When I've heard, that because of a single death, which might be attributed to something perhaps related to the vaccine, someone has decided to pause vaccinations in a whole country for two weeks, and then several other countries followed the suite, my first question was:
"But, how many more people will die because of delaying vaccinations for 14 days?!"
Because, on the one side we have "perhaps 1 per B*100 000 000" (guesstimate based on this) and on the other we have something like "at least A*100", and without knowing A and B, how can I do any cost-benefit calculation and form opinion on this?
I'm skeptical in cases like this, because politicians obviously care more about signaling their care about safety, then they actually care about safety. For example "pausing vaccinations because they might have side effects" clearly helps to achieve the first goal, regardless of whether or not it indeed increases public safety. And it can be even worse, if the signaling is aimed not at the citizens, but at someone else.
I've realized, that I don't know how many excess deaths are caused by delaying vaccination for two weeks.
My first intuition was that it's roughly 14*number of deaths per day attributed to COVID. But this isn't the correct way to count this for various reasons.
So, I thought that my last resort is to create such a simulation myself, which borders with insanity given how difficult statistics are and how easily one can shoot themselves in foot. But, since nobody else seems to have created such a simulation for me (or my google skills don't match their SEO skills), I'm forced to try. So here it is:
Obviously it is very simplified, as I am not an epidemiologists (nor a statistician) and moreover, even if I had added more parameters to the model, I would have no idea how to set them to plausible values, and all I wanted to achieve is to build some mental model of how pausing vaccinations impacts total deaths - not compute the exact death toll of Austria. Also, I was a bit encouraged by Robin Hanson's frequent use of simple models as intuition-pumps. Also, I thought that maybe by making my model explicit someone more knowledgeable than me will have easier time pointing me my mistakes.
What are my takeaways from this simple model?
- I don't know why, but I forgotten, and was surprised by the fact, that pandemic can end before everyone is vaccinated, dead or recovered. You can survive the pandemic not vaccinated and never being sick, because herd immunity causes that each sick person infects less than one person, and the virus goes extinct. This is not an invitation to avoid vaccinations - quite the opposite, as the more of us are vaccinated the sooner we reach herd immunity and more lives are saved!
- Starting vaccinations earlier has a tremendous impact on the total number of deaths: for example starting them 100 days sooner can mean several times less deaths (but these are all fake numbers).
- If vaccination starts "too late", that is when the number of infections is already falling down, then the impact of vaccination on the death toll is smaller (relatively to number of deaths) because most of "preventable" deaths have already happened.
- Delaying vaccinations even by a single day, even when the infections are already falling down, still can costs us additional, needless, sad deaths...
- Delaying vaccinations for two weeks, depending on when the vaccination started can costs us huge increase in total deaths (on several percents) or small (relative) increase of deaths (less then a permil) - there's no simple rule, you have to count/simulate it! Certainly it always costs us more than one death.
TL;DR: If a politician doesn't show any analysis or statistical model supporting their claim, and are just saying "we need to delay vaccinations for two weeks as we care about your safety" then it looks like signalling - not a well thought out decision.
Let me know if you know some better model/simulation/approach/answer for this kind of problem.