Post #1201: COVID-19 trend to 8/2/2021: Too soon to say that growth in new cases is slowing


Most states other than Florida have reported new numbers for COVID-19 case counts.  With that, there was about a 50% increase in new cases over the last seven days.  The U.S. now averages 26.5 new cases / 100K /day.

Data source for this and other graphs of new case counts:  Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 8/3/2021, from”  The NY Times U.S. tracking page may be found at

I think I see a bit of a downward bow in that curve.  That is, some slowing of the rate of growth of new cases.  Maybe, maybe not.

On the one hand, it’s premature to say anything until Florida reports in, as they currently have something like one-fifth of U.S. new cases.  My gap-fill algorithm isn’t smart enough to mimic the upward trend in cases in Florida, so the rate you’re seeing assumes that Florida’s new cases rate leveled off over the weekend.  That’s probably an understatement of reality.

On the other hand, if we date the real start of this wave to roughly 6/29/2021, we’ve been in this ultra-high-growth scenario for five full weeks now.  Seems like we should be about due for some slowdown.  Even given the lag between infection and full reporting, at some point, the gravity of the situation has to start sinking in and people will start to protect themselves.

On the other, other hand, if history is a guide, a lot of people in authority won’t get serious until the ICUs are full.  So we haven’t seen a whole lot of razor-sharp guidance from (e.g.) states.  To the contrary, it seems like a lot of places, including Florida, are doing their best to make it seem like this is still no big deal.  Substituting spin for action while offering lukewarm guidance regarding COVID-19 hygiene.

On the bright side, at the rate things are going, it won’t be long before that strategy doesn’t work any more.  Once you start storing bodies in refrigerated trucks, it’s hard to pretend that the situation is under control.  So, as you see those stories proliferate, just realize that this is how public health policy works in the U.S. these days.  Each such story brings us closer to the point where states start to take action.

It’s just classic crisis management.  We wait until it’s a crisis.  Then we manage it.

Just to track how fast things are moving, this wave is now clearly visible as the second-worst U.S. wave on record.  That’s a change from just three days ago.

Here’s how it looked three days ago:

Here’s how it looks today.  No guide line needed.

There’s really not a lot else to say.

I’ll update my 50-states graph, just because.  That’s Louisiana at the top, and Florida close behind.

And, like clockwork, now that Louisiana’s hospitals are overflowing, the Governor had decided to act, reinstating their mask mandated yesterday.  By contrast, Florida is still being Florida.  They are led, after all, by a governor whose most profound policy response to COVID-19 so far was to propose a constitutionally-protected right to party.

By eye, it seems like a given that this wave is destined to be worse than the U.S. winter wave.  Particularly when I look at my “hysteresis” graph, to see how far the U.S. public’s reaction continues to lag behind reality.  This is updated to 8/1/2021:

Source:  Mask data from Carnegie-Mellon COVID Delphi project.  Case count data calculated from:  The New York Times. (2021), reference given above.

Consistent with that remarkable lack of response, here’s my God-as-cosmic-hairdresser graph.  As if some great power has combed out what was a tangle of state lines.  Even now, the only strand that’s clearly visibly out-of-alignment is Missouri — the orange line about sixth from the top.  Otherwise, it surely appears that case growth is more-or-less unconstrained everywhere.  That’s what makes them all line up.

And so, while we’re not at crisis levels of new cases in the majority of the U.S., it surely seems like we’ll be there in another couple of weeks.  And nothing much is changing to stop that from happening.

Formally, the projection looks like this today, given where we are and the rate of growth over the past seven days.  Just a bit over two weeks now until we top the peak new case rate for the U.S. third (winter) wave.

Post #1200: Lethal dose testing and a takeaway from the Provincetown, MA outbreak.

“In general with respiratory viruses, the outcome of infection – whether you get severely ill or only get a mild cold – can sometimes be determined by how much virus actually got into your body and started the infection off. It’s all about the size of the armies on each side of the battle, a very large virus army is difficult for our immune systems army to fight off.

Source:  Professor Wendy Barclay, Imperial College, London, quoted in this article.

Sometimes I get the feeling that people really don’t quite understand how vaccines work.  Or how viral infections work.  Or what risk means.

That’s why I’m starting off with this quote.  If you can grasp that quote, then you will understand why a vaccine isn’t a free pass to engage in any behavior.  A vaccine gives our “immune systems army” a leg up.  If you manage to give the virus an even bigger leg up, by upping your exposure, you can more than offset the benefit of the vaccine.

To be clear, people seem to act as if vaccines are magic, and that if you are vaccinated, you have a low risk of infection independent of how you behave Or perhaps a better word would be “binary”.  They act as if, once you are vaccinated, you’re good to go. No matter what you do.

And I’m just here to say, that just ain’t so.  That is, in fact, wrong.

What COVID-19 vaccine does is speed up and generally improve your immune system’s response to the virus.  This reduces your risk that a given dose of virus will be able to replicate out-of-control for long enough to cause a noticeable infection.  In particular, it reduces your risk that a given dose of virus will replicate so much that it causes a serious infection.

If you change your circumstances enough, and up your exposure to the virus enough, you can more-than-offset that benefit of vaccination.  The upshot is that if you use vaccinated status as an excuse to spend hours in crowded, noisy bars, well, guess what.  You might actually be at higher risk of infection that if you’d remained unvaccinated and didn’t hang around in bars.

I went over this back in January, in response to the question “If I’m vaccinated, do I still have to wear a mask?”  (Post #959).  But since nobody is going to go back and read old blog posts, I think this is worth re-phrasing, particularly in light of the Provincetown MA outbreak.

But this time, I’m taking a different tack.

Let me start by discussing lethal dose testing of viruses.

Lethal dose testing.

What exactly happens when you get infected with a virus?

The best way to describe it is that when a virus invades your body, it sets off a race between viral replication on the one hand, and viral destruction by your antibodies and the rest of your immune system on the other hand. 

If you start with very few virus particles, and you already have antibodies to that virus circulating in your system, then you’ve skewed the race so that your immune system is likely to win.  And you get to keep on living.  At the extreme, the race is so one-sided that you have an asymptomatic infection.  Your immune system swats the virus down without even triggering normal symptoms of an infection.

And, to be clear, a typical estimate is that 40% of COVID-19 infections are completely asymptomatic.  (Versus, say, about 16 percent of common flu infections.)  In the extreme, extreme case, you might kill off the virus so quickly that no testing will ever show you were infected.  You might not even develop enough of the antibodies signalling past infection that blood test will reveal the presence of a past mild infection.

By contrast, if you start with a heavy dose of the virus and no antibodies circulating in your system, then the race is skewed in favor of the virus.  It has a big head start before your body can start fighting it.  And in that situation, you get sick and maybe you don’t get to keep on living.

Obviously, this abstracts from all the person-level variations that may matter.   Older people famously have a lower immune response when in comes to fighting infection.  Antibodies have some crossover, so (e.g.) exposure to related diseases might allow some of your existing antibodies to flag COVID-19 for destruction.  And, just, in general, people may vary.  I’m abstracting away from all of that.

Note that two things matter: 

One is the readiness of your system to recognize and take on that particular virus (your existing antibodies to that virus).  By exposing you to key proteins found on the surface of COVID-19, the mRNA vaccines we are currently using prime your immune system with antibodies that will attach to COVID-19 and flag it for destruction. And so, when the virus shows up, you’ve got a jump-start on fighting it.  (Your body also has the “memory” of those proteins and so can rapidly ramp up production of additional antibodies.)

The second is the amount of your exposure to the virus — the amount of virus you manage to inhale.  If you managed to get a very small dose, it’ll take a while before the virus can replicate to dangerous levels.  By contrast, if you inhaled a massive number of viral particles at a one go, then the virus starts the race with the upper hand.

(In fact, for various viral diseases, scientists estimate the “minimum infective dose”, which is the smallest number of  viral particles the typical person must inhale to trigger infection.  This can be as few as dozen or so particles for some diseases.  I’ve seen vague estimates of about 100 particles for COVID-19, but I have not tracked down any definitive study of that).

Now you’re ready for the concept of lethal dose testingAnd in particular, lethal dose testing of viruses that typically don’t cause death.  Because, the fact of the matter is, if you give an animal a large enough dose of some infectious virus, you can guarantee that the virus wins the race, and that the animal dies of the infection.  Even if that virus isn’t typically lethal at normal exposure levels.

And so, all ethical concerns aside, it’s a common laboratory practice to determine the the amount of virus it takes to kill (say) half of the exposed animals (“LD50”) or the minimum amount it takes to kill all of them (LD100).  (The LD here is, I think, lethal dose.)

I’m not going to go into that, except to say that the practice exists, is considered normal, and is protested by animal rights advocates.  In fact, it’s plausible that your flu vaccine was tested, in part, by lethal dose testing, as in this bit of research on mice.

None of that particularly matters here.  All that matters is that you understand that there is plausibly a dose-response relationship in viral infections.  So much so that if you challenge animals with a big enough dose of a virus that’s typically not lethal, you can kill them.  Even if they are otherwise healthy. And in some cases, even if they are vaccinated.  Just by giving that virus a big enough head start over the animal’s immune system.

The upshot is that if you change your behavior in such a way as to give yourself a bigger dose of COVID-19, the plausible response is that you’re more likely to get infected. 

That’s obviously true if you’re not vaccinated.  And that’s also true if you are vaccinated.  It’s just not obvious to most people.


When a clinical trial showed that the Pfizer vaccine was 91% effective, what did that mean, exactly?

In a nutshell, it meant that for two groups with equal levels of exposure to the virus, the vaccinated group only had 9% as many symptomatic infections as the unvaccinated group.

The key phrase there is in italics.  Much of the point of the entire randomized double-blind trial method was to ensure that that key phrase was true, to within some small random error.

Let me outline the COVID-19 vaccine clinical trial method from this scholarly publication , more-or-less the same as in this scholarly publication, putting key elements in boldface.

To test the vaccine, they randomly assigned volunteers to receive either the vaccine or a placebo.  Because half got the placebo, the participants carried on with their lives as they had been, including maintaining mask, social distancing, and other COVID hygiene.  None of them could count on becoming immune.

Then — and only then — did researchers count the number of people who showed up with symptoms and tested positive for COVID-19.  They found that there were just over 10 symptomatic, diagnosed COVID infections in the placebo group for every one in the vaccine group.  From that, they concluded that the vaccine reduced symptomatic COVID infections by 91%, relative to the placebo group, while both groups maintained existing COVID-19 hygiene and existing exposure levels.

And that’s what they mean by 91% effective. 

Please note how much this estimate of vaccine effectiveness depends on behavior.  Given equal behavior in both groups, researchers found only 9% as many COVID-19 infections in the vaccinated group than in the placebo group.

If you give the vaccine to a group that has a much higher exposure to the virus, you’re going to get more infections that you’d expect, based on the clinical trial results.  This is exactly what happened to the measured efficacy of the Chinese vaccine.  Under research conditions, in a randomized controlled trial, the vaccine was 75% effective.  In the real world, it was more like 50%.  That was attributed to giving the vaccine to a heavily-exposed population (health care workers).

And, guess what?  If you start to do things that greatly increase your exposure to COVID-19, you’re going to be the equivalent of those Chinese health care workers.

Note that the CDC initially told vaccinated individuals to keep their masks on and keep up other aspects of COVID-19 hygiene.  Why?  At that time, there was a lot of COVID-19 still circulating in the community.  If you got vaccinated, and dropped all hygiene, you (at least partially) offset the benefits of the vaccine, in terms of your overall risk of getting an infection.

CDC only told the vaccinated to drop their hygiene after levels of circulating virus had fallen to very low levels.

And now, with higher levels of virus circulating again, it’s completely unsurprising that the CDC has once again suggested that vaccinated individuals wear a mask in indoor public spaces.  At least where there’s a lot of virus about.

It’s not even hard to figure out the relative risk.  Crudely, at least.  If the vaccine is about 90% effective, your risk of infection, unvaccinated, when there are 2 new cases / 100K /day, is roughly the same as your risk of infection, vaccinated, and there are 20 new cases / 100K / day.

It’s really not rocket science, is it?

The upshot is that vaccination reduces your absolute chance of symptomatic COVID-19 infection by 91% if and only if you maintain your pre-vaccine level of COVID hygiene.  And if the amount of virus in circulation in the community remains constant.

In other words, your risk of getting infected drops by 91%, when you get vaccinated, if and only if your exposure remains the same as it was before you got vaccinated.  But if you couple that vaccination to an increase in risk-taking behavior, you could easily offset (some, most, or more-than-all of) that 91% reduction.  E.g., if you go from being a shut-in, pre-vaccine, to hanging around maskless in bars, post-vaccine, you may actually have upped your odds of getting infected.

My point is that the 91% reduction isn’t some absolute number.  It’s relative to your current odds.  If you do other things to change your odds of infection, that matters.  If your environment changes to change your odds of infection, that also matters.

I guess I’ve beaten this to death.  It’s all about the risk, the dose, and the odds.  Vaccination gives your immune system a leg up on the race between COVID-19 exposure and COVID-19 infection.  But that’s all it does.  It’s not a magic bullet in this case.  If it reduces your odds of infection an average of 91% against the Delta variant, for the first six months following vaccination.  If you engage in behavior that increases your exposure ten-fold, then all you  are doing is breaking even.

My guess is that the largely-vaccinated participants in those Provincetown July 4th parties probably didn’t grasp that at the time.  But I bet they do now.

Post #1198: Breakthrough infections and the Provincetown outbreak revisited.


Last week, the CDC published research in which they found that 74% of the infections in the outbreak following July 4th celebrations in Provincetown, MA were breakthrough infections.  That is, infections of fully-vaccinated individuals.

This has been all over the news.  Needless to say, the lunatic fringe has been having a field day with this.

I wrote this up in my last post, where I took a guess as to why that rate might be so high.  My guess was that they found most of the people via contact tracing, and that individuals who refused to get vaccinated were likely to refuse to cooperate with contact tracing.  That’s all conjecture, but not unreasonable.

There turns out to be a far more straighforward explanation of the high rate of breakthrough cases in the Provincetown, MA outbreak.  And it boils down to this:  If 100% of persons are vaccinated, then 100% of infections will be breakthrough cases.  And if nearly 100% are vaccinated, then nearly 100% will be breakthrough cases.

And, to speak plainly,  nearly 100% of residents of Provincetown, MA are, in fact, fully vaccinated.  Massachusetts data (below) show that more than 95% of Provincetown residents are fully vaccinated, and that Barnstable County hasthe highest  vaccination rate of any county in Massachusetts.  That high rate of vaccination doesn’t fully explain the 74% figure, but it goes a long way toward it.

I’d like to say that I thought to check this on my own, but I didn’t.  My wife corresponded with an acquaintance of hers who lives in Provincetown.  After her acquaintance read my blog post, her immediate reaction was that “we have a very high rate of vaccination here”, or words to that effect.  Then, and only then, did I bother to look up the facts.

That said, I’m just a no-name no-readership blogger.  Shame on the U.S. CDC, and on the mainstream media, for not even bothering to look up the easily-available vaccination-rate data.  All this ammunition provided to the nut-o-verse could have been avoided if they’d done a simple bit of due diligence, and caveated their findings by pointing out the extraordinarily high rate of vaccination at the epicenter of the outbreak.

Details follow.

A naive calculation.

I will eventually get around to trying to list all the things that can affect the fraction of infections that are observed as breakthrough infections.  But let me start with the obvious one first:  The fraction of the persons involved who are vaccinated.

Obviously, if 100% of persons in an area are vaccinated, then breakthrough infections will account for 100% of infections.   And if nearly 100% are vaccinated, then nearly 100% will be breakthrough infections.

If all other things were equal — if the vaccinated and un-vaccinated populations were otherwise completely identical in composition, behavior, risk factors, and exposure — we can calculate an “expected” fraction of all cases that ought to be breakthrough cases.   It’s just a bit of simple math in a spreadsheet.

I’ve highlighted the yellow cell to show roughly where the U.S. is right now. 

At present, about half of the entire U.S. population is fully vaccinated, per the U.S. CDC.

As an aside, I will point out that I would normally use just the adult population, or perhaps the 12-and-older population.  But when I looked at current reported COVID-19 infection rates by age, I found a startling thing:  Per capita, young children now have a higher infection rate than the elderly. 

Source:  CDC COVID data tracker.

I reviewed the true (randomized clinical trial) effectiveness of the Pfizer vaccine, against the Delta variant, in Post #1192.  You can see the original research at this link.  For the six months following vaccination, the Pfizer vaccine shows an average 91% effectiveness in preventing symptomatic infections.

Hence, for the U.S., the naive calculation puts us at the intersection of the top row (50% vaccinated) and next-to-last column (90% effective).  For the U.S. as a whole, we’d expect something like 9% of all infections to be breakthrough infections.

But note how “leveraged” these numbers are.  Once you get down to the bottom rows of the table — to the point where nearly everyone is vaccinated — you’ll frequently find that the majority of infections would be expected to be breakthrough infections.

Revisiting the Provincetown/Barnstable County, MA incident.

While I was busy taking a guess at why 74% of infections in the Provincetown July 4th outbreak were breakthrough infections, my wife did the scientific thing and actually gathered some data.  She corresponded with a friend who lives in Provincetown, MA.

Among other things, her correspondent noted that they have an extremely high vaccination rate in Provincetown. But is it true?  Does Provincetown, MA have an exceptionally high vaccination rate?

Source:  Massachusetts Department of Public Health Weekly COVID-19 Municipality Vaccination Data.

I’d say so.  If those numbers don’t jump off the page and slap you in the face, you haven’t been paying attention.  In the town that was the epicenter of the outbreak, more than 95% of almost every age group is fully vaccinated.

(It’s typical not to show exact percentages in a case like this due to privacy concerns.  In typical in health  data reporting, you don’t want to put out data that would let anyone calculate single-digit counts of individuals.  If someone could multiply the exact percentage by the population and come up with a count of less than ten,in any one cell of the table, that would raise health data privacy concerns. So they fuzzy it up a bit.)

Now let me revisit my naive table.  If the outbreak had been limited to Provincetown itself, using this naive (all-other-things-assumed-equal) calcuation, you’d have expected two-thirds of the cases to be breakthrough cases.  As shown below, in yellow.

But that hardly makes for a shocking headline, does it?  “Provincetown MA COVID-19 outbreak has slightly higher-than-expected rate of breakthrough infections.”  That’s thin gruel, as clickbait goes.

That said, Provincetown itself has a tiny resident population.  Separately, Massachusetts data show that for Barnstable County as a whole (the county in which Provincetown is located), 84% of those age 12 and up have at least one shot; 76% of that population is fully vaccinated.  (This series of celebrations was described as drawing crowds consisting largely of young men.)  Plausibly, if we restrict this to adults (which is were the infections in this outbreak largely occurred), arguably somewhere around 90% of the adult population of that county is partially or fully vaccinated.

If we then assume that cases were drawn uniformly from the county, at that vaccination rate, all other things equal, we’d only have expected half the cases to be breakthrough infections.  Versus the 74% actually observed.

Again, not exactly a startling finding, is it?  “Provincetown MA COVID-19 outbreak has 50% higher-than-expected rate of breakthrough infections.”

Of all the popular press reporting that was done about this event, and all the CDC research that was done about this event, don’t you wish that even one responsible party could have looked that up and made that known?  Instead of some no-name no-readership blogger.

Because now the numbers make a whole lot more sense.  All you need to say is that at the center of the outbreak — Provincetown itself — more than 95% of the population is fully vaccinated.  That’s it.  That’s all the caveat you would have needed to have added to have that 74% breakthrough figure make a whole lot more sense, and be a whole lot less sensational.

Let me end this here.  I contend that any of several factors could easily explain the excess rate of breakthrough infections, beyond my “naive” estimate shown above.  Just off the top of my head, the four main factors might be:

  • These individuals were found via contact tracing, and those who failed to vaccinate are probably less likely to cooperate with contact tracing, and so would not be found.  Thus the contact-traced population would overstate the fraction of infected persons who were vaccinated.
  • Persons who were vaccinated might have been more likely to attend these celebrations, given that it was, in fact, safer for them to attend than for the un-vaccinated to attend.  Thus the fully-vaccinated might have been over-represented among party attendees compared to the county resident population.
  • Contract tracing identifies both symptomatic and asymptomatic infections, and the COVID-19 vaccines are not as effective at preventing asymptomatic infections.  (I’ll expand on that point in a separate post).
  • The population of pary-goers may otherwise differ systematically from all individuals in terms of age, sex, and risk factors.


No matter how you slice it, just that one tiny caveat — the publicly-available information on the vaccination rate of Provincetown MA — could easily have put this into context.  And easily have avoided the storm of disinformation that followed release of the CDC research.

This isn’t the first time the CDC has done something like this.  By this, I mean, fed raw meat to the lunatic fringe by doing flat-footed science instead of understanding the policy context.

I documented a similar incident nearly a year ago, in Post #793.  When the CDC began compiling COVID-19 death rate data, the fringe made a big deal out of the fact that only 6% of individuals dying with COVID-19 had COVID-19 as the sole diagnosis on the death certificate.  (As a person who has used death certificate data before, that struck me as normal, as I explained in that post.)  The nut-o-verse, starting with Fox News, went crazy about that for a while, claiming that the CDC had deliberately overstated COVID-19 deaths.

The punch line is that the CDC had, in fact, literally said that 94% of persons dying with some mention of COVID-19 had COVID-19 as the underlying cause of death.  The only problem was, they buried that in the middle of a completely separate document,  US CDC, technical notes for COVID-19 death data release.  You had to read the fine print, in the methodology document, to know that the 94% of what the CDC was counting was individuals who died from COVID-19 (i.e., for whom the physician of record listed COVID-19 as the underlying cause of death).

I am sure there are people, even now, who are convinced that the CDC grossly exaggerated COVID-19 deaths, based in part on that Fox-News-pushed line of disinformation.  All of which could have been avoided if the CDC had at least superfically looked at their research through a policy lens, and adjusted the focus accordingly.

Now we have a whole new crop of anti-vaxxers who are convinced that the COVID-19 vaccine doesn’t work.  Once again, thanks to the CDC’s inability to view their research in a policy context, and do some simple due diligence to try to explain why they found the high breakthrough rate that they found.

Post #1197: Breakthrough hysteria

Virginia updates its estimates of breakthrough and non-breakthrough COVID-19 infections on Friday.  I thought it was worth posting the data for the most recent week.

I’ll get to why I thought this was worthwhile below.

Lack of cooperation in COVID-19 contact tracing

The nice thing about Virginia’s estimate is that it’s “clean”, in the sense of being based on a match between two lists:  Persons vaccinated, and persons with a positive test.  It doesn’t require any cooperation from those who were infected, or any contact tracing, or any of that.

And that’s a good thing, because, as it turns out, a lot of people refuse to cooperate with COVID-19 contact tracing.  For example, three-quarters of persons in New Jersey routinely refused to cooperate with COVID-19 contact tracing.  Roughly half of Maryland residents ignore COVID-19 contact tracing requests  Lack of cooperation with contact tracers has been publicly noted in North Dakota.  Only about half of persons contacted in Texas would cooperate.  Similar results hold in Pennsylvania,   North Carolina, and   New York.

And in Massachusetts, more than half of residents won’t even pick up the phone when a contact tracer calls.  In fact, the Massachusetts contract tracing efforts have become so dysfunctional that the Commonwealth of Massachusetts recently cancelled its main contract for that service.  (By contrast, their track record early in the pandemic was pretty good.)

In fact, one might say that refusing to cooperate with COVID-19 contact tracing is more-or-less a nation-wide phenomenon.

I wonder who the non-cooperators are?

Now, before I go further, I want to ask a question.

Consider two individuals.

Individual A got vaccinated in a timely fashion, and follows CDC guidance regarding COVID-19 hygiene.

Individual B refuses vaccination and refuses to wear a mask or otherwise engage in COVID-19 hygiene.

Which person do you think is more likely to to ignore a request for COVID-19 contact tracing?  Is it the vaccinated, mask-using Individual A?  Or the anti-vaccine, no-mask individual B?

My guess is that that it’s Individual B.  And while I can’t find any study that says that directly, that’s consistent with national survey-based results on that subject.  Less than half of those surveyed said they would be comfortable with all the required aspects of COVID-19 related contact tracing.  And — where have we seen this before — willingness to cooperate splits strongly along party lines, with Democrats being much more willing to cooperate with contact tracing than Republicans.  Much the same as  COVID-19 vaccination does.

And so, is there a practical lesson here?  I sure think so.

If you identify a cohort of individuals through contact tracing, you’ll end up with a cohort that differentially skips the un-vaccinated.  Not by design, but simply because those who won’t cooperate with a request to get vaccinated are largely the same people who won’t cooperate with a request to trace their contacts once they’ve gotten a COVID-19 infection.

Relevance to this week’s Morbidity and Mortality Weekly.

You have no doubt been seeing headlines about a July 4th outbreak in Provincetown, Massachusetts where it is claimed that three-quarter of those who were infected were fully vaccinated.  That’s based on research by CDC published in this weeks Morbidity and Mortality Weekly Report.

(Of all the people blathering about this week”s issue of the MMWR, I’d bet that I’m just about the only one who routinely read the MMWR as part of my professional life.)

The nut-o-sphere has been having a field day with this, and it inevitably morphs into the bogus claim that three-quarters of all COVID-19 cases in Massachusetts are breakthrough infections.  This, despite the fact that the Massachusetts Department of Public Health went out of its way to say otherwise, just prior to publication.

But let’s be boring and do the math, using current data for all of Massachusetts.  Based on the most recent week of reporting, reporting from Massachusetts says that 38% of new COVID-19 cases are “breakthrough” cases, that is, cases among the vaccinated.  This particular period includes the bulk of the reporting for that outbreak.  It is unclear whether they include partially-vaccinated individuals in that total.  Currently, 84% of the adult population in Massachusetts has received at least one dose, 75% of the adult population is fully vaccinated.  I’ll assume they only include the fully-vaccinated.

So, doing the math, based on the data as-reported:

Relative risk of infection, for the vaccinated, in Massachusetts, during this period = (38%/75%) / (62%/25%) = 20%.

That’s high enough to be interesting.  That’s above the 10% that keeps popping up every time I do this calculation with observational data.  It’s vastly higher than the rate observed in Virginia.

But it’s a far cry from 74%.

And so, how on earth did the CDC manage to arrive at a figure of 74% for that one outbreak?  When you get right down to it, how did the CDC know those people attended those parties, so they would know the set of people from which to calculate that 74%?

It’s not like they’ve implanted microchips in people, to track them.  As far as we know.

The only way the CDC could identify those people is if those individuals voluntarily told them, one way or the other.  And I think the key phrase for understanding this extreme estimate of breakthrough infections is this pair of seemingly-innocuous lines in the methodology section:

“During July 10–26, using travel history data from the state COVID-19 surveillance system, MA DPH identified a cluster of cases among Massachusetts residents. Additional cases were identified by local health jurisdictions through case investigation.

In other words, what you’re looking at in this study isn’t the universe of people who attended those parties.  It’s the people who attended those parties and then cooperated fully with the subsequent contact tracing.

And, best guess, that’s how you ended up with that eye-popping 74% figure.  The sample is restricted to individuals who cooperated with contact tracing in some form.  And so the sample probably skips most of those who have refused to get vaccinated.

There is no doubt that there was quite an outbreak from what was described as a series of packed parties in bars.  Seems like every time I read about outbreaks these days, it’s from parties of some sort.

It’s absolutely true that the breakthrough infection rate currently being reported in Massachusetts is higher than I would expect, even accounting for the fact that this is observational data.

And, apparently, this is the research that convinced the CDC that fully-vaccinated individuals are perfectly capable of spreading COVID-19.

But it’s not 74% of all new infections.  Breakthrough infections accounted for 74% of the individuals that the CDC identified, via contact tracing, as having attended those parties.  In effect, based on those who would voluntarily report the whereabouts of themselves and their friends.

What the rate for the actual universe of party-goers is is not known.  Short of locking up the entire town and interrogating then under torture, that’s simply not knowable.

Post #1196: COVID-19 hysteresis


Hysteresis, not hysteria.

Webster’s Dictionary defines hysteresis as “a retardation of an effect when the forces acting upon a body are changed …”.  Wikipedia offers a different take on it, that “Hysteresis is the dependence of the state of a system on its history.” 

No matter which way you look at it, a system with hysteresis is one that clings to its recent past, and does not change fully to reflect current conditions. Continue reading Post #1196: COVID-19 hysteresis

Post #1192: Randomized clinical trial results demonstrate that COVID-19 vaccines remain effective for at least six months.

I recent posts I’ve discussed results released by the Israeli Ministry of Health last week.  These got a lot of press because they appear to show a rapid decline in immunity from COVID-19 vaccines.  The Israelis inferred that immunity to infection was almost gone after six months.

That was an extraordinary result, and got a lot of attention because if it were true, it would have serious implications for health policy.

As I discussed those results, I hope I made it clear that the methods used in the Israeli study were weak.  That wasn’t a controlled trial, it was “observational data”, contrasting cohorts of Israelis based on what month they had been vaccinated.  Those cohorts differed not just in terms of how long ago they were vaccinated, but also in terms of health risk, age, and occupational mix.

Earlier today, I went looking for any evidence of that rapid dropoff in immunity in Virginia’s data.  I couldn’t find it. Near as I can tell, there’s been no uptick in breakthrough infections in Virginia, despite the onset of the Delta wave of COVID-19.

We now have direct evidence from a randomized, controlled clinical trial that immunity from the Pfizer vaccine remains high for at least six months.  That’s based on research that was reported today.  You can see the original research at this link.

Here’s the key table, below.  Yes, the effectiveness of the vaccination falls somewhat over time.  But no, it does not plummet.  If falls off at a fairly modest rate, comparable to other vaccines.  The authors of the study characterize it as declining roughly 6 percent every two months.  This is what I would call a perfectly normal result for a vaccine:

Source:  Six Month Safety and Efficacy of the BNT162b2 mRNA COVID-19 Vaccine,

Once you develop full immunity, the efficacy of the vaccine in preventing a symptomatic COVID-19 infection is:

  • 96% effective in months 1 and 2.
  • 90% effective in months 3, and 4.
  • 84% effective in months 5 and 6.

Over the entire six-month period, the vaccine had an average effectiveness of 91% in preventing symptomatic disease, and 97% effectiveness in preventing severe disease.  (There was no testing to see the extent to which it prevented asymptomatic infections).

The method used here is the gold standard.  It’s a double-blind randomized trial with placebo.

This randomized clinical trial is a far more reliable way to estimate the effectiveness of the vaccine than the “observational data” studies from Israel and other places.  Here, we can be certain the vaccinated and unvaccinated groups are otherwise identical (to within sampling error), because individuals were randomly assigned to one group or the other.  By contrast, in the Israeli study, the groups vaccinated in January and June were vastly different in terms of age, risk, and occupational mix.  The resulting differences in breakthrough infection rate for those two groups (one with vaccination just one month old, one with vaccination six months old) reflected not just the age of the vaccination, but also any effects of the large difference in risk, age, and occupational mix between those two groups.

The only uncertainty left is whether there is something unique about the Delta variant that would invalidate these results.  The prevalent strains in the locations and time that this study took place did not include Delta.  But I think it’s not plausible to suggest that these results held for all of the strains in circulation at the time, but that, uniquely, there would be a big dropoff in immunity for Delta (and only Delta).  That is especially given that he vaccines are known to be effective against Delta, just not quite as effective as they were against the native strain of COVID-19.  There’s no reason grounded in basic science to think that such a thing was possible, let alone likely.

I think this provides the definitive answer to the question “Do you need a booster shot at six months”.  The answer is no.  Protection against symptomatic disease remains good, protection against severe disease remains even better.  That’s what the controlled clinical trial now shows.

And, for sure, with these results, the U.S. is not going to approve booster shots at six months.  Not only do you not need it, but it’s not going to be possible to obtain it legally in the U.S.

It may be a coincidence that this research come out today in preprint (no-peer-reviewed) form.  But it may well be that this was hustled into preprint in response to the Israeli Ministry of Health findings that were released last week.  That would have been the right thing to do, to make it clear that the huge dropoff in immunity observed in the Israeli results was an artifact of methods, and was not a real effect.

With that cleared up, I will return to my task of calculating the odds of infection and harm, for the fully-vaccinated population, in this U.S. Delta wave.

Post #1191: Breakthrough infections in Virginia suggest little loss of vaccine-created immunity over time.

Background:  Why breakthrough infections suddenly matter.

Two posts ago (Post #1189), I went into the new findings from Israel regarding breakthrough infections of the Delta variant.  Their data suggest that by six months after the time of vaccination, the Pfizer vaccine has almost completely lost its ability to prevent infections with Delta.  It still does a good job of preventing hospitalization and death, just not infections.

I’m not sure if that’s a real result, or just an artifact of the way in which Israel went about vaccinating people.  Their sample size was small, and their results were odd in that younger people appeared to lose immunity at a much higher rate than the elderly.

The Israeli results aren’t from a clinical trial.  They come from comparing the current infection rates of cohorts of Israelis who were vaccinated in January, February, and so on.  The members of those cohorts aren’t randomly selected, but differ systematically.  The earliest cohorts (the persons vaccinated first) focused on high-risk individuals, the elderly, and health care workers.

The upshot is that by contrasting cohorts of individuals based on month of vaccination, you aren’t looking solely at the effect of time-since-vaccination.  You are also looking at the effect of being elderly, being at high risk, and working in the health care system.  Plausibly, some of those other factors would influence your odds of being exposed to Delta and picking up a breakthrough infection.

Some aspects of their results suggest that at least some of what they observe is an artifact of who was selected for those cohorts.  In particular, they found that immunity fades to a much greater degree among the non-elderly, which is the exact opposite of what you would expect, given the generally weaker immune response of the elderly.   (That weaker response is why there are annual flu shots specifically formulated for the elderly, with an enhanced dose designed to stimulate those aging immune systems).

That said, the finding is out there.  And if it’s true — if what the Israelis are seeing is in fact an indication that the vaccine’s protective effects fade profoundly within half a year — that has major implications for individuals and for our public health strategy.

But is it true, or just an artifact of their methods? 

Excellence in public data:  Virginia

Faced with something like this — some hazy finding, showing a huge and important effect, from a small number of cases, in a distant land, that nobody has seen before, using non-randomized data  — you get the drift — my first reaction is to see if anybody else says anything even remotely similar.  And I want to see that based on data that I understand and trust.

It seems to me that tracking breakthrough infections ought to be a piece of cake for U.S. states.  As I understand it, state health departments know which individuals have been vaccinated.  (There’s a caveat here for vaccines that flowed through various Federal programs, including the armed forces, Veterans’ Administration, and the U.S. Indian Health Service.  But states distributed the vast majority.)  For sure, state health departments know which individuals have had a positive test.  I’d be shocked if both lists didn’t contain the Social Security Number (SSN).  And even if not, name/gender/age/address is good enough to match up 99+% of those entries absent a unique identifier such as SSN.  (I speak from experience there, because figuring out how to make such “soft” merges between data files used to be part of my job.)

In short, all a state needs to do is match up the list of the vaccinated and the list of the infected.  The people who are on both lists constitute your breakthrough infections.  You’ll miss a few — individuals who moved into or out of state, individuals whose cases were dealt with by Federal rather than state systems — but in most states, those exceptions should be a trivial fraction of the population.

And so, for months now, I’ve wondered why states haven’t done that.

Turns out, Virginia has.  Virginia now has a web page devoted to tracking breakthrough infections.  It’s titled “Cases by Vaccination Status”, but that’s breakthrough infections.  And I sure wish other states would follow suit.

I’m going to take one paragraph to put in a plug for the Virginia Department of Health.  I’ve been using Federal, state, and sometimes local government data sources for more than a year now, tracking the pandemic.  Virginia’s public-facing data is head and shoulders above the rest.  A lot of times when I’ve wanted to discuss a national issue, I “illustrate” it with data from Virginia.  That’s because Virginia was the only place I could find the data files, publicly available, that would allow me to do it.  When you see that — when the data meet the analytical needs — you know that the people creating the data are almost certainly the same as the people who are using the data.  That’s how they end up providing usable data files.

In light of the Israeli findings, I would love to see Virginia’s data tabulated by month of vaccination.  Even though those monthly cohorts were not randomly selected, I’d at least like to see whether or not the crude finding that appears in the Israeli data — that breakthrough infections become common by six months after vaccination — before considering the Israeli results further.

But let me try to do the next best thing.  Let me at least look to see of those breakthrough infections are rising, as they plausibly should as the vaccinations age.  If the Israeli findings are true and not spurious.

In any case, by looking at the Virginia data for the past couple of weeks, we can be reasonably sure that, so far, as of about a week ago, breakthrough infections were uncommon here in Virginia.  This, despite a reasonably high fraction of the population being vaccinated.

Below, the breakthrough cases would be 1 minus the percentage shown.  So, in this case, (1 – 98.54% = ) ~ 1.5% of infections were breakthrough cases for fully-vaccinated individuals.  The remainder (98.54%) were among the un-vaccinated.

To interpret that, you need to realize that there’s considerable uncertainty around these numbers.  It’s not “statistical uncertainty”, because this is a census of cases, not a sample.  It’s more like “natural variation”, when small numbers of infections occur within a very large population pool.  Each number is a bit shaky, so to speak, but not because we’ve drawn a sample.  They are shaky just because there are so few of them and they may fluctuate from day to day.

In addition, you need to know that there is a strong age-related correlation in vaccination rate, hospitalization rate, and mortality rate.  So you can’t just take this raw count and infer that (e.g.) the vaccines are better at preventing infection than they are at preventing hospitalization.  That’s not true.  Arguably, the reason you’re seeing breakthrough cases as a higher fraction of hospitalizations than of infections is that hospitalization is strongly concentrated in the elderly, who have a very high rate of vaccination.  I’d have to age-adjust the infection and hospitalization numbers separately if I wanted to get a true apples-to-apples comparison of impact on infection versus impact on hospitalization.

What’s at issue with the Israeli findings is the infection rate.  So let me just state this plainly, and do a bit of math.  Almost all these infections are in adults, so let me focus on the adult population.

As of this most recent two-week period available, the fully-vaccinated population accounted for:

  • 64% of the adult population.
  • 1.5% of the infections.

Doing the math, that means that the observed effectiveness of the vaccines, against COVID-19, in Virginia, over this period, is:

(1.5/64) / (98.5/36) = <1%

(Ah, well, what I really mean to say is that the effectiveness is >99%.  The chance of getting infected is <1% of the chance for a non-vaccinated individual.)

In Virginia, during this most recent time period, if you were vaccinated, your chance of having a COVID-19 infection was less than one percent of the chance faced by an un-vaccinated person.

That’s substantially better than the clinical trials found.  So, no doubt there’s a behavioral aspect to number.  The vaccinated aren’t chosen at random, but instead are drawn from the rational population possessed of common sense.  The unvaccinated, by contrast, are largely a mix of the irrational and those ideologically-driven to reject the vaccine.  Almost without a doubt, the unvaccinated are also the ones who reject COVID-19 hygiene.

And so, this is probably best interpreted as saying that if you’re vaccinated and adopt common-sense COVID-19 hygiene measures, your risk of getting infected is less than one percent of the risk faced by those who can’t be bothered to do either.

In Virginia.  As of a couple of weeks back.

And so, whatever is driving those Israeli findings does not appear to have started happening here yet.

Now I need to ask a couple of more questions.

First, does this reflect the Delta variant?  I’d say yes.  I can’t find any direct measure of that, because CDC didn’t sequence enough samples to provide a state-level estimate for Virginia.  But I can infer it from the fact that this period is squarely in the middle of the current upsurge in cases in Virginia.

The pale blue lines mark the start and end dates used in the breakthrough calculation above.  Those increases didn’t really get going until Delta dominated, and Virginia is right in line with the rest of the South Atlantic states.  The CDC shows that, during this period, about two-thirds of cases in this region were the Delta variant.  Between those two pieces of evidence, I’m fairly confident in saying that the breakthrough rate above is largely reflective of Delta infections.

The next question to ask is, has this changed over time?  That’s easy enough to answer.  Let me set the dates to span an equivalent period on the downslope of the curve above, and see what the Commonwealth says the breakthrough infection rate was.

And the short answer is that breakthrough infection, as a percent of total, was actually higher at the start of June than it is now.  That’s a time period when the Alpha variant was still dominant.  Those accounted for 4.5 percent of total infections — in line with the clinical trials data — compared to less than one percent in the most recent period.

Here’s the kicker:  If you download yet another one of Virginia’s data files, you can readily calculate that 24% of Virginia’s vaccine doses were administered before March 1, 2021.

In other words, somewhere around one-quarter of Virginia’s vaccinated individuals fall into the categories that should be suffering a massive loss of immunity to COVID-19 now, if the Israeli results are true.  And yet, we are seeing no uptick in breakthrough infections.  To the contrary, based on the two time periods I looked at, those breakthrough infections actually fell.

My conclusion, based on publicly-available data from Virginia, is that whatever is happening in Israel surely does not seem to be happening in Virginia.  The Israeli findings shows a massive reduction in immunity for those whose immunizations were several months old.  If true, given that almost a quarter of Virginia COVID-19 immunizations are five months old or older, given the estimated effect from Israel, that really should have started boosting the rate of breakthrough infections by now.  And no such thing has happened.

This analysis could be done more cleanly by tabulating by date of vaccination, but that would require the person-level data that only the Commonwealth possesses.  I hope they’ll take a quick cut at that and make the results now.  Otherwise, these Israeli results would seem to through a monkeywrench into any planning for the pandemic.


I want to be clear that I think Israel’s Ministry of Health did the right thing in releasing their statistical analysis.  In fact, I’d say they were ethically compelled to do so.  And, based on the news reporting, the accompanying text (in Hebrew, which I cannot read) did mention all the relevant caveats, in that the monthly cohorts of the vaccinated were not randomly chosen.

It’s a tough call.

On the one hand, Israel was a couple of months ahead of most other countries.  If this result were real, they’d be the first to have it show up in their national data. And if it were real, they really would be compelled to offer a warning to other countries that might be subject to the same loss of immunity within a couple of months.

On the other hand, you don’t want to make health care policy based on spurious results.  (Though this would hardly be the first time that happened).  Consider the the expense and hassle of providing booster shots on a semi-yearly basis to the entire vaccine-accepting population.  Now consider the risk of doing that for no reason, if the Israeli result are spurious.  (And I note that Israel itself has not yet decided to do that, based on their own results.)

So it’s a tough call.  Alerting other public health agencies to this possibility seems like the right thing to do.  The US CDC and FDA aren’t going to make any sort of snap decision on booster shots.  They are going to gather the evidence, and make up their own minds.  And, based on what I can see in Virginia, they are going to find that the Israeli results are not replicated in other places.  That will tell them that the correlation observed there is an artifact of something about the Israeli experience and not a failure of vaccine-generated immunity.  And the scientific method will have done the right thing in filtering out fact from fiction.