Tag Archives: Seroprevalence

CDC Makes a Bum Lead Steer: Alternate Reality vs. The Herd

16 Sunday May 2021

Posted by in Herd Immunity, Pandemic

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Jordan Schachtel enjoyed some schadenfreude last week when he tweeted:

“I am thoroughly enjoying the White House declaring COVID over and seeing the confused cultists having a nervous breakdown and demanding the continuation of COVID Mania.”

It’s quite an exaggeration to say the Biden Administration is “declaring COVID over”, however. They’re backpedaling, and while last week’s CDC announcement on masking is somewhat welcome, it reveals more idiotic thinking about almost everything COVID: the grotesquely excessive application of the precautionary principle (typical of the regulatory mindset) and the mentality of “zero COVID”. And just listen to Joe Biden’s tyrannical bluster following the CDC announcement:

“The rule is now simple: get vaccinated or wear a mask until you do.

The choice is yours.”

Is anyone really listening to this buffoon?Unfortunately, yes. But there’s no federal “rule”, unless your on federal property; it constitutes “guidance” everywhere else. I’m thankful our federalist system still receives a modicum of respect in the whole matter, and some states have chosen their own approaches (“Hooray for Florida”). Meanwhile, the state of the pandemic looks like this, courtesy of Andy Slavitt:

False Assertions

The CDC still operates under the misapprehension that kids need to wear masks, despite mountains of evidence showing children are at negligible risk and tend not to be spreaders. Here’s some evidence shared by Phil Kerpen on the risk to children:

The chart shows the fatality risk by age (deaths per 100,000), and then under the assumption of a 97% reduction in that risk due to vaccination, which is quite conservative. Given that kind of improvement, an unvaccinated 9 year-old child has about the same risk as a fully vaccinated 30 year-old!

The CDC still believes the unvaccinated must wear masks outdoors, but unless you’re packed in a tight crowd, catching the virus outdoors has about the same odds as a piano falling on your head. And the CDC insists that two shots of mRNA vaccine (Pfizer or Moderna) are necessary before going maskless, but only one shot of the Johnson and Johnson vaccine, even though J&J’s is less effective than a single mRNA jab!

Other details in the CDC announcement are worthy of ridicule, but for me the most aggravating are the agency’s implicit position that herd immunity can only be achieved through vaccination, and its “guidance” that the unvaccinated should be dealt with coercively, even if they have naturally-acquired immunity from an infection!

Tallying Immunity

Vaccination is only one of several routes to herd immunity, as I’ve noted in the past. For starters, consider that a significant share of the population has a degree of pre-existing immunity brought on by previous exposure to coronaviruses, including the common cold. That doesn’t mean they won’t catch the virus, but it does mean they’re unlikely to suffer severe symptoms or transmit a high viral load to anyone else. Others, while not strictly immune, are nevertheless unlikely to be sickened due to protections afforded by healthy vitamin D levels or because they are not obese. Children, of course, tend to be fairly impervious. Anyone who’s had a bout with the virus and survived is likely to have gained strong and long-lasting immunity, even if they were asymptomatic. And finally, there are those who’ve been vaccinated. All of these groups have little or no susceptibility to the virus for some time to come.

It’s not necessary to vaccinate everyone to achieve herd immunity, nor is it necessary to reach something like an 85% vax rate, as the fumbling Dr. Fauci has claimed. Today, almost 47% of the U.S. population has received at least one dose, or about 155 million adults. Here’s Kerpen’s vax update for May 14.

Another 33 million people have had positive diagnoses and survived, and estimates of seroprevalence would add perhaps another 30 million survivors. Some of those individuals have been vaccinated unnecessarily, however, and to avoid double counting, let’s say a total of 50 million people have survived the virus. Some 35 million children in the U.S. are under age 12. Therefore, even if we ignore pre-existing immunity, there are probably about 240 million effectively immune individuals without counting the remaining non-susceptibles. At the low end, based on a population of 330 million, U.S. immunity is now greater than 70%, and probably closer to 80%. That is more than sufficient for herd immunity, as traditionally understood.

The Herd Immunity Threshold

Here and in the following section I take a slightly deeper dive into herd immunity concepts.

Herd immunity was one of my favorite topics last year. I’m still drawn to it because it’s so misunderstood, even by public health officials with pretensions of expertise in the matter. My claim, about which I’m not alone, is that it’s unnecessary for a large majority of the population to be infected (or vaccinated) to limit the spread of a virus. That’s primarily because there is great variety in individuals’ degree of susceptibility, social connections, aerosol production, and viral load if exposed: call it heterogeneity or diversity if you like. Variation across individuals naturally limits a contagion relative to a homogeneous population.

Less than 1% of those who caught the virus died, while the others recovered and acquired immunity. The remaining subset of individuals most vulnerable to severe illness was thus reduced over time via acquired immunity or death. This is the natural dynamic that causes contagions to slow and ultimately peter out. In technical jargon, the virus reproduction rate “R” falls below a value of one. The point at which that happens is called the “herd immunity threshold” (HIT).

A population with lots of variation in susceptibility will have a lower HIT. Some have estimated a HIT in the U.S. as low as 15% -25%. Ultimately, total exposure will go much higher than the HIT, perhaps well more than doubling exposure, but the contagion recedes once the HIT is reached. So again, it’s unnecessary for anywhere near the full population to be immune to achieve herd immunity.

One wrinkle is that CIVID is now likely to have become endemic. Increased numbers of cases will re-emerge seasonally in still-susceptible individuals. That doesn’t contradict the discussion above regarding the HIT rate: subsequent waves will be quite mild by comparison with the past 14 months. But if the effectiveness of vaccines or acquired immunity wanes over time, or as healthy people age and become unhealthy, re-emergence becomes a greater risk.

Sub-Herd Immunity

A further qualification relates to so-called sub-herds. People are clustered by geographical, social, and cultural circles, so we should think of society not as a singular “herd”, but as a collection of sub-herds having limited cross-connectivity. The following charts are representations of different kinds of human networks, from Nathan D. Grawe’s review of “The Rules of Contagion, by Adam Kucharski:

Sub-herd members tend to have more degrees of separation from individuals in other sub-herds than within their own sub-herd. The most extreme example is the “broken network” (where contagions could not spread across sub-herds), but there are identifiable sub-herds in all of the examples shown above. Less average connectedness across sub-herds implies barriers to transmission and more isolated sub-herd contagions.

We’ve seen isolated spikes in cases in different geographies, and there have been spikes within geographies among sub-herds of individuals sharing commonalities such as race, religious affiliation, industry affiliation, school, or other cultural affiliation. Furthermore, transmission of COVID has been dominated by “super-spreader” events, which tend to occur within sub-herds. In fact, sub-herds are likely to be more homogeneous than the whole of society, and that means their HIT will be higher than we might naively calculate based on higher levels of aggregation.

We have seen local, state, or regional contagions peak and turn down when estimates of total incidence of infections reach the range of 15 – 25%. That appears to have been enough to reach the HIT in those geographically isolated cases. However, if those geographical contagions were also concentrated within social sub-herds, those sub-herds might have experienced much higher than 25% incidence by the time new infections peaked. Again, the HIT for sub-herds is likely to be greater than the aggregate population estimates implied, The upshot is that some sub-herds might have achieved herd immunity last year but others did not, which explains the spikes in new geographic areas and even the recurrence of spikes within geographic areas.

Conclusion

It’s unnecessary for 100% of the population to be vaccinated or to have pre-existing immunity. Likewise, herd immunity does not imply that no one catches the virus or that no one dies from the virus. There will be seasonal waves, though muted by the large immune share of the population. This is not something that government should try to stanch, as that would require the kind of coercion and scare tactics we’ve already seen overplayed during the pandemic. People face risks in almost everything they do, and they usually feel competent to evaluate those risks themselves. That is, until a large segment of the population allows themselves to be infantalized by public health authorities.

Note: This post also appears on The American Reveille.

Auspicious COVID News for Thanksgiving

25 Wednesday Nov 2020

Posted by in Coronavirus, Herd Immunity

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There are some hints of good news on the spread of the coronavirus in a few of the “hot spots“ that developed this fall. This could be very good news, but it’s a bit too early to draw definitive conclusions.

The number of new cases plateaued in Europe a few weeks ago. Of course, Europe’s average latitude is higher than in most of the U.S., and the seasonal spread began there a little earlier. It makes sense that it might ebb there a bit sooner than in the U.S. as well.

In the U.S., cases shot up in the upper Midwest four to six weeks ago, depending on the state. Now, however, new cases have turned down in Iowa, Nebraska, North Dakota, South Dakota, and Wisconsin (first chart below), and they appear to have plateaued in Illinois, Kansas, Minnesota, and Missouri (second chart below, but ending a few days earlier). These are the hottest of the recent hot states.

These plateaus and declines were preceded by a decline in the growth rates of new cases around 10 days ago, shown below.

The timing of these patterns roughly correspond to the timing of the spread in other regions earlier in the year. It’s been suggested that after seroprevalence reaches levels of around 15% – 25% that individuals with new antibodies, together with individuals having an existing pre-immunity from other coronaviruses, is enough to bring the virus reproduction rate (R) to a value of one or less. That means a breach of the effective herd immunity threshold. It’s possible that many of these states are reaching those levels. Of course, this is very uncertain, but the patterns are certainly encouraging.

Deaths lag behind new infections, and it generally takes several weeks before actual deaths by date-of-death are known with any precision. However, we might expect deaths to turn down within two to three weeks.

Deaths by date-of-death are strongly associated with emergency room patients from three weeks prior who presented symptoms of COVID-like illness (CLI) or influenza-like illness ((ILI). The following chart shows CLI and ILI separately for the entire U.S. (ILI is the lowest dashed line), but the last few observations of both series, after a peak on November 15th, suggest a downturn in CLI + ILI. If the relationship holds up, actual U.S. deaths by date-of-death should peak around December 7th, though we won’t know precisely until early in the new year.

As a side note, it continues to look like the flu season will be exceptionally mild this year. See the next chart. That’s tremendous because it should take some of the normal seasonable pressure off health care resources.

So Happy Thanksgiving!

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Note: I saved all those charts over the last few days but lost track of the individual sources on Twitter. I’m too lazy and busy to go back and search through Twitter posts, so instead I’ll just list a few of my frequent sources here with links to recent posts, which are not necessarily apropos of the above: Don Wolt, Justin Hart, AlexL, The Ethical Skeptic, Aaron Ginn, and HOLD2.

Predicted November COVID Deaths

08 Sunday Nov 2020

Posted by in Pandemic, Public Health

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Reported COVID deaths do not reflect deaths that actually occurred in the reporting day or week, as I’ve noted several times. Here is a nice chart from @tlowdon on Twitter showing the difference between reported deaths and actual deaths for corresponding weeks. The blue bars are weekly deaths reported by the COVID Tracking Project. The solid orange bars are the CDC’s “provisional” deaths by actual week of death, which is less than complete for recent weeks because of lags in reporting. Still, it’s easy to see that reported deaths have overstated actual deaths each week since late August.

I should note that the orange bars represent deaths that involved COVID-19, though a COVID infection might not have actually killed them. This CDC report, updated on November 4th, shows the importance of co-morbidities, which in many cases are the actual cause of death according to pre-COVID, CDC guidance on death certificates.

Leading Indicators

Researchers have studied several measures in an effort to find leading indicators of COVID deaths. The list includes new cases diagnosed (PCR positivity) and the percentage of emergency room visits presenting symptoms of COVID-like illness (%CLI). These indicators are usually evaluated after shifting them in time by a few weeks in order to observe correlations with COVID deaths a few weeks later. Interestingly, @tlowdon reports that the best single predictor of actual COVID deaths over the course of a few weeks is the sum of the %CLI and the percentage of ER patients presenting symptoms of influenza-like illness (%ILI). Perhaps adding %ILI to %CLI strengthens the correlation because the symptoms of the flu and COVID are often mistaken for one another.

The chart below reproduces the orange bars from above representing deaths at actual dates of death. Also plotted are the %Positivity from COVID tests (shifted forward 2 weeks), %CLI (3 weeks), the %ILI (3 weeks), and the sum of %CLI and %ILI (3 weeks, the solid blue line). My guess is that %ILI contributes to the correlation with deaths mainly because %ILI’s early peak (which occurred in March) led the peak in deaths in April. Otherwise, there is very little variation in %ILI. That might change with the current onset of the flu season, but as I noted in my last post, the flu has been very subdued since last winter.

What About November?

So where does that leave us? The chart above ends with our leading indicator, CLI + ILI, brought forward from the first half of October. What’s happened to CLI + ILI since then? And what does that tell us to expect in November? The chart below is from the CDC’s web site. The red line is %CLI and the yellow line is %ILI. The sum of the two isn’t shown. However, there is no denying the upward trend in CLI, though the slope of CLI + ILI would be more moderate.

As of 10/31, CLI + ILI has increased by almost 40% since it’s low in early October. If the previous relationship holds up, that implies an increase of almost 40% in actual weekly COVID deaths from about 4,000 per week to about 5,500 per week by November 21 (a little less than 800 per day).

FiveThirtyEight has a compilation of 13 different forecast models with projections of deaths by the end of November. The estimate of 5,500 per week by November 21, or perhaps slightly less per week over the full month of November, would put total COVID deaths at the top of the range of the MIT, UCLA, Iowa State, and University of Texas models, but below or near the low end of ranges for eight other models. However, those models are based on reported deaths, so the comparison is not strictly valid. Reported deaths are still likely to exceed actual deaths by the end of November, and the actual death prediction would be squarely in the range of multiple reported death predictions. That reinforces the expectation an upward trend in actual deaths.

Third Wave States

States in the upper Midwest and upper Mountain regions have had the largest increases in cases per capita over the past few weeks. Using state abbreviations, the top ten are ND, SD, WI, IA, MT, NE, WY, UT, IL, and MN, with ID at #11 (according to the CDC’s COVID Data Tracker). One factor that might mediate the increase in cases, and ultimately deaths, is the possibility of early herd immunity: in the earlier COVID waves, the increase in infections abated once seroprevalence (the share of the population with antibodies from exposure) reached a level of 15% to 25%.

Unfortunately, estimates of seroprevalence by state are very imprecise. Thus far, reliable samples have been limited to states and metro areas that had heavy infections in the first and second waves. One rule of thumb, however, is that seroprevalence is probably less than 10x the cumulative share of a population having tested positive. To be very conservative, let’s assume a seroprevalence of four times cumulative cases. On that basis, half the states in the “top ten” listed above would already have seroprevalence above 15%. Those states are ND, SD, WI, IA, and NE. The others are mostly in a range of 12% to 15%, with MI coming in the lowest at about 9%.

This gives some cause for optimism that the wave in these states and others will abate fairly soon, but there are a number of uncertainties: first, the estimates of seroprevalence above, while conservative, are very imprecise, as noted above; second, the point at which herd immunity might cause the increase in new cases to begin declining is real guesswork (though we might have confirmation in a few states before long); third, we are now well into the fall season, with lower temperatures, lower humidity, less direct sunlight, and diminishing vitamin D levels. We do not have experience with COVID at this time of year, so we don’t know whether the patterns observed earlier in the year will be repeated. If so, new cases might begin to abate in some areas in November, but that probably wouldn’t be reflected in deaths until sometime in December. And if the flu comes back with a corresponding increase in CLI + ILI, then we’d expect further increases in actual deaths attributed to COVID. That is only a possibility given the weakness in flu numbers in 2020, however.

Closing Thoughts

I was excessively optimistic about the course of the pandemic in the U.S. in the spring. While this post has been moderately pessimistic, I believe there are reasons to expect fewer deaths than previous relationships would predict. We are far better at treating COVID now, and the vulnerable are taking precautions that have reduced their incidence of infections relative to younger and healthier cohorts. So if anything, I think the forecasts above will err on the high side.

False Positives, False Cases, False Deaths

14 Monday Sep 2020

Posted by in Coronavirus, Pandemic

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The tremendous increase in testing for COVID-19 (C19) this summer was associated with an increase in cases. Most of these tests were so-called PCR tests with samples collected via deep nasal swabs. More testing did not fully explain the increased case load, but false positives (FPs) still accounted for a substantial share. That’s especially true in light of the decline in positivity rates, which reflected a decline in the actual prevalence of active infections. FPs also account for a substantial share of the deaths attributed to COVID, which are obviously cases of false attribution. If a test for C19 is positive, it will be listed on the death certificate.  

COVID Case Inflation

The exaggeration of confirmed cases due to FPs is more substantial as the prevalence of active infection declines. That’s because the share of true positives in the tested population declines, while the share of false positives must rise due to the greater share of uninfected individuals in the population.

Now, as the contagion is waning in former hot spots, there is a danger that FPs create the impression of persistence in the case counts. That’s costly not just for those incorrectly diagnosed, but also in terms of medical resources, for communities subject to excessive public intervention, such as inappropriate lockdowns, and in terms of the fear promoted by these inaccuracies.

FPs are extremely disruptive when testing is relied upon in critical situations such as health care staffing, or even among sports teams. For example, at the University of Arizona, out of 25 positive tests on September 3, only 10 were confirmed as positives in later tests. The NFL has also had its share of false positives. 

Lax Testing Standards

There is evidence that testing standards under CDC guidance are so broad that a large number of inactive, non-infectious cases are being flagged as positives (see the chart above for the intuition, as well as the graphic at the bottom of this post). The tests sometimes amount to a coin flip when it comes to evaluating positives; some of the positives might even come from non-novel coronaviruses such as the common cold! This paper by Andrew N. Cohen, Bruce Kessel, & Michael G. Milgroom – CKM) questions the guidance of public health authorities on testing more generally. From the abstract (my emphasis):

“Unlike previous epidemics, in addressing COVID-19 nearly all international health organizations and national health ministries have treated a single positive result from a PCR-based test as confirmation of infection, even in asymptomatic persons without any history of exposure. …  positive results in asymptomatic individuals that haven’t been confirmed by a second test should be considered suspect.”

False Positive Math

When I wrote about “The Scourge of False Positives” in July. I noted that a test specificity of 95% implies that 5% of uninfected individuals will falsely test positive. Unfortunately, that still produces a huge number of FPs when testing is broad. That’s NOT a good reason to avoid broad testing; it just means that positive tests should be confirmed by another test. (In this case, two tests with the same specificity reduce a 5% false positive rate to 0.25%. That’s why fast, cheap tests are necessary for confirmation.

Again, exaggerated case counts due to FP’s become more severe as a contagion wanes. That’s because FPs become an increasingly large share of positive test results and overstate the persistence of the virus. If active infections fall to 1% of 750,000 daily tests, or 7,500 true cases, the 5% specificity implies 37,125 FPs: true positives would be only 17% of positive cases. Much worse than a coin flip! And again, which cases are infectious?

How Bad Are FPs, Really?

This recent research, also authored by CKM, explains the reasons why FPs are usually an issue in the real world, despite the tests’ reportedly perfect reactivity to anything other than the virus’ genetic fragments. CKM find that the median FP rate in their sample of “tests of tests” was 2.3%. That means 23 out of every 1,000 uninfected people tested will test positive.

If that seems small to you, suppose the true prevalence of active infection in a population is 4%. If 1,000,000 people are tested and there are no false negatives (unlikely), then 40,000 infected people will be identified by the test. However, another 22,000 uninfected people will also test positive ((1,000,000 – 40,000 infected) x 0.023). That means the number of positive tests will be inflated by 55%. They’ll all receive some form of treatment or ordered into quarantine. Expanded Testing and FPs This summer, the volume of daily tests increased from about 150,000 a day in early April to more than 750,000 a day in July. That’s a 400% increase, but the true prevalence of active infection in the expanded test population during the summer was almost certainly lower than in the spring. Suppose active infections fell from 10% of the test population in the spring to 5% in the summer. That means the daily number of “true positives” would have risen from 15,000 to 35,000 in the expanded test population (and again I assume no false negatives for simplicity). The number of FPs, however, would have risen from 3,105 to 16,445. Therefore, FPs would have accounted for 40% of the increase in “confirmed” cases between spring and summer.

False COVID Deaths

FPs are also inflating COVID death counts. PCR tests are routinely given at hospital admission for any cause, and even after sudden death, especially as the availability of tests increased late in the spring. This subset of the tested population will certainly have its share of FPs. If such a patient dies, regardless of underlying cause, it might well be attributed to COVID-19 as it will still appear on the death certificate. The same has occurred in the case of traffic fatalities, suicides, and other sudden deaths.

Antibody Tests

The FP problem also plagues tests of seroprevalence, which determine whether an individual has had the virus or is cross-protected against the virus by antibodies acquired via non-novel coronavirus infections. The consequences of these antibody FPs can be serious as well, because it means a positive test might not ensure immunity. As the exposed share of the population increases, however, the FP share of antibody tests is diminished.

Conclusion

As long as testing is required, dealing with FPs (and false negatives, of course) requires repeated testing, as CKM state unequivocally. And the tests must be fast to be of any use. The current testing regime must be overhauled to prevent false positives from costly impositions on the lives of uninfected patients, consuming unnecessary medical resources, making unrealistic assessments of cases and deaths, and unnecessary suspensions of normal human social activity and liberty.

COVID Immunity, Herd By Herd

01 Tuesday Sep 2020

Posted by in Coronavirus, Herd Immunity

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Too many public health authorities remain in denial, but epidemiologists are increasingly convinced that heterogeneity implies a coronavirus herd immunity threshold (HIT) that is greatly reduced from traditional models and estimates. HIT is the share of the population that must be infected before the contagion begins to recede (and the transmission ratio R falls below one). Traditional models, based on three classes of individuals (Susceptibles, Infectives, and Recovered – SIR), predict a HIT of 60% or more. However, models that incorporate variation in susceptibility, transmissibility, and occupational or social behavior reduce the HIT substantially. Many of these more nuanced models show that the HIT could be in a range of just 15% to 25%. If that is the case, many regions are already there!

For background, I refer you to the first post I wrote about heterogeneity in late March, more detailed thoughts from early May, examples and more information on the literature later in May. I’ve referenced it repeatedly in other posts since then. And now, more than five months later, even the slow kids at the New York Times have noticed. The gist of it: if not everyone is equally susceptible, for example, a smaller share of the population needs to be “immunized via infection” to taper the spread of the virus.

Some supporting evidence appears in the charts below, courtesy of Kyle Lamb on Twitter. The first chart shows a seven-day average of C19 cases per million of population for ten states that reached an estimated 10% antibodies. These antibodies confer at least short-term immunity against C19. Most of these states saw cases/m climb at least through the day when the 10% level was reached, though Rhode Island appears to have been an exception.

The second chart shows the seven-day average of cases/m in the same states starting seven days after the 10% immunity level was reached. I’d prefer to see the days in the interim as well, but the changes in trend are still noteworthy. All of these states except Louisiana had a downturn in the seven-day average of new cases within a few weeks of breaching the 10% infection level (Louisiana had distinct and non-coincident outbreaks in different parts of the state). These striking similarities suggest that things turned as the infection level reached 15% or more, consistent with many of the epidemiological models incorporating heterogeneity.

Next, take a look at the states in which C19 surged most severely this summer. The new cases are not moving averages, so the charts are not quite comparable to those above. However, the peaks seem to occur prior to the breach of the 15% infection level.

Speculation about early herd immunity has been going on for several months with respect to various countries and even more “micro” settings such as cruise ships and military vessels, where populations are completely isolated. Early on, this “early” herd immunity was discussed under the aegis of “immunological dark matter”, but we know now that T-cell immunity has played an important role. In any case, anti-body expression (or seroprevalence) at around 20% has been linked to reversals in C19 cases and deaths in several countries. As Yinon Weiss notes, New York City and Stockholm were both C19 hotspots in the spring, both have seen deaths decline to low levels, and they have little in common in terms of public health policy. London as well. The one thing they share are similar levels of seroprevalence.

An important qualification is that herd immunity is not relevant at high levels of aggregation. That is, herd immunity won’t be achieved simultaneously in all regions. The New York City metro area might have reached its HIT in April, but Florida (or perhaps only Miami) might have reached a HIT in July. Many areas of the Midwest probably still aren’t there.

In the absence of a new mutation of C19, the final proof of herd immunity in many of the former hotspots will be in the fall and winter. We should expect at least a few cases in those areas, but if there are more intense contagions, they should be confined to areas that have not yet seen a level of seroprevalence near 15%.