Periodically, I’ll come across a headline from Dr. Andrew Bostom, who has been a prominent contrary voice in Rhode Island going after the diktats of the public health establishment.  We’re on the same side, generally, and I often agree with his overarching points, but every time I look into his arguments, I find he’s seems to be misrepresenting something.  So, for example:

… July, 2021 SARS-CoV-2 (covid-19) infection data collected by the Rhode Island Department of Health, with presentation of the findings by both vaccination, and prior infection status, provide independent validation of these NNT/NNH results (4,5). While 30% of these total (n=2127) new SARS-CoV-2 infections occurred among persons fully covid-19 vaccinated (639/2127), only 3.4% of those with a prior infection, regardless of vaccination status, were infected in July (73/2127). Fully vaccinating those with a prior covid-19 infection did not lower this percentage at all (22/639=3.4% fully vaccinated; 51/1488=3.4% not fully vaccinated).

These statements do not accurately reflect the numbers he presents.  It is not true that “3.4% of those with a prior infection, regardless of vaccination status, were infected in July” because his denominator is wrong.  2,127 is not the number of people with prior infection, but the number of people infected in July total.  Likewise, as far as I can tell, the fact that his ratios produce 3.4% for both the vaccinated and unvaccinated is an entirely meaningless coincidence.  All it means is that 3.4% of vaccinated people who were infected in July had previously been infected, and 3.4% of unvaccinated people who were infected in July had previously been infected.  This might be interesting but for the fact that breaking people up by vaccination, on one hand, and previous infection, on the other, does not produce equally sized groups.

That said, in making this error, Bostom dramatically understates the protection that previous infection provides.  I’d need more-detailed data to fine tune this, but roughly speaking, only 0.048% of all people who had been infected with COVID-19 by the beginning of the month caught COVID again in July.  This compares with 0.108% of all people who had been vaccinated, which is in keeping with various findings recently reported that natural immunity is better than vaccinated immunity.*

It’s important to note, however, that vaccination improves outcomes across the board.  Very roughly, these numbers suggest that being vaccinated cuts your risk in about half whether you’ve had COVID before or not.  Unvaccinated people who caught COVID for the first time in July were 0.16% of all people who had not yet caught it, while vaccinated COVID-virgins were 0.07%.  Looking at those who had already had COVID and caught it again in July, the percentages are 0.034% unvaccinated and 0.014%.

The effect gets more pronounced when you look at people in the hospital.  Of all people who had not yet been infected with COVID, 0.007% were not vaccinated and wound up in the hospital with COVID in July.  The percentage for those who had been vaccinated was 0.002%, so less than a third.  Of all people who had previously been infected, the percentages are 0.008% and 0.001%.  So, again, vaccination improves outcomes.

This holds true if we change the denominator to people who caught COVID in July.  Based on these numbers, being vaccinated makes it much less likely you’ll end up in the hospital if you do catch COVID, whether or not you’ve had it before.  Of particular note, almost one out of every four unvaccinated people who had already had COVID and caught it again in July was hospitalized.  If they’d been vaccinated, it was less than one in 10.  In short, no matter your situation, being vaccinated makes it less likely you’ll test positive for COVID, and if you do test positive, it makes it less likely you’ll find yourself in the hospital.**

Finally, turning to the worst outcome, we find that only six people died while testing positive for COVID in July, and they were all unvaccinated people who had not had COVID before and were over 30.

While making decisions about your own health, though, remember that these numbers remain small.  If you’ve had COVID before, if you’ve been vaccinated, or if you’re young, the possibility that you’ll have a severe experience with COVID in any given month are miniscule.  (And, frankly, the odds are small for most people anyway.)  This is why at the very least, any government, employer, or other organization considering a vaccine mandate should also allow proof of natural immunity, and also why we should be leaving young children alone.

Bostom’s point does remain valid, though, that the vaccines have risks, which should make mandates even less acceptable.  However, I’m not confident that his specific numbers are truly relevant to the decision for three reasons.

First, I can’t confirm his numbers from the study that he cites for vaccine risks, although it’s definitely possible I’m simply missing something.  He claims that “the proportion reporting one moderate to severe symptom was higher in the previous SARS-CoV-2 infected group  (56% v 47%),” but these numbers aren’t anywhere I can find, so it’s not clear what they really signify.  (Indeed, it’s hard to see how they can reconcile with the percentages shown in Figure I.)

Second, his calculation of the number needed to treat people with the vaccine is based on any positive test, which isn’t really the number we should care about.  We know going into vaccination that there might be some side effect.  The question is how well it protects against outcomes from the virus that are worse.

And third, his mixing and matching of studies to measure the benefits of vaccines against the harms comes with complications.  The study of vaccine side effects, for example, comes from the United Kingdom and specifically states that the mRNA vaccines (Pfizer and Moderna) produced more side effects, but fewer serious side effects than the alternatives.  This is relevant to the study out of Israel because nearly everybody there received mRNA.

* A key number we don’t have is how many people were both vaccinated and previously infected.  If people who had been previously infected were much more likely to be vaccinated, too, then these numbers would equalize.  Intuitively, that seems unlikely, but it does possibly have some effect.

** Important reminder: These numbers are for people who test positive while in the hospital, whether or not they’re there because of COVID.  It’s possible, therefore, some other variable (like obesity) is playing a role.