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

Posted on August 2, 2021


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.