Tag Archives: Super-Spreaders

Allocating Vaccine Supplies: Lives or “Justice”?

29 Tuesday Dec 2020

Posted by in Pandemic, Public Health, Uncategorized, Vaccinations

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There are currently two vaccines in limited distribution across the U.S. from Pfizer and Moderna, but the number and variety of different vaccines will grow as we move through the winter. For now, the vaccine is in short supply, but that’s even more a matter of administering doses in a timely way as it is the quantity on hand. There are competing theories about how best to allocate the available doses, which is the subject of this post. I won’t debate the merits of refusing to take a vaccine except to say that I support anyone’s right to refuse it without coercion by public authorities. I also note that certain forms of discrimination on that basis are not necessarily unreasonable.

The vaccines in play all seem to be highly effective (> 90%, which is incredible by existing standards). There have been a few reports of side effects — certainly not in large numbers — but it remains to be seen whether the vaccines will have any long-term side effects. I’m optimistic, but I won’t dismiss the possibility.

Despite competing doctrines about how the available supplies of vaccine should be allocated, there is widespread acceptance that health care workers should go first. I have some reservations about this because, like Emma Woodhouse, I believe staff and residents at long-term care facilities should have at least equal priority. Yet they do not in the City of Chicago and probably in other areas. I have to wonder whether unionized health care workers there are the beneficiaries of political favoritism.

Beyond that question, we have the following competing priorities: 1) the vulnerable in care homes and other elderly individuals (75+, while younger individuals with co-morbidities come later); 2) “essential” workers of all ages (from police to grocery store clerks — decidedly arbitrary); and 3) basically the same as #2 with priority given to groups who have suffered historical inequities.

#1 is clearly the way to save the most lives, at least in the short-run. Over 40% of the deaths in the U.S. have been in elder-care settings, and COVID infection fatality rates mount exponentially with age:

To derive the implications of #1 and #2, it’s more convenient to look at the share of deaths within each age cohort, since it incorporates the differences in infection rates and fatality rates across age groups (the number of “other” deaths is much larger than COVID deaths, of course, despite similar death shares):

The 75+ age group has accounted for about 58% of all COVID deaths in the U.S., and ages 25 – 64 accounted for about 20% (an approximate age range for essential workers). This implies that nearly three times as many lives can be saved by prioritizing the elderly, at least if deaths among so-called essential workers mimic deaths in the 25 – 64 age cohorts. However, the gap would be smaller and perhaps reversed in terms of life-years saved.

Furthermore, this is a short-run calculation. Over a longer time frame, if essential workers are responsible for more transmission across all ages than the elderly, then it might throw the advantage to prioritizing essential workers over the elderly, but it would take a number of transmission cycles for the differential to play out. Yes, essential workers are more likely to be “super-spreaders” than work-at-home, corporate employees, or even the unemployed, but identifying true super-spreaders would require considerable luck. Moreover, care homes generally house a substantial number of elderly individuals and staff in a confined environment, where spread is likely to be rampant. So the transmission argument for #2 over #1 is questionable.

The over-riding problem is that of available supply. Suppose enough vaccine is available for all elderly individuals within a particular time frame. That’s about 6.6% of the total U.S. population. The same supply would cover only about 13% of the younger age group identified above. Essential workers are a subset of that group, but the same supply would fall far short of vaccinating all of them; lives saved under #2 would then fall far short of the lives saved under #1. Quantities of the vaccine are likely to increase over the course of a few months, but limited supplies at the outset force us to focus the allocation decision on the short-term, making #1 the clear winner.

Now let’s talk about #3, minority populations, historical inequities, and the logic of allocating vaccine on that basis. Minority populations have suffered disproportionately from COVID, so this is really a matter of objective risk, not historical inequities… unless the idea is to treat vaccine allocations as a form of reparation. Don’t laugh — that might not be far from the intent, and it won’t count as a credit toward the next demand for “justice”.

For the sake of argument, let’s assume that minorities have 3x the fatality rate of whites from COVID (a little high). Roughly 40% of the U.S. population is non-white or Hispanic. That’s more than six times the size of the full 75+ population. If all of the available doses were delivered to essential workers in that group, it would cover less than half of them and save perhaps 30% of minority COVID deaths over a few months. In contrast, minorities might account for up to two-thirds of the deaths among the elderly. Therefore, vaccinating all of the elderly would save 58% of elderly COVID deaths and about 39% of minority deaths overall!

The COVID mortality risk to the average white individual in the elderly population is far greater than that faced by the average minority individual in the working age population. Therefore, no part of #3 is sensible from a purely mathematical perspective. Race/ethnicity overlaps significantly with various co-morbidities and the number of co-morbidities with which individuals are afflicted. Further analysis might reveal whether there is more to be gained by prioritizing by co-morbidities rather than race/ethnicity.

Megan McArdle has an interesting column on the CDC’s vaccination guidelines issued in November, which emphasized equity, like #3 above. But the CDC walked back that decision in December. The initial November decision was merely the latest of the the agency’s fumbles on COVID policy. In her column, McArdle notes that the public has understood that the priority was to save lives since the very start of the pandemic. Ideally, if objective measures show that identifiable characteristics are associated with greater vulnerability, then those should be considered in prioritizing individuals who desire vaccinations. This includes age, co-morbidities, race/ethnicity, and elements of occupational risk. But lesser associations with risk should not take precedence over greater associations with risk unless an advantage can be demonstrated in terms of lives saved, historical inequities or otherwise.

The priorities for the early rounds of vaccinations may differ by state or jurisdiction, but they are all heavily influenced by the CDC’s guidelines. Some states pay lip service to equity considerations (if they simply said race/ethnicity, they’d be forced to operationalize it), while others might actually prioritize doses by race/ethnicity to some degree. Once the initial phase of vaccinations is complete, there are likely to be more granular prioritizations based on different co-morbidities, for example, as well as race/ethnicity. Thankfully, the most severe risk gradient, advanced age, will have been addressed by then.

One last point: the Pfizer and Moderna vaccines both require two doses. Alex Tabarrok points out that first doses appear to be highly effective on their own. In his opinion, while supplies are short, the second dose should be delayed until all groups at substantially elevated risk can be vaccinated…. doubling the supply of initial doses! The idea has merit, but it is unlikely to receive much consideration in the U.S. except to the extent that supply chain problems make it unavoidable, and they might.

On the Meaning of Herd Immunity

09 Saturday May 2020

Posted by in Pandemic, Public Health, Risk

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Immunity doesn’t mean you won’t catch the virus. It means you aren’t terribly susceptible to its effects if you do catch it. There is great variation in the population with respect to susceptibility. This simple point may help to sweep away confusion over the meaning of “herd immunity” and what share of the population must be infected to achieve it.

Philippe Lemoine discusses this point in his call for an “honest debate about herd immunity“. He reproduces the following chart, which appeared in this NY Times piece by Carl T. Bergstrom and Natalie Dean:

Herd immunity, as defined by Bergstrom and Dean, occurs when there are sufficiently few susceptible individuals remaining in the population to whom the actively-infected can pass the virus. The number of susceptible individuals shrinks over time as more individuals are infected. The chart indicates that new infections will continue after herd immunity is achieved, but the contagion recedes because fewer additional infections are possible.

We tend to think of the immune population as those having already been exposed to the virus, and who have recovered. Those individuals have antibodies specifically targeted at the antigens produced by the virus. But many others have a natural immunity. That is, their immune systems have a natural ability to adapt to the virus.

Heterogeneity

At any point in a pandemic, the uninfected population covers a spectrum of individuals ranging from the highly susceptible to the hardly and non-susceptible. Immunity, in that sense, is a matter of degree. The point is that the number of susceptible individuals doesn’t start at 100%, as most discussions of herd immunity imply, but something much smaller. If a relatively high share of the population has low susceptibility, the virus won’t have to infect such a large share of the population to achieve effective herd immunity.

The apparent differences in susceptibility across segments of the population may be the key to early herd immunity. We’ve known for a while that the elderly and those with pre-existing conditions are highly vulnerable. Otherwise, youth and good health are associated with low vulnerability.

Lemoine references a paper written by several epidemiologists showing that “variation in susceptibility” to Covid-19 “lowers the herd immunity threshold”:

“Although estimates vary, it is currently believed that herd immunity to SARS-CoV-2 requires 60-70% of the population to be immune. Here we show that variation in susceptibility or exposure to infection can reduce these estimates. Achieving accurate estimates of heterogeneity for SARS-CoV-2 is therefore of paramount importance in controlling the COVID-19 pandemic.”

The chart below is from that paper. It shows a measure of this variation on the horizontal axis. The colored, vertical lines show estimates of historical variation in susceptibility to historical viral episodes. The dashed line shows the required exposure for herd immunity as a function of this measure of heterogeneity.

Their models show that under reasonable assumptions about heterogeneity, the reduction in the herd immunity threshold (in terms of the percent infected) may be dramatic, to perhaps less than 20%.

Then there are these tweets from Marc Lipsitch, who links to this study:

“As an illustration we show that if R0=2.5 in an age-structured community with mixing rates fitted to social activity studies, and also categorizing individuals into three categories: low active, average active and high active, and where preventive measures affect all mixing rates proportionally, then the disease-induced herd immunity level is hD=43% rather than hC=1−1/2.5=60%.”

Even the celebrated Dr. Bergstrom now admits, somewhat grudgingly, that hereogeniety reduces the herd immunity threshold, though he doesn’t think the difference is large enough to change the policy conversation. Lipsitch also is cautious about the implications.

Augmented Heterogeneity

Theoretically, social distancing reduces the herd immunity threshold. That’s because infected but “distanced” people are less likely to come into close contact with the susceptible. However, that holds only so long as distancing lasts. John Cochrane discusses this at length here. Social distancing compounds the mitigating effect of heterogeneity, reducing the infected share of the population required for herd immunity.

Another compounding effect on heterogeneity arises from the variability of initial viral load on infection (IVL), basically the amount of the virus transmitted to a new host. Zvi Mowshowitz discusses its potential importance and what it might imply about distancing, lockdowns, and the course of the pandemic. In any particular case, a weak IVL can turn into a severe infection and vice versa. In large numbers, however, IVL is likely to bear a positive relationship to severity. Mowshowitz explains that a low IVL can give one’s immune system a head start on the virus. Nursing home infections, taking place in enclosed, relatively cold and dry environments, are likely to involve heavy IVLs. In fact, so-called household infections tend to involve heavier IVLs than infections contracted outside of households. And, of course, you are very unlikely to catch Covid outdoors at all.

Further Discussion

How close are we to herd immunity? Perhaps much closer than we thought, but maybe not close enough to let down our guard. Almost 80% of the population is less than 60 years of age. However, according to this analysis, about 45% of the adult population (excluding nursing home residents) have any of six conditions indicating elevated risk of susceptibility to Covid-19 relative to young individuals with no co-morbidities. The absolute level of risk might not be “high” in many of those cases, but it is elevated. Again, children have extremely low susceptibility based on what we’ve seen so far.

This is supported by the transmission dynamics discussed in this Twitter thread by Dr. Muge Cevik. She concludes:

“In summary: While the infectious inoculum required for infection is unknown, these studies indicate that close & prolonged contact is required for #COVID19 transmission. The risk is highest in enclosed environments; household, long-term care facilities and public transport. …

Although limited, these studies so far indicate that susceptibility to infection increases with age (highest >60y) and growing evidence suggests children are less susceptible, are infrequently responsible for household transmission, are not the main drivers of this epidemic.”

Targeted isolation of the highly susceptible in nursing homes, as well as various forms of public “distancing aid” to the independent elderly or those with co-morbidities, is likely to achieve large reductions in the effective herd immunity ratio at low cost relative to general lockdowns.

The existence of so-called super-spreaders is another source of heterogeneity, and one that lends itself to targeting with limitations or cancellations of public events and large gatherings. What’s amazing about this is how the super-spreader phenomenon can lead to the combustion of large “hot spots” in infections even when the average reproduction rate of the virus is low (R0 < 1). This is nicely illustrated by Christopher Moore of the Santa Fe Institute. Super-spreading also implies, however, that while herd immunity signals a reduction in new infections and declines in the actively infected population, “hot spots” may continue to flare up in a seemingly random fashion. The consequences will depend on how susceptible individuals are protected, or on how they choose to mitigate risks themselves.

Conclusion

I’ve heard too many casual references to herd immunity requiring something like 70% of the population to be infected. It’s not that high. Many individuals already have a sort of natural immunity. Recognition of this heterogeneity has driven a shift in the emphasis of policy discussions to the idea of targeted lockdowns, rather than the kind of indiscriminate “dumb” lockdowns we’ve seen. The economic consequences of shifting from broad to targeted lockdowns would be massive. And why not? The health care system has loads of excess capacity, and Covid infection fatality risk (IFR) is turning out to be much lower than the early, naive estimates we were told to expect, which were based on confirmed case fatality rates (CFRs).

The Opportunity of Skewed Coronavirus Transmission

30 Monday Mar 2020

Posted by in economic growth, Pandemic

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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.