Post hoc ergo propter hoc
Alarming news titles have flooded mainstream media around the world: 29 persons died after anti-Covid19 vaccination in Norway. For the urgent vaccination issue, the number appears too large to be ignored. And intuitively, is it likely that an individual would die within this short term for reasons other than the vaccination?
However, let’s ponder. The total number of vaccinated persons in Norway so far has been 42.000. Is it big compared to the total number of Norwegians over 74 years old? The so called population pyramid for Norway enables a look-up over the distribution. Respective annual mortality rates are, of course, age-dependent: the probability to die within the next year grows rapidly after 75:
Using the actuarial data from USA that account for the non-uniform distribution of age and age-dependent risks, and by neglecting the variable time-after-vaccination (roughly 1…30 days), we can sum up the counts to the right of grey dotted line and obtain the number of all people above 74 living in Norway: 393.240. Of which 42.000, i.e. 10.7%, were vaccinated. Of which, in turn, 29 were reported dead after the vaccination within one month. Summing up the numbers of the dot-dashed line shows that 29.549 of 393.240 would die within one year in total, and therefore 259 of just those vaccinated should have died withing the first month for general reasons, related to neither vaccination nor Covid-19. This is ~9-fold excess over the 29.
Indeed, the authorities seem to emphasize deaths of a selected group of individuals. It was not completely clear who contributed to the group of deceased 29, but it apparently is a minority of vaccinated persons who have died within the month. “All the reported deaths related to elderly people with serious basic disorders,” Norwegian Medicines Agency said in a written response to Bloomberg. “Most people have experienced the expected side effects of the vaccine, such as nausea and vomiting, fever, local reactions at the injection site, and worsening of their underlying condition.” In other words, 29/259=11.1% of the vaccinated and deceased persons developed such symptoms just before death. Is it too many, given similarity of such signs to many other diseases’ course? How often symptoms of same severity were observed among vaccinated who then successfully recovered and developed immunity?
The calculation above is pretty simplistic, but might be nonetheless worth considering. Having observed formal side effects of the vaccination in the deceased and claiming “after this, therefore because of this” would be fallacious. In this crucial moment, so sensitive to rumours and conspiracy theories, it is worth awaiting for a more careful, statistically and clinically grounded conclusion.
