It seems incredible that only a year ago the vaccines for COVID-19 seemed so far away, and yet today it is not only that they have already arrived, but also that the speed we have reached in vaccinations was practically unimaginable just a few months ago. I am not going to go into political readings, I am left with the incredible work being done by health workers, essential for all this to be possible.

When I was given my second dose, just over a week ago, I shared this reflection, the speed with which the population is being vaccinated, and even she herself, who is part of the enormous collective effort to achieve this goal, told me that she also found it surprising and fascinating. The vaccines we dreamed of just a few months ago are now reaching ages we thought would have to wait much longer. I have friends in their twenties who have already received their first jab.

So, these days we can find headlines of the most striking, like this one from CNet which states that 99% of deaths from COVID-19 have occurred among people who have not yet received the vaccines. The problem is that, even being true, there are some aspects that we must consider when reading this information. And is that it starts from a triumphalism that, although positive for public opinion, can be somewhat misleading and, in the medium term, give us some displeasure, because the headlines will turn in the opposite direction.

Vacunas y sesgo del superviviente: ¿cómo leer los datos?

The fundamental factor that the headline does not take into account is, of course, the percentage of the population that has already received the vaccines. And it may seem silly but it is not at all, because it does not have the same value if we talk about 10% of the population vaccinated, as in the case of the Bahamas or Lebanon, than if we talk about values above 70%, as in Iceland and Malta. Not to mention the case of Gibraltar, where more than 99% of the population has already been vaccinated.

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With a very low vaccination rate, this data hardly adds anything, it is almost like having said it last year, when the vaccines were still being developed, the key is to check to what extent that 99% is maintained as the percentage of the population vaccinated is increasing.The percentage of the vaccinated population is increasing. And that is precisely the point I was making earlier about how simplistic analyses can translate into false bad news and, incidentally, into arguments used by antivaccinationists (and I am referring to conspiracists, not to those who have some reasonable misgivings).

From zero to one hundred… or from one hundred to zero

There will come a time when the majority of hospitalized people will be vaccinated people“. The phrase is not mine, it is from a tweet by Javier Álvarez Liébana, a mathematician with a PhD in statistics and dedicated, among other things, to dissemination through the Internet. But I reproduce it because it reflects exactly the point I want to make in this reflection. To make it easier to understand, I return to the headline format with respect to vaccines that I mentioned at the beginning.

Let’s imagine a country called Freedonia (yes, I love Marx Brothers movies), with a population of one million inhabitants, and all of them have received their vaccinations. At that moment the Kappa variant (seems to me the most appropriate for the Marxes) is ravaging the world and, as a result, 100 citizens of Freedonia have had to be hospitalized and one of them has died of complications.

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The day after this unfortunate event, the local media will be reporting extensively on what has happened, and it will not be long before, somewhere, we read something like100% of those hospitalised and killed by Kappa were vaccinated‘. What does that headline tell us? That vaccines are not effective. Is this true? Not at all. The problem is that there are missing dimensions in that reading.

Álvarez Liébana relates it, quite rightly, to traffic accidents and hospital admissions in relation to the use of seat belts. Are more people admitted if they were wearing seat belts than if they weren’t? Yes. Does this mean that seat belts are unsafe? No. What it means is that the deaths of unbelted people have not been taken into account. And that’s the key statistic, the percentage of deaths in accidents with and without seat belts. With vaccines? The same.

There will come a time when the vast majority of the population is vaccinated, when our immune systems are already able to respond to the coronavirus mutations in the same way as they do to the flu variants, and the path to vaccination will be more difficult.The fastest way to get to that point, as of today, is vaccines. But that doesn’t mean that pathogen and disease are going to disappear completely from our lives, unfortunately.

I recommend, to better understand this concept and the survivor fallacy, reading this Twitter thread, also by Álvarez Liébana (the only thing I reproach him for is confusing the Royal Air Force with the Royal Navy), in which he tells us how the interpretation of data can change substantially when a new dimension is removed or added.