Infections in vaccinated with covid-19: the use without context of statistical data leads to false conclusions

The Minister of Health of the Community of Madrid, Enrique Ruiz Escudero, reports on the epidemiological and health care situation due to coronavirus in the region on July 23. Isabel Infantes / Europa Press

In recent days, headlines have been read warning about the increase in deaths from coronavirus among people with a complete vaccination schedule. Some media has even stated that "Vaccinated people are six times more likely to die from

variants

of the covid." While the increase in cases of vaccinated and infected people is real, and to be expected when vaccines are not perfect, this news is misleading. Many of these examples show how the blind or contextless use of statistical results can lead to false conclusions.

A large part of these errors come from partial or biased analyzes of the data offered in scientific studies, such as that of the Public Health England (PHE) published on July 9, 2021. This report collects the cases of disease in the United Kingdom due to delta variant, which at the time of data collection accounted for more than 97% of new infections.

In it it is observed that the number of deaths in people with two doses of vaccine is increasing: they are 118 of the 257 deceased, that is, 46%.

However, this does not mean that the vaccines are not working.

In fact, they are the results that one would expect from any treatment with a certain probability of error.

More information

• Five reasons to distrust the herd immunity planned this summer in Spain

• Those vaccinated and those cured of the covid can transmit the coronavirus even if they do not have symptoms

Suppose an ideal situation in which everyone had the complete vaccination schedule.

A PHE analysis estimates that the Pfizer vaccine prevents hospitalization due to the delta variant in 96% of cases.

In this case, 100% of those hospitalized - and of the deceased - would be vaccinated, but the risk of suffering serious consequences would be 25 times lower than without the vaccine - that is, it would be reduced by 96%.

On the other hand, according to the PHE, about 36% –92 out of 257– of the deaths correspond to unvaccinated people.

Calculating the percentages of deaths among those infected vaccinated and not vaccinated, it is obtained that 1.09% of the vaccinated infected died, while "only" 0.13% of the unvaccinated did so.

These figures are the ones that have been used in the most alarmist or anti-vaccine headlines, drawing conclusions such as that "vaccinated people are six times more likely to die."

Again, these statements are incorrect and may result from misinformation or malicious processing.

As supported by numerous studies, the probability of being infected with or without having received the vaccine is completely different, even compared to the Delta variant

In the first place, in these news the calculated probabilities are being confused: those of the report correspond to "dying being vaccinated and infected" and not to "dying being vaccinated", as stated in the headline. This nuance is very relevant, since we are calculating the probability on very different groups, without taking into account where the vaccine is most effective: avoiding infections. And, indeed, as supported by numerous studies, the probability of getting infected with or without having received the vaccine is completely different, even compared to the delta variant. For example, Pfizer maintains an 88% average effectiveness after the second dose.

One could delve into the probability of contagion, vaccination coverage or other factors, but even staying with the aforementioned values, when we analyze the data more carefully, we verify that the argument is still false. In many cases, like this one, it may be necessary to take into account a third variable with a strong causal relationship in this problem, such as age. Indeed, if we divide the population into those under and over 50 years of age, the percentages of deaths among those vaccinated are 0.036% in the first group and 2.2% in the second, while in the unvaccinated they amount to 3% and 5.6 %, respectively. Therefore, deaths are lower among vaccinated people in both groups.

The Simpson Paradox or Simpson-Yule effect, which occurs when the association between two variables (mortality and vaccination rates) changes completely when the effect of a third variable (age) is taken into account –controlled–

Thus, the conclusion of the study would be the opposite to that obtained without dividing by age.

This apparently counterintuitive result is an example of what is known as the Simpson Paradox or Simpson-Yule effect, which occurs when the association between two variables (mortality and vaccination rates) changes completely when taken into account. the effect of a third variable (age) is taken into account - it is controlled -.

The explanation for this phenomenon lies in the differences in the incidence of the disease between the groups. We know that its effects are more serious in older people and, precisely because of this, its vaccination rate is higher - over 80% in the United Kingdom. However, although the vaccine increases the chances of survival in this group, it is still lower than in other younger age groups. As the proportion of elderly people is much higher in the group of vaccinated infected (48.3%) than in the unvaccinated group (1.76%), the global difference indicated above is observed, but this does not imply - in any way - a increased mortality with vaccination.

Paradoxes like Simpson's appear with some frequency in real problems and reveal the dangers of working with proportions, in particular, of groups of very different sizes, or with subgroups that have different properties.

It is a clear example of the importance of not drawing conclusions from statistical studies when not all the data are available.

Thus, despite what alarmist and misinformed voices say, without any doubt, as the PHE report and many others point out, to minimize the consequences of a possible contagion with the delta variant, it is advisable to get vaccinated.

José Luis Torrecilla

is an assistant professor at the

Autonomous University of Madrid

Editing and coordination

: Ágata A. Timón G Longoria (ICMAT).

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