COVID and the Simpson Paradox
Alarming data showing the amount of vaccinated people admitted to hospital compared to non-vaccinated people may give rise to concern. This is not a true reflection of the data and partly due to what is known as the Simpson Paradox.
The simple conclusion is that if out of 100 hospitalized by Covid, 70 are vaccinated and 30 are not, that means that those who have the full schedule are more affected by the virus than those who did not receive doses. This is a major causality error that creeps into the argument of the anti-vaxxers and conspiracy theorists.
Is a non-vaccinated person more likely to be infected than a vaccinated person? Yes. Is it easier for a non-vaccinated person to die of coronavirus than a vaccinated person? Of course. As well as being admitted to a hospital ward or entering an ICU, as a result of a complication of Covid-19 infection.
The latest report from the Ministry of Health reflects the different possibilities of falling ill, being admitted to hospital, and dying from the virus depending on whether a person is vaccinated or not according to different age groups.
From November 29 to December 5, which is the last week analyzed, the incidence of infections among those vaccinated in Spain was 147 cases per 100,000 inhabitants – a total of 54,004 positives. Among the unvaccinated, this incidence was 310 positives per 100,000 inhabitants -12,415 infected.
The data shows that those who are not vaccinated play Russian roulette with the coronavirus. A person between 60 and 79 years old is 16 times more likely to die from Covid if they are not vaccinated than if they have the full vaccine schedule. The key is not in the global number of infected, but in the rate.
This is explained by Simpson’s paradox, which is a statistical anomaly where a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics and is particularly problematic when frequency data is unduly given causal interpretations. To establish the real effect of the vaccine, the data needs to be divided into subgroups of age.
From October 11 to December 5, 206 vaccinated and 70 unvaccinated people have died from coronavirus in Spain. By looking at the raw data, the vaccinated dead are almost three times higher. But the ratio of those who died with the vaccine must be established based on the number of people with a full regimen and booster dose, which is much higher than the total of those who have not received the vaccine.
99.2% of Spaniards between 70 and 79 years are vaccinated, the same as 97.7% of those between 60 and 69. There are 206 deaths from Covid among millions and millions of Spaniards who have been double vaccinated, while 70 have died among a few tens of thousands of those who refused to be vaccinated.
Therefore, the death rate for vaccinated people between 60 and 79 years is 0.29 per 100,000 people, while the rate for the unvaccinated is 4.71, which means that a vaccinated person is 16 times less likely to die – which results in the division of 4.71 by 0.29- than a non-vaccinated one.
In the same way, in this age group the risk of infection in a vaccinated person is six times lower, that of hospitalization 14.5 times less, and the chance of being admitted to an ICU is 24 times less.
These large differences that are seen between 60 and 79 years, one of the age groups most affected by Covid, are also seen in the rest of the age groups.
From 12 to 29 years, the risk of becoming infected for a vaccinated person is three times lower than for an unvaccinated person, according to data from the Ministry of Health, in the same way that the risk of hospitalization is also 11.5 times lower.
Between 30 and 59 years of age, which is currently one of the bands with the highest level of contagion only below those under 12 years of age, the risk of hospitalization for an unvaccinated person is seven times higher.
Among those over 80, who were the first to receive the booster doses, the possibility of dying for an unvaccinated person is ten times higher, while they have seven times more possibilities of being admitted than a person with all their doses.
If you are unsure about your vaccine status or would like a antigen or PCR test for travel purposes, you can contact English speaking healthcare providers through the ESHA Spain business directory.
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