaccine mandates seem to assume. Instead, it often means that society can respect differences in the preferences of individuals by allowing varied approaches to problem-solving across jurisdictions, as well as across public and private institutions. This latter notion of advancement respects individual freedom and facilitates experiential social learning. But is that varied approach wise in a world of communicable diseases?

One standard of “community” protection assumes that vaccines work with a high degree of certainty within groups of individuals, especially with a second booster. The share of the population vaccinated against most common childhood diseases is fairly high. In fact, these shares mostly exceed their respective “community protection thresholds” — the percentage required to prevent a particular disease from spreading. That means achieving so-called “herd immunity”. Of course, that will not be true across many local subgroups. Nevertheless, if one accepts this standard, a runaway contagion in the U.S. is an extremely remote possibility, affording some flexibility for respecting preferences for and against vaccination.

My Friend, the Vaccine Resistor

One of my best friends is a passionate vaccine resistor (VR). I won’t say he’s “vaccine hesitant” because that doesn’t come close to his position. I won’t call him an “anti-vaxxer” because he doesn’t mind if others avail themselves of vaccines (and besides, the term has taken on such derogatory connotation. He’s a fine fellow, very smart, lots of fun to be with, and we have plenty of mutual interests. We’ve argued about vaccinations before, and a few other medical and nutritional issues, but we mostly stay out of each others’ ways on these topics.

But I recently witnessed my pal get into a “debate” on social media with a mutual acquaintance and some of her connections. She happens to be a nurse. She’d posted a photo of an attractive young woman in a t-shirt imprinted, “Vaccines Cause Adults”. My buddy spoke up and said “Not for everyone!’, and he posted a link to an article that he felt supported his position. Of course, a number of barbed responses came his way. Okay, some of those were fair debate points, though barbed, but others were quite derisive, ad hominem attacks on him. He responded by posting links to more articles and research, which might not have been productive. It’s usually a waste of time to argue with people on social media. But to his great credit he maintained his equanimity. The episode made me feel a bit sad. People can be such assholes on social media. I was put off by the nurse’s refusal to moderate . That’s a typical pattern: posters allow their other friends to hurl terrible insults at anyone who disagrees, even when it’s an old friend. Mind you, I stayed on the sidelines in this case, except that I originally “liked” the nurse’s meme.

Later, I had a private exchange with my friend. I’m on board with vaccinations. I believe that widespread immunization contributes to public health, but I told him there are certain points on which I can sympathize with VRs. Without knowing the details, he encouraged me to write a blog post on the subject. I’m not sure he’ll like the results. However, as noted above, I’m willing to make a few concessions to my buddy’s side of the argument, and I wish we could identify a path that would settle the debate.

My Standpoint

This is one part my pal won’t like. Are VRs anti-science? First, VR’s come in several varieties. Some might resist only some vaccines and not others. But VRs do not disavow empiricism, as they claim their own set of empirical findings to support their position, however one might regard the research quality. 

I believe many VRs are misled by a serious post hoc ergo propter hoc fallacy: after this, therefore because of this. For example, for many observers, the purported link between autism and the measles, mumps and rubella vaccine was put to rest when the British medical journal Lancet retracted the original article supporting that claim as faulty. That doesn’t wash with more radical VRs, many of whom seem to have someone on the autism spectrum in their own families. They are understandably sensitive, but please forgive me: that suggests a need to find some external explanation, a source of blame not related to genetics.

Radical VRs are selective proponents of the precautionary principle: any risk of harm from a vaccine delivered in any amount is too great a risk. They seem reluctant to acknowledge the reality of a dose-response relationship, which bears on the risks of exposure to certain compounds often present in vaccine formulations. VRs will not acknowledge that vaccines present a manageable risk. And then there are the misleading references to disease incidence counts, as opposed to disease incidence rates, that are all too common (though my friend is almost certainly innocent on this count).

Vaccine resistance is not a new phenomenon, as the cartoon above from 1802 illustrates. Certain people will always find the idea of injecting germs into their systems deeply unsettling. Of course, that’s a very natural basis of resistance. A person’s body is their own property, after all. My default position is that an individual’s control over their own body is inviolable, and parents should always be the first authority over decisions about their children. The real issue, however, is the question of whether unvaccinated children inflict external costs on others.

Points of Contention

The major objections of VRs fall into several categories: 1) preservatives; 2) multiple viruses; 3) vulnerable infants; 4) contra-indications; 5) inefficacy; and 6) free choice. There may be others, but I’ll go with those.

Preservatives: Some vaccines still use a form of mercury, but a much more innocuous variant than the one VRs found so objectionable a few decades ago. Still, they object. And they object to many other compounds used in minute quantities as preservatives, such as formaldehyde, which occurs naturally in our bodies. I think the following test is helpful: if it were proposed that VRs take new versions of the vaccines that had zero preservatives, many would still refuse, especially if they were asked to pay the additional cost of providing them in that form. Thus, preservatives are revealed to be something of a side show.

Multiple Viruses: VRs object to the administration of vaccines that inoculate against several viruses in one dose or within a short window of time. This objection has some plausibility, since an injection of several different “bugs’ at once might place excessive stress on the body, even if the risk is still small. But again, would VRs volunteer to take single strain vaccines in a schedule over a lengthier period of time? Probably not.

Vulnerable Infants: VRs say it’s too risky to vaccinate infants in their first few months of life. This too is a plausible objection, and it would seem like a relatively easy concession to make in the interests of compromise … except, it won’t ever be good enough. Radical VRs will not agree to having their children vaccinated at any age.

Contra-Indications: There are undoubtedly genetic factors that pre-dispose certain individuals to an adverse reaction to certain vaccines. These might be rare, so an effort to compromise by requiring a thorough genetic profile before vaccination would be costly. I believe profiling is a reasonable demand for individuals to make, however, provided they pay the cost themselves.

Inefficacy: My friend posted an intriguing article about the drastic declines that occurred in the incidence of various diseases before the introduction of vaccines to prevent those diseases. This might not be the same link, but it makes the same argument. That doesn’t mean vaccines don’t work, of course. There is a vast literature that shows that they do. Bing it! And in cases such as smallpox, the use of “folk applications” of puss to a small scratch in the skin were in use long before the vaccine was available. Nevertheless, the VRs contend that the historical rates of disease incidence provide evidence against vaccinating. They also contend that diseases like measles are not serious enough to warrant precautions like vaccines. Measles can be deadly, though not as deadly as the flu.

Free Choice: This is the point on which I’m most sympathetic to VRs. Again, we own our own bodies and should have authority over our own minor children, yet communicable diseases seem to be a classic case of externality. Susceptible individuals may inflict a cost on others by refusing vaccination or segregation. Other people own their bodies too, and they have a right to avoid exposure. They too can isolate themselves or take precautions as they deem necessary. If both parties wish to participate in society, then both hold rights they allege to be threatened by the other. That complicates the task of reconciling these interests in private, voluntary ways, and yet they often are reconciled privately.

Solutions?

The debate today often revolves around mandatory vaccination, which would be an extreme measure relying on the coercive power of the state. The rationale is that even a vaccinated majority would be subject to an unnecessarily high risk of infection when in frequent contact with an unvaccinated minority. It’s difficult to endorse such broad intrusiveness when we’re dealing with a negative externality of such minute probability. And such a policy is not at all defensible without exceptions for individuals for whom a vaccine is contra-indicated.

Tolerating differences in vaccination rules across cities, school districts, or even states, may be a reasonable approach to settling the debate in the long run. These variations allow empirical evidence to accumulate on the efficacy of different vaccine regimes. It also allows individuals and families to “vote with their feet”, migrating to jurisdictions that best suit their preferences. These are the basic foundations of federalism, a principle of great usefulness in preserving freedoms while addressing regional differences of opinion on contentious issues.

Michigan has a policy allowing unvaccinated children to attend schools, but a waiver must be obtained requiring the child’s parents to attend a vaccine education program. The policy is credited with increasing vaccination rates. The problem is that VRs tend to view this requirement as an infringement on their rights. Advocates of the policy might argue that the situation should be viewed as an arms-length, voluntary exchange between two parties, in this case a family and a public entity. The vaccine education program is just the price one must pay in lieu of vaccination. The exchange is not arms length, however, as it would be if the school were a private entity. The VR parents who refuse the waiver are not rebated for taxes paid for local schools. In fact, like all taxes, the payment is coerced.

It’s not always necessary to appeal to some form of government action, even at local levels. For example, private schools may require vaccination among enrollees, and private businesses, especially health care providers, may require staff to be vaccinated. Life and health insurers may wish to price risk differently for the unvaccinated. VRs might object that they are subject to discrimination by institutions requiring immunization, or who price discriminate in favor of the immunized, but VRs are free to form competitive institutions, even on small scales or as mutual companies. To the extent that such private rules are unjustified, the institutions who discriminate are likely to learn or lose eventually. That’s the beauty of market solutions. In these ways, non-coercive private governance is far preferable to action by the state.

Dr. Jeffrey Singer is an advocate of immunization who opposes mandatory vaccine laws, as he explained a few years ago in “Vaccination and Free Will“. He suggested elsewhere, in “Seeking Balance In Vaccination Laws“, that schools, instead of requiring immunization, could mitigate the risk of a contagion by insisting that unvaccinated children be held out of school when a particular threat arises and remain out until it passed. That’s a reasonable idea, but I suspect many pro-vax parents would fear that it doesn’t go far enough in protecting against the introduction of a disease by an unvaccinated child.

Conclusion

Recent increases in the incidence of diseases such as measles, mumps and whooping cough are extremely troubling. Whether these outbreaks bear any relationship to patterns of vaccination in the population is certainly a valid question. To the extent that more families and individuals wish to be immunized, and that private institutions wish to take action to increase vaccination rates within their sphere of influence, I’m all for it. Vaccination laws are a different matter.

Political action at the local level might mean that school districts and other public entities will require vaccinations or vaccine education programs. Alternatives exist for those refusing to vaccinate, but broad mandatory vaccination is too coercive. Such measures carry significant costs, not least of which is a loss of liberty and normalization of losses of liberty. It’s not clear that a vaccination mandate at the national level, or even a state vaccination mandate, can offer benefits sufficient to justify those costs. Nudges are irritating and may be costly, but forcible intrusions are way out-of-bounds. Unfortunately, there are parties that simply can’t resist the temptations of behavioral control, and that’s worthy of resistance. Let’s continue to muddle through with an essentially federalist approach to vaccination policy. I regard that as a hallmark of an advanced society.

 

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