Category Archives: Risk

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).

Beepocamyth: Neonics Don’t Kill the Buzz

08 Saturday Feb 2020

Posted by in Agriculture, Biodiversity, Environment, Risk

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False claims that a certain class of pesticides threaten the world’s bee populations are commonplace, and we hear the same more recently about various species of birds. The origins of the “beepocalypse” rumor were not based on scientific evidence, but on a narrative that developed among environmental activists in response to a phenomenon called Colony Collapse Disorder (CCD) that began around 2006, roughly a decade after neonicotinoid pesticides (so-called neonics) replaced earlier, more toxic compounds as the pesticides of choice. But Jon Entine writes at The Genetic Literacy Project:

“What causes CCD? It still remains a mystery, in part. But researchers turned up historical examples of CCD-like bee die offs across the globe over hundreds of years, well before the introduction of pesticides, but activist groups would have none of it.”

CCD essentially tapered off by 2009, according to Entine, and the number of honeybee colonies are higher now that before the introduction of neonics. See Entine’s charts at the link showing changes in honeybee populations over time. In Australia, where the use of neonics has been especially heavy, bee populations have grown steadily and remain quite healthy.

Entine’s article provides a nice summary of the real and imagined threats to the world’s bee populations as well as distorted claims associated with normal winter die-offs. He provides a number of useful links on these subjects, and he summarizes research showing the lack of any real threat to bees from neonics:

“Over the past seven years, there have been a flood of studies about the potential impact of neonics on bees. Many small-scale, forced-feeding studies that generally overdosed bees with neonics found various negative effects; not a surprise, many entomologists have said, as they do not replicate real world impacts.

In contrast, a multitude of large-population field studies—the ‘gold-standard’ of bee research—have consistently demonstrated there are no serious adverse effects of neonic insecticides on honeybees at the colony level from field-realistic neonic exposure. …

By last year, even the Sierra Club—for years one of the leading proponents of the honeybee Armageddon narrative—was backpeddling, writing: ‘Honeybees are at no risk of dying off. While diseases, parasites and other threats are certainly real problems for beekeepers, the total number of managed honeybees worldwide has risen 45% over the last half century.'”

Then Entine turns his attention to another front in the war on pesticides: a Canadian study in which white-crowned sparrows were force-fed a mixture of seeds and pesticide via gavage — ie, through a tube:

“Only sparrows force-fed the highest dosage were affected, and then only temporarily. They stopped eating, quickly lost body weight and fat, became disoriented and paused their migratory flight—all after tube full of chemicals was forced down their throat and into their stomach. … That said, within a few days of what was likely a trauma-inducing experience, all recovered completely and continued their migration normally.”

Yet the authors reported that the very existence of some wild birds is threatened by neonics, and the media, always eager to report a crisis, ran with it.

Paul Driessen also describes the junk science underlying misleading narratives regarding pesticide use. It is a driving force behind legislation in the House and Senate that would ban the use of neonics in National Wildlife Refuges, where the Fish & Wildlife Service permits farmers to grow various crops. Driessen has some advice for Rep. Nydia Velázquez (D-NY), a sponsor of the legislation:

“She should also recognize potentially serious threats to bees, wildlife, soils, waters and plants in refuges from sources that she, her colleagues and their environmentalist and media allies routinely ignore: solar panels, for instance. Not only do they blanket many thousands of acres, allowing little to grow beneath or between them. They can also leach cadmium and other metals into soils and waters. They should no longer be built near wildlife refuges.

Finally, it’s not just bees. It’s also birds, and bats – which are already being killed and even eradicated in many areas by America’s 56,000 wind turbines. Imagine what Green New Deal turbine numbers would do.”

More perspective is offered in this excellent six-part (and growing?) “Pesticides and Food” series (all at the link) by Kayleen Schreiber:

  1. Has pesticide use decreased? Yes, dramatically in per capita and per unit of output.
  2. Have pesticides improved?  Yes, with dramatically lower toxicity, improved biodegradability, and lower use rates.
  3. How dangerous is glyphosate (a herbicide)? Not very. Covered in my last post. Glyphosate is only 1/10th as toxic as caffeine.
  4. How do organic pesticides compare to synthetic pesticides? It’s a mixed bag, with great variability across both classes. Organics are more toxic in some applications, and synthetics are more toxic in others.
  5. Soil health: Are synthetic pesticides more sustainable than “natural” organics?  Organics require more tillage, which creates sustainability problems.
  6. Pesticide residues — Something to worry about? The USDA finds little residue in its testing, with extremely low detection rates for both organics and synthetics.

 

 

Certainty Laundering and Fake Science News

05 Wednesday Dec 2018

Posted by in Global Warming, Risk, Science

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Intriguing theories regarding all kinds of natural and social phenomena abound, but few if any of those theories can be proven with certainty or even validated at a high level of statistical significance. Yet we constantly see reports in the media about scientific studies purporting to prove one thing or another. Naturally, journalists pounce on interesting stories, and they can hardly be blamed when scientists themselves peddle “findings” that are essentially worthless. Unfortunately, the scientific community is doing little to police this kind of malpractice. And incredible as it seems, even principled scientists can be so taken with their devices that they promote uncertain results with few caveats.

Warren Meyer coined the term “certainty laundering” to describe a common form of scientific malpractice. Observational data is often uncontrolled and/or too thin to test theories with any degree of confidence. What’s a researcher to do in the presence of such great uncertainties? Start with a theoretical model in which X is true by assumption and choose parameter values that seem plausible. In all likelihood, the sparse data that exist cannot be used to reject the model on statistical grounds. The data are therefore “consistent with a model in which X is true”. Dramatic headlines are then within reach. Bingo!

The parallel drawn by Meyer between “certainty laundering” and the concept of money laundering is quite suggestive. The latter is a process by which economic gains from illegal activities are funneled through legal entities in order to conceal their subterranean origins. Certainty laundering is a process that may encompass the design of the research exercise, its documentation, and its promotion in the media. It conceals from attention the noise inherent in the data upon which the theory of X presumably bears.

Another tempting exercise that facilitates certainty laundering is to ask how much a certain outcome would have changed under some counterfactual circumstance, call it Z. For example, while atmospheric CO2 concentration increased by roughly one part per 10,000 (0.01%) over the past 60 years, Z might posit that the change did not take place. Then, given a model that embodies a “plausible” degree of global temperature sensitivity to CO2, one can calculate how different global temperatures would be today under that counterfactual. This creates a juicy but often misleading form of attribution. Meyer refers to this process as a way of “writing history”:

“Most of us are familiar with using computer models to predict the future, but this use of complex models to write history is relatively new. Researchers have begun to use computer models for this sort of retrospective analysis because they struggle to isolate the effect of a single variable … in their observational data.”

These “what-if-instead” exercises generally apply ceteris paribus assumptions inappropriately, presuming the dominant influence of a single variable while ignoring other empirical correlations which might have countervailing effects. The exercise usually culminates in a point estimate of the change “implied” by X, without any mention of possible errors in the estimated sensitivity nor any mention of the possible range of outcomes implied by model uncertainty. In many such cases, the actual model and its parameters have not been validated under strict statistical criteria.

Meyer goes on to describe a climate study from 2011 that was quite blatant about its certainty laundering approach. He provides the following quote from the study:

“These question cannot be answered using observations alone, as the available time series are too short and the data not accurate enough. We therefore used climate model output generated in the ESSENCE project, a collaboration of KNMI and Utrecht University that generated 17 simulations of the climate with the ECHAM5/MPI-OM model to sample the natural variability of the climate system. When compared to the available observations, the model describes the ocean temperature rise and variability well.”

At the time, Meyer wrote the following critique:

“[Note the first and last sentences of this paragraph] First, that there is not sufficiently extensive and accurate observational data to test a hypothesis. BUT, then we will create a model, and this model is validated against this same observational data. Then the model is used to draw all kinds of conclusions about the problem being studied.

This is the clearest, simplest example of certainty laundering I have ever seen. If there is not sufficient data to draw conclusions about how a system operates, then how can there be enough data to validate a computer model which, in code, just embodies a series of hypotheses about how a system operates?”

In “Imprecision and Unsettled Science“, I wrote about the process of calculating global surface temperatures. That process is plagued by poor quality and uncertainties, yet many climate scientists and the media seem completely unaware of these problems. They view global and regional temperature data as infallible, but in reality these aggregated readings should be recognized as point estimates with wide error bands. Those bands imply that the conclusions of any research utilizing aggregate temperature data are subject to tremendous uncertainty. Unfortunately, that fact doesn’t get much play.

As Ashe Schow explains, junk science is nothing new. Successful replication rates of study results in most fields are low, and the increasing domination of funding sources by government tends to promote research efforts supporting the preferred narratives of government bureaucrats.

But perhaps we’re not being fair to the scientists, or most scientists at any rate. One hopes that the vast majority theorize with the legitimate intention of explaining phenomena. The unfortunate truth is that adequate data for testing theories is hard to come by in many fields. Fair enough, but Meyer puts his finger on a bigger problem: One simply cannot count on the media to apply appropriate statistical standards in vetting such reports. Here’s his diagnosis of the problem in the context of the Fourth National Climate Assessment and its estimate of the impact of climate change on wildfires:

“The problem comes further down the food chain:

  1. When the media, and in this case the US government, uses this analysis completely uncritically and without any error bars to pretend at certainty — in this case that half of the recent wildfire damage is due to climate change — that simply does not exist
  2. And when anything that supports the general theory that man-made climate change is catastrophic immediately becomes — without challenge or further analysis — part of the ‘consensus’ and therefore immune from criticism.”

That is a big problem for science and society. A striking point estimate is often presented without adequate emphasis on the degree of noise that surrounds it. Indeed, even given a range of estimates, the top number is almost certain to be stressed more heavily. Unfortunately, the incentives facing researchers and journalists are skewed toward this sort of misplaced emphasis. Scientists and other researchers are not immune to the lure of publicity and the promise of policy influence. Sensational point estimates have additional value if they support an agenda that is of interest to those making decisions about research funding. And journalists, who generally are not qualified to make judgements about the quality of scientific research, are always eager for a good story. Today, the spread of bad science, and bad science journalism, is all the more virulent as it is propagated by social media.

The degree of uncertainty underlying a research result just doesn’t sell, but it is every bit as crucial to policy debate as a point estimate of the effect. Policy decisions have expected costs and benefits, but the costs are often front-loaded and more certain than the hoped-for benefits. Any valid cost-benefit analysis must account for uncertainties, but once a narrative gains steam, this sort of rationality is too often cast to the wind. Cascades in public opinion and political momentum are all too vulnerable to the guiles of certainty laundering. Trends of this kind are difficult to reverse and are especially costly if the laundered conclusions are wrong.