Immune to reason
Are you more at risk from vaccinated or unvaccinated asymptomatic people. The answer should be obvious, but perhaps not in the direction you think.
The greatest tragedy of the COVID-19 is obviously the sickness and death that resulted. The greatest tragedy of how we acted during the COVID-19 pandemic is arguably how we treated the unvaccinated. Families were split and broken by vaccination status, unvaccinated parents denied access to their children, and Federal public employees were denied their salaries based on failures to do basic math.
Having had an education and career intimately involved in risk analysis, I’m ashamed to say I’m not sure whether I’m more appalled at the harms and mistreatment of unvaccinated people or at the failure of professionals, and the public at large, to understand how to calculate or intuit relative risks. Unfortunately, the psychology of fear tends to undermine those rational abilities.
Let me narrow it down to one simple question. Suppose you have a choice for a meeting. In one room, the person is unvaccinated. In the other room, the person is vaccinated. Both are asymptomatic. Which room would you prefer, assuming you wanted to minimize your chances of catching COVID-19? Put more clearly:
Are you more likely to get a SARS-CoV-2 infection from an asymptomatic vaccinated person, or an asymptomatic unvaccinated person?
Most people, including the Canadian government, appear to get the answer very wrong.
Let’s start with where many people seem to go wrong. If I asked would you prefer to be in a room with a randomly assigned unvaccinated person or a randomly assigned vaccinated person, most get this correct. Assuming equal likelihood of exposure, an unvaccinated person is more likely to be contagious than a vaccinated person. That should be obvious from the point of the vaccines. The unvaccinated person is more likely to become infected, to become sick, and carry more of the virus for longer. In such a circumstance it does indeed make more sense to chose to meet with the vaccinated person.
That isn’t the question though. They aren’t randomly assigned. These are asymptomatic people. Unvaccinated people exposed to the virus are far more likely to be symptomatic. That is, after all, the point of the COVID-19 vaccines — to reduce the likelihood of becoming symptomatic when exposed to the SARS-CoV-2 virus. That’s literally what vaccines do by stimulating the immune system. The question here is which individual is more likely to be an asymptomatic carrier of the SARS-CoV-2 virus? A "COVID Mary”, if you will.
Perhaps the answer is more obvious if we start from the extremes. Imagine that COVID-19 were perfectly infectious and made unvaccinated people instantly sick on contact. Imagine that the vaccines were perfect and kept 100% of vaccinated people from getting sick when exposed to the virus. Now which room is more likely to have the asymptomatic carrier? Well it can’t be the unvaccinated person; in this extreme case, unvaccinated people can’t be asymptomatic carriers; there’d be no such thing. There would be a 0% chance of them being infected and contagious. All of the COVID Mary’s would, by definition, have to be vaccinated. For the vaccinated person, their chance of being a carrier would essentially be the average public exposure rate over the prior few days.
The reality hasn’t been that extreme because the there is a pre-symptomatic phase, not all unvaccinated people became symptomatic, and some vaccinated people did become symptomatic. However, that just pull us away from the 0% and 100% cases. There would have to be a serious mitigation factor for them to reverse such that the unvaccinated person became more likely to be an asymptomatic carrier.
To understand the relative risk, it is important first to understand the difference between the virus, an infection, and the disease. The virus SARS-CoV-2 is the physical entity that is transmitted in water droplets via the air. An infection occurs when you breath in the virus and the droplets rest in the mucus and epithelial (outer) layers of your airways — lungs, throat, mouth, sinuses, nose. COVID-19 is the disease; it is synonymous with symptomatic infection by SARS-CoV-2 virus. You cannot have “asymptomatic COVID-19” as the disease refers to the symptoms; what you would have is “asymptomatic SARS-CoV-2 infection”.
Vaccines do not stop you from breathing in the droplets or from the virus settling in your airways. That is a matter of physics. Masks might, but that is a different issue from vaccines. What the vaccines do — or are supposed to do — is keep the virus from migrating into the body and reproducing internally and/or reducing the symptoms (ideally to zero) if the virus does get in. The vaccines might also help your immune system kill off the virus that is resting in your airways (“shedding”) so reduce the duration of infection and the amount of virus contained in your breath during that period. In other words, given an infection, vaccines may reduce the chances of transmission. In fact, this potential capability is, unfortunately, just about the only factor discussed with respect to vaccination and transmission. However, it is far from the largest or most important factor.
It helps to take a look at an empirical measurement to show the numbers. McCormick et al. studied household transmissions from January to April 20211 . Their goal was to study variants, but their data allows us to look at these relative risks.
McCormick et al. collected data from 493 individual who lived in a house with another (primary) infected person. The study looked at rates of secondary infections (transmission) to these 493 other individuals in the households.
Of these 493 individuals, 402 were unvaccinated and 29 were fully vaccinated. (An additional 32 were recently vaccinated deemed to be not fully effective, and 30 were partially vaccinated. We’ll leave these cases out to compare fully vaccinated versus unvaccinated.) Of the 402 unvaccinated, 108 tested positive for SARS-CoV-2 during the investigation. Of the 29 vaccinated, 6 tested positive. For symptoms:
One fully vaccinated secondary case was symptomatic (13%); the other 5 were asymptomatic (87%). Among unvaccinated secondary cases, 105/108 (97%) were symptomatic
Risk of infection given exposure
Of the 29 fully vaccinated people, 6 (20.7%) became infected. Of the 402 unvaccinated people, 108 (26.9%) became infected. The vaccinated-to-unvaccinated relative risk of becoming infected is 20.7/26.9 = 77%. This implies that, given an exposure to the virus, the probability of becoming infected is roughly 23% lower if you are fully vaccinated vs unvaccinated.
Great. The vaccines appear to work to lower the infection rate. (I’ll ignore the uncertainty size since that isn’t important here. We can accept as assumed true that vaccines may have lowered the rate of viral infection.)
Risk of symptoms given infection (aka, COVID-19)
Of the 6 vaccinated people infected by the virus, 1 was symptomatic (16.7%) and 5 (83.3%) were asymptomatic. Of the 108 unvaccinated people infected, 105 were symptomatic (97.2%) and 3 (2.8%) were asymptomatic. The vaccinated-to-unvaccinated relative risk of becoming sick (symptomatic), given an infection, is 16.7/97.2 = 17.2%. This implies that, given an infection, the probability of becoming sick (symptomatic) is roughly 82.8% lower if you are fully vaccinated vs unvaccinated.
Great. The vaccines appear to work to lower the rate of getting sick when infected. That is, after all, the point of the vaccines, and this element is what keeps people out of hospitals and morgues.
Risk of symptoms (COVID-19) given exposure
You can combine the above two conditional cases. Of the 29 fully vaccinated people, 1 was symptomatic (3.4%). Of the 402 unvaccinated people, 105 were symptomatic (26.1%). The vaccinated-to-unvaccinated relative risk of becoming sick, given exposure to the virus, is 3.4/26.1 = 13%. This implies that, given exposure to the virus, the probability of becoming sick is roughly 87% lower if you are fully vaccinated vs unvaccinated.
Great. That is ultimately what people want from the vaccination for their own personal safety and health.
Risk of transmission given asymptomatic status
None of the above risks were the question asked at the top of this article: Are you more likely to get a SARS-CoV-2 infection from an asymptomatic vaccinated person, or an asymptomatic unvaccinated person?
Of the 29 fully vaccinated people, 1 of them was symptomatic and 28 of them were asymptomatic. These 28 people make up the first group of interest: fully vaccinated asymptomatic people. Of these 28, 5 (17.8%) of them were infected.
Of the 402 unvaccinated people, 105 were symptomatic and 297 were asymptomatic. These 297 people make up the second group of interest: unvaccinated asymptomatic people. Of these 297 people, 3 (1.0%) of them were infected.
The vaccinated-to-unvaccinated relative risk of an asymptomatic person being infected, given exposure to the virus, is 17.8/1.0 = 1780%, or 17.8 times the risk from the vaccinated versus the unvaccinated person.
Making sense of it
If the math doesn’t make intuitive sense, pause for second and think it through. In the room with the vaccinated asymptomatic person, it could be any one of those 28 individuals, and 5 of them are infected. Your odds of getting one of those 5 is exactly 5 in 28, or 17.8%. In the room with the unvaccinated asymptomatic person, it could be any one of those 297 individuals, and 3 of them are infected. Your odds of getting one of those 3 is exactly 3 in 297, or 1.0%. You are 17.8 times more likely to get an infected vaccinated person than an infected unvaccinated person — given that they are both asymptomatic.
It’s actually worse than this. This assumes equal likelihood of exposure. In normal times, that is a reasonable assumption. During “lockdown”, when only vaccinated people were allowed in restaurants, in airplanes, or generally anywhere the virus tended to be transmitted, the likelihood of vaccinated people being exposed to the virus was much higher than unvaccinated people.
This should be obvious from intuition. Unvaccinated people get sick from COVID-19 far more than vaccinated people. That means unvaccinated people essentially have a big sign on their forehead indicated whether they are infected or not. The “sign” here is their symptomatic status. Vaccination removes the sign. With vaccinated people, you have no idea if they are infected, and generally they don’t know either because they tend to mostly be asymptomatic. Unless they are tested, how would they know?
Since the unvaccinated person is asymptomatic, they are very likely not infected. The vaccinated person’s asymptomatic status tells you almost nothing about their infection status.
If this is so obvious from intuition and from empirical data, why did the public get this one so wrong? Why did people exclude their unvaccinated family members from Christmas gatherings. Why did a Quebec superior judge suspend an unvaccinated father’s visitation rights with his 12-year old child2? How did it make sense to anyone that being around one unvaccinated person — their father — put her at more risk than being around two vaccinated people (their mother and step-father), plus his half-siblings, or the many people at school and other enclosed spaces? It never made any risk-based sense. (The father was quickly given back visitation rights, but not because of the bad math or recognition of which house was riskier3.)
Government Mandates
How did the Canadian government get it so wrong? Their mandatory vaccination policy was based on three objectives4:
3.1.1 To take every precaution reasonable, in the circumstances, for the protection of the health and safety of employees. Vaccination is a key element in the protection of employees against COVID-19.
3.1.2 To improve the vaccination rate across Canada of employees in the core public administration through COVID-19 vaccination.
3.1.3 Given that operational requirements may include ad hoc onsite presence, all employees, including those working remotely and teleworking must be fully vaccinated to protect themselves, colleagues, and clients from COVID-19.
The first two objectives can be argued on separate grounds of overriding individual rights, and whether the federal government had any mandate for public health measures which are provincial responsibilities. But only the third objective makes reference to safety of the workplace, and makes no sense at all. Not only is an unvaccinated, asymptomatic colleague less likely to be infected than a vaccinated, asymptomatic colleague, but a remote worker asked to come onsite ad hoc has a much lower likelihood of exposure to the virus than somebody who has been working onsite around other people. (At the time this was implemented, federal and provincial “lockdown” rules were in place at restaurants, gyms, travel, and other places that the virus spread, making it far more likely the vaccinate person was exposed too.)
This never made any sense. All else being equal, getting vaccinated makes you personally safer. However, you’d be much safer if everybody around you was unvaccinated. If they were symptomatic, their vaccination status was irrelevant to the risk to you; stay away from them. If they were asymptomatic, you’d be safer around the unvaccinated person.
Why do people still continue to get this wrong? I have three hypotheses. First, many people seem to confuse the virus and the disease. In these cases, people seem to think that you need to become sick with COVID-19 to spread the virus, and since vaccinated people are less likely to get COVID-19 than unvaccinated people, they assume then the vaccinated are less likely to be spreading it.
That misunderstands viruses and disease. What spreads is the virus, SARS-CoV-2, not the symptoms. Remember, the vaccines do nothing to stop you from breathing in the virus droplets, nor having them settle in your airways. Yes, they might shed faster there, but that is merely the hypothetical lower rate of transmission given equal rates of exposure AND regardless of symptomatic status. Yes, the asymptomatic vaccinated person sheds the infection faster than the symptomatic unvaccinated person. But that is moot compared to their relative symptomatic status. You are not in a room with that slower-shedding symptomatic unvaccinated person because they are symptomatic. You very well may be in the room with the faster-shedding-but-still-infected asymptomatic vaccinated person.
My second hypothesis is that people don’t understand conditional risks very well. People tend to understand absolute risks and direct relative risks. A random unvaccinated person is more likely to be infectious than a random vaccinated person. But, the unvaccinated person is far more likely to be symptomatic. If you remove all of the symptomatic people, the unvaccinated people are very unlikely to have been exposed or carrying the virus (1% in above study compared to 17.8% of vaccinated).
My third hypothesis is ingroup/outgroup tribal psychology. This is the “us vs them” psychology that drive people to hate each other based on grouping them into categories. This is perhaps the best understood and reproduceable phenomenon in psychology, from Realistic Conflict Theory and the Robbers Cave Experiment, to Jane Elliot’s 1968 demonstration of creating hatred in her classroom by eye colour. All it takes to create fervent hatred is to divide people up into groups and continually claim that one of the groups is causing harm to the other. This behaviour was very common during the pandemic, with calls to tax the unvaccinated5, “Let them die.”6, isolate them7, and all sorts of nasty, hate-filled beliefs about them.
There really were, and are, people who feared and hated unvaccinated people. If you’ve had those feelings, those are the same feelings held by people in tribalistic fights, from holy wars to 1930s Germany, to portions of American political discourse since 2016. The same feeling of self-righteousness, the same hatred and disgust of “them”, the same de-humanization, and the same justifications for allowing “them” to be harmed, denied income, kept from seeing their children, and removed from your group of friends and family.
I suspect all three played a part, and fed off each other. The question is whether we’ll learn anything from this. Will justice come to those who were mistreated? Will cooler heads prevail and families and friends mend their relationships? Or, will fear and ignorance continue to dominate?
McCormick DW, et al., COVID-19 Household Transmission Team. SARS-CoV-2 infection risk among vaccinated and unvaccinated household members during the Alpha variant surge - Denver, Colorado, and San Diego, California, January-April 2021. Vaccine. 2022 Aug 5;40(33):4845-4855. doi: 10.1016/j.vaccine.2022.06.066. Epub 2022 Jul 4. PMID: 35803846; PMCID: PMC9250903.
Joe Lofaro, Quebec judge suspends unvaccinated father's visitation rights with child, CTV News, Jan. 12, 2022.
Staff, Judge restores visiting rights for Quebec father unvaccinated against COVID-19, The Canadian Press, Feb. 9, 2022.
Government of Canada, Policy on COVID-19 Vaccination for the Core Public Administration Including the Royal Canadian Mounted Police, November 15, 2021.
Joe Lofaro, Quebec wants to tax the unvaccinated, but is that legal?, CTV News, Jan. 11, 2022.
Toronto Star tweet, Aug 26, 2021.
Oliver Browning, Noam Chomsky calls for unvaccinated to be ‘isolated’ from society in resurfaced clip, 2022.
Yes. Great to see another article from you.
I think there is one factor that you are not accounting for (I know that is a bold statement to make given our relative expertise :-)) and that is the relative infectiousness of the asymptomatic yet infected vaccinated (AIV) and the asymptomatic infected unvaccinated (AIU). Taken to an extreme andassuming that infectiousness is directly correlated with viral load, if the AIV has a viral load that is 100th that of the AIU I'd take my chances with the AIV. On the other hand, if the AIV has the same viral load as the AIU, I'd take my chances with the AIU.
Great to have you writing again. Sadly, I think your third hypothesis applies to the majority of people. I had also been wondering about the normal, everyday people who decided to bring in vax mandates for their companies/clubs/charities/sports leagues... What reasoning did they use to decide that they had the moral high ground to force/coerce people into a personal medical decision? Then I was listening to Jennifer Sey talking about her battle with Levi's, and she mentioned the Milgram Experiments. And that's when it all made sense. They were able to abdicate all personal responsibility because someone in a perceived position of higher authority (our gov't health officials for example) told them it was ok. That it was safe. That it was effective. That it was for the good of everyone else. But, it wasn't. But, we can't talk about that.