Impact of population mixing: The tractability problem
During graduate school, once upon a time, I asked my professor an obvious question: “The assumptions of this model are clearly wrong, so why are we learning it?”
He answered, without a hint of irony, “Yes, but it’s tractable”.
The model relied on the assumption of ordinal utility and the details do not really matter. But my point was, simply, teaching us models based on incorrect assumptions is about as useless as teaching us about a geocentric universe. That professor taught me a valuable lesson: All modellers are wrong, some are honest.
Generally, that’s why I don’t write about theoretical models. They tend towards simplicity to the point of absurdity. The old quip that “some are useful” neglects the antipodal “most are not useful”, and, as we have seen with the coronavirus and climate change models, can blur or even obscure people’s world views to the point where they become dangerous, society-devouring fanatics.
But a couple people pointed out a paper from David Fisman titled Impact of population mixing between vaccinated and unvaccinated subpopulations on infectious disease dynamics, so I decided to give it a read.
The paper points out that “[s]imple mathematical models can often provide important insights into the behaviour of complex communicable diseases systems”. The model is definitely simple, but the insights garnered from it are about as useful as a modeller playing tic-tac-toe with himself.
Here is the setup:
Agents in the model can be vaccinated or unvaccinated.
They can exist within three states: “susceptible to infection”, “infected and infectious”, or “recovered from infection with immunity”.
They treat vaccinated individuals as “all-or-nothing”, which essentially means vaccinated individuals either get a perfectly sterilizing vaccine or a saline solution.
Contact between groups can range from completely random to highly assortative (the unspoken assumption of a vaccine passport system).
The R0 does not change and vaccine immunity does not wane.
The modellers did not imagine that a scenario could exist where vaccine effectiveness could be negative and chose parameters accordingly.
The results are obvious because their entire model is just overly complicated algebra: the vaccinated get infected at higher rates when unvaccinated are presented and unvaccinated do worse with unvaccinated. This model is so insightful that I had to double check the credentials of the modellers because I could have sworn they were 3rd year undergraduate students.
If you set up the model in the same way, but assume vaccine effectiveness is strictly negative, then you get the opposite result. Unfortunately for the modellers, negative effectiveness is all we have been seeing in most data sources lately. They never bothered to parameterize based on the real world data we have been seeing for months and instead chose fantastical vaccine effectiveness numbers that never existed for omicron (see below regarding the first omicron outbreak).
Nor did the authors even bother to stress test their model despite ample real world data available to do so. A simple difference-in-differences or well designed regression discontinuity would go a long way towards validating their model. Do they really expect us Neanderthals with “antivaccine sentiment” to do it for them?
But forget all of that. They are essentially making an argument for a passport system and ignored waning immunity, they ignored negative effectiveness (in both the first few weeks and now with omicron in the general vaccinated population respectively), they ignored sub-characteristics of populations, behavioral differences, population densities, non-sterilizing vaccination, and eventually widespread societal impacts. They ignored a thousand other variables all so they could have a simple, tractable model that tells vaccine enthusiasts what they want to hear.
The thing about tractability when dealing with human beings is we are not so easily controlled.
Models are used instead of research, knowledge and science.
My brother works at university, and his department uses models for everything due it being cheaper than loading up a lorry with equipment and setting up an experiment in the area of interest. Simple as that.
F.e. they, and all agencies depending on their department (geology) use the same models, as underlay for decisionmaking and policy, handling of permits and so on. If anyone, say a farmer wanting to open new pastures, wants to use actual data from reality, they have to pay for it themselves, and the model still takes precedence juridically.
I'm sure it's obvious why models has been /the/ fad in both science, business and governement these past 15-20 years.
Cheap, efficient, not correct but correct enoguh for purpose. Establishes a high threshold for any kind of competition, private or political, and his impenetrable to 95% of the public, us neither having access to the actual model's structure or the knowhow re: the math behind it.
It's the magician's hat, really.
A lecturer I had in studying "the history of ideas and the ideas of history" (sorry, but that's the best translation I can manage) used an anecdote (purely fictional I think) about historical China: the Mandarins, fearing loss of power due to a growing class of craftsmen and professionals and also fearing that succesful colonisation of far-away areas (such as East Africa) would further loosen their control, decided that Pi equals 3. It's close enough.
Hence, all crafts, arts, et cetera were obligated to use '3' for Pi. Meaning that the Mandarins, controlling the very definitions of reality, could retain power since virtually the entire people instead blamed the craftsmen, artisans, and so on.
So now we have situations like a one nearby, where a small scale farmer can't move his herd to a new pasture, because according the model the manure and run off would travel uphill 150 meters, then through bedrock, and then sweep down into a river. Because that's what the model shows when applied to the rounded numbers for the relevant data for his general area. Acually going there, having a look, taking soundings, and making test? Why? That might mean the farmer could succesfully develop his small scale local food production. Can't have that. Better people in his area stay dependent on one of the three food chains of Sweden.
That's why we use models.
Thanks for taking a look. I am appalled that the legacy media were all spouting the headlines yesterday morning, the same day the study was released. The opening paragraph of the G and M version is quite damning:
"People who have not been vaccinated against COVID-19 contribute disproportionately to the risk of infection among those who have been vaccinated, according to a new study being released as Canadians navigate a phase of the pandemic with few public-health measures remaining."
And then there was the quote in the G and M article from the Pierre Elliott Trudeau Foundation’s COVID-19 Impact Committee chair, lending her endorsement to the models.
So the Fisman article is published yesterday in the CMAJ and all of these articles in MSM just simultaneously pop up.
"Conflicts of interest noted: Competing interests: David Fisman has served on advisory boards related to influenza and SARS-CoV-2 vaccines for Seqirus, Pfizer, AstraZeneca and Sanofi-Pasteur Vaccines, and has served as a legal expert on issues related to COVID-19 epidemiology for the Elementary Teachers Federation of Ontario and the Registered Nurses Association of Ontario. He also served as a volunteer scientist on the Ontario COVID-19 Science Advisory Table. Ashleigh Tuite was employed by the Public Health Agency of Canada when the research was conducted. The work does not represent the views of the Public Health Agency of Canada. No other competing interests were declared."
Unfortunately, although I could see something stank with the "study," most people will just not their head in agreement, and go back to being jerks to us abstainers.
Thanks again, for lending us your stats viewpoint on this one.