COVID-19: Let’s Talk Again of the Base Rate Fallacy

by Raywat Deonandan, PhD
Epidemiologist & Associate Professor
University of Ottawa
(I add my credentials to these COVID-19 blog posts in case they get shared. I want readers to know that my opinion is supposedly an educated and informed one)

Since the start of the pandemic, the general public has received a rapid education in some of the terms with which only Epidemiologists used to be familiar. Ideas and words like “herd immunity” and “reproduction number” are now casually bandied about people who had never heard the word “epidemiology” before 2020.

Another term that I hope more people would take the time to learn and understand is “base rate fallacy.” It’s an important concept to help dispel some of the misinformation around vaccine effectiveness that fuels much of the anti-vax narrative.

As of this date, the Ontario COVID-19 dashboard is reporting 690 unvaccinated and 1770 fully vaccinated people hospitalized for the disease. The predictable misinterpretation is that, not only do vaccines not work, but that the vaccinated constitute the majority of people in hospitals!

This fallacy comes about from a failure to appreciate the base population from which these numbers arise —the “base rate.” As my very first Epidemiology professor put it, we should always be asking, “What’s the denominator?”

As of today, 77.5% of Ontarians, or 11.5 million people, have been vaccinated, leaving about 3 million unvaccinated. So the risk of hospitalization is given by the proportion of those two numbers who end up hospitalized. For the vaccinated, that works out to about 154 hospitalizations per million jabbed people. But for the unvaccinated, it’s 230 per million people.

So, a focus on risk puts those odd hospitalization numbers into context: the unvaccinated remain profoundly more likely to be hospitalized for COVID than do the vaccinated. This is exemplified in this simple graphic that’s been knocking about the Interwebs:

In recent days, however, a confusing trend has emerged in Ontario, as seen in the official provincial case data:

It shows that since Dec 23, 2021, the vaccinated have had a higher risk of COVID infection than the did the unvaccinated.

WTF is going on here? It behooves us not to hide from these data or to minimize them, but instead to wrestle with them. The hospitalization data is clear: it’s the unvaccinated who are greatest at risk from a bad outcome from COVID.  But what of mere infection?

I suggest that two elements are at play here: (a) testing bias, and (b) exposure bias.

Testing Bias

It’s telling that this “paradox” only manifests since the end of December. This is when the Omicron variant took hold of Ontario and made testing a scarce commodity. It is now difficult to get a PCR test (and only PCR tests end up in the official count; rapid antigen tests do not). So those people seeking testing are (a) eligible to be tested and (b) willing to line up for hours to be tested.

Who are these people? First, there are essential workers, such as health care workers, who need to prove negative status to return to work. PCR capacity is largely reserved for such people. They are overwhelmingly more likely to be vaccinated. And they are highly likely to test positive because that’s why they’re showing up in the first place.

Remember that the stereotype of the unvaccinated person in Ontario is someone who minimizes the risk of COVID. So they are far less motivated to seek testing, even when showing symptoms. They are ideologically incentivized to consider it to be nothing more than a “bad flu”. That segment of the unvaccinated who do get tested might get swept up in an outbreak investigation or sentinel surveillance in a hospital setting, where the likelihood of testing positive is lower.

Related, there is a strong suspicion that many vaccinated people are overconfident in the face of Omicron. They learned careless behaviours in the Delta variant era, and did not change behaviour when Omicron showed its immunity-evading face. They might be more likely than before to take unnecessary risks with exposure, and are now paying the price through infection.

This is related to the next reason…

Exposure Bias

In Ontario right now, who is allowed into high exposure settings? Restaurants? Bars? Gyms? The so-called “vaccine passport” system ensures that it’s the fully vaccinated who are overwhelmingly the people present at such superspreading opportunities. They’re the ones removing their masks to eat in a restaurant chock full of strangers, while a super-contagious airborne variant rages through the community.

This was not a problem in the pre-Omicron era when Delta and the previous variants were reasonably well controlled with distancing, capacity limits, and casual mask wearing. In fact, in my opinion the passports were a major reason the epidemic was being well controlled. The effect of vaccine passports had of keeping the “dry kindling” of unvaccinated people out of formal crowded areas had the intended impact of preventing super-spreading events.

But Omicron changed all that. The vaccinated are now almost as vulnerable as the unvaccinated in becoming infected with Omicron (though much less severely). And the vaccinated are more likely to be exposed to Omicron in a super-spreading environment.

The result: a greater risk of infection amongst the vaccinated, as compared to the unvaccinated.


To be clear, this does not mean that vaccination raises your chances of becoming infected. In fact, on an individual basis, the opposite is true: vaccination, especially triply dosed, increases the production of neutralizing antibodies and therefore lowers the individual probability of infection.

Instead, what this means is that the behaviour and context of the vaccinated increases their chances of infection.

And the nature of our skewed testing means that we’re more likely to detect cases amongst the vaccinated than the unvaccinated.


Of course, all of this is speculation. I don’t know for sure. What I do know is this:

(a) vaccination continues to be the very best protection against bad symptoms, hospitalization, and death from COVID; and

(b) when all the data from weeks back are considered (not just the days since Omicron took over), vaccination is the single best protection reducer of risk of infection, hospitalization, and ICU usage, as per these graphs extracted from data posted by the Ontario Science Table:

So get jabbed, people. Vaccination remains our best personal choice for staying out of the hospital and out of the morgue.