Last Monday at 10.30AM I eagerly queued up at the International Red Cross site of Padova, the town where I live and work, to receive a first vaccination shot against Covid-19. I duly received my dose and went back home with some relief. Little did I know that my relief would turn to anger very soon.
My anger arose when I soon heard the news that the treatment with the vaccine I had been given, Astra-Zeneca, was being temporarily stopped, following the detection of a possible adverse reaction. But you should read on before you conclude that I am an idiot (as you indeed should, if the above was all there is to it).

Of course I am not scared at all by the possible side effect that was cited as the reason for the interruption of AZ's vaccine distribution! What infuriated me on Monday was the close call: I realized that in a parallel Universe, somewhere, my vaccination might have been stopped by that totally irrational decision. For that is what it is.

The facts are now in the news: the decision followed a report by researchers at the Paul Ehrlich institute, who compared the rate of a rare form of neural thrombosis in individuals who received the AZ shot to the expected number, seven to 1. After the vaccination, the condition was reported in seven people (six women and one man), out of 1.6 millions who received the shot so far in Germany; and three of them died of it.

Seven to one, in statistical terms, is a significant effect. If one is the expected number of cases, and it is (as it is) a Poisson variable, then the probability of observing seven or more is 8.3*10^-5, corresponding to a 3.8 sigma effect. Hence the observation may indeed correspond to an increased chance of being hit by neural thrombosis, with respect to normal population not receiving the AZ vaccine. So what am I complaining about?

I am complaining because I do not see a cost/benefit analysis accompanying those numbers. If because of the observation we delay the vaccination campaign by one week, for example, in Italy alone we will keep uncovered about 500,000 people for one week longer than if there had been no stop (in Italy at present we have been administering about 180,000 shots a day, from three kinds of vaccines, so mine is a ballpark estimate, but one which can't be wrong by much).

Given the rate of contagions at present (>20k per day in a 60M people country), among those 500,000 about 200 will get infected during that week, and five of them will die. And this is Italy alone. Of course the above is a very rough, back-of-the-envelope calculation, but you can't be very wrong with it. Not by more than a factor of 2.

Now, how many of those 500,000 people, if vaccinated, would have died of AZ's hypothesized collateral effect? Here we are helped by knowing that the number of vaccinated individuals with AZ in Germany was 1.6 millions. That is the denominator in the calculation that resulted in a prediction of one case of thrombosis expected in that population. So in 0.5 million vaccinations, we should expect 0.3 cases of thrombosis if the vaccine does not cause it, or 2.3 cases if we extrapolate the seven german cases. And about one death. One.

Besides the fact that we should not just consider the individual risks and benefits of getting a vaccination shots, but also to the common good (a country of unvaccinated individuals is, nowadays, a sorry place to live in), I believe the numbers above connotate the decisions of Italy, Germany, France and other countries as little short of criminal, as it amounts to increasing the expected number of deaths. A tight monitoring of the rate of thromboses should have been put in place, but no stopping of the vaccination campaign with AZ's vaccine called.

And there's an even more disturbing little factoid that I came across while reading an informative note by the Ehrlich institute. They were already monitoring the rate of those alleged reactions after their initial noticing of a few cases, and on Monday they decided conclusively that there was a problem by observing two more such cases. Those two additional cases brought up the significance of the observation from a five observed vs one expected to a situation of seven to one (which as I mentioned, is a 3.8 sigma effect). Now, there is a blatant example of "sampling to a foregone conclusion", a known mistake in statistical practice. If you watch a running estimate, which is subjected to statistical fluctuations, and wait for long enough, you will eventually see it fluctuate in the direction you want to detect, by the amount you consider significant. That is bad, and it invariably leads you to overestimate the effect you are trying to assess.

See, you study political sciences, make a career as a politician, and one day you grab the prize, and become a governor of a region or a head of state. Good for you, but please, never forget that being there means having immense power to kill, even though in an indirect, undifferentiated way. You stop a vaccine for a week? You are killing five people. You don't? Maybe you are killing more. Alas, there's no mention of how to take those decisions in the old books from your laurea course in political sciences. You should have taken a minor in statistics, but oh, those ugly formulas! (They are indeed ugly, I'll admit).

The memo is the following, anyway:

1) Every week of stopping of AZ's vaccination campaign causes a number of avoidable deaths in the range of few dozens in Europe (it depends on how many doses would be administered under no restriction, which is a number I do not have easy access to here).

2) The stopping manages to avoid up to about five to ten deaths by thrombosis per week (but I suspect fewer, due to the "sampling to a foregone conclusion" practice candidly admitted by the German institute).

3) As I wrote on Monday evening on social media, "Can I suddenly die tonight by some rare adverse reaction to the vaccine, and be reincarnated in some universe populated by fewer imbeciles? Pretty please?"

Alas, no such luck, so far.