Some statistical perspective on anecdotal claims of vaccine-induced complications

On social media, it was inevitable that we would start to see anecdotal reports of serious medical conditions experienced after taking a vaccine, and claims that these were related to the vaccines.

For any new medical treatment, including a vaccine, it is important to follow up and document all adverse events experienced by those receiving the treatment to ensure there are no dangerous side effects that are indeed caused by the treatment but not seen in the clinical trials. This is required by the FDA after the emergency use authorizations for the various SARS-CoV-2 vaccines, and has helped recognize the rare but potentially serious anaphylactic allergic reaction to one of the ingredients in the mRNA vaccine, so that precautions can be taken when administered to treat any such reaction should it occur.

However, in our world dominated by social media, it is possible for someone to post a video, picture, or story of someone experiencing a horrific medical condition shortly after receiving the vaccine that in fact is not related to the vaccine, and this type of post is likely to go viral and feed vaccine hesitancy.

One of the tricky statistical issues of population wide vaccination is that it is unavoidable that some bad medical things having nothing to do with the vaccine will happen to manifest right after receiving vaccine injection by random chance alone so will appear to that person and others as related or caused to the vaccine even if it is not. In this post I will try to explain this more carefully.

Suppose a person has a heart attack within an hour of receiving the first dose of vaccine, and their family makes a social media post that goes viral, and a few others in the comments mention they too have had a family member have a heart attack right after receiving the vaccine. This will seem like incontrovertible evidence to many that it was caused by the vaccine. But let's look at the statistics.

There are about 1.5 million heart attacks per year in the USA, which corresponds to >4000/day and >170 heart attacks per hour. Thus, if we vaccinate everyone in the USA sometime in 2021, we would expect about 170 to have heart attacks in the hour just after vaccination by random chance alone, and we can use statistical calculations to compute probabilities of these events.

Given the USA population of roughly 328 million, the probability of a person having a heart attack in a given hour (across the entire population), say the hour after receiving vaccination, is given by 170/328,000,00= 0.000000518, or roughly 1 in 1.9 million. Thus it is very unlikely for any given person to have a heart attack in the hour after vaccination. However, across the population it is bound to happen, and in fact is all but certain to happen many times even if in fact the vaccine did nothing to increase the probability of a heart attack.

If we let Y=# of heart attacks within an hour of vaccination given vaccination of entire American population, Y follows what we call a "Binomal distribution" with N=328 million trials and even probability P=0.000000518, and can use this to compute probabilities about Y. From this distribution, we can find that

Prob(Y>170) = 0.523,

Prob(Y>124)=0.9999

This means that that it is more likely than not that at least 170 would have heart attacks within an hour of vaccination and it would be virtually certain (99.99% chance) that we would see at least 124 heart attacks within an hour after vaccination, even if it had nothing to do with the vaccine.

This applies to other relatively rare medical conditions as well. The extremely large number of vaccinations makes it inevitable that medical complications will occur immediately after vaccination by random chance alone, even if they have nothing to do with the vaccine. The coincidence will make it erroneously appear to observers that it was clearly caused by the vaccine. This is why we must take care in interpreting individual anecdotal reports on social media.

Of course, I am NOT saying that such a condition could not be caused by the vaccine -- of course it could be. That is why it is vitally important to ensure all adverse events are recorded and rigorously studied so any serious adverse event that is in fact caused by the vaccine can be discovered and taken into account.

But I am warning about not automatically assuming from anecdotal reports that medical conditions arising just after vaccination are necessarily caused by vaccination.

Population vaccination is essential if we are going to have any hope of getting the pandemic under control anytime soon, and thus it is crucial to combat any misinformation or flawed logic contributing to hesitancy of people to consider the vaccine.

Image from USA Today