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What can a single catastrophic reaction tell us about the Pfizer vaccine?
It might seem axiomatic that we can’t draw conclusions from one case. Single cases are nothing more than anecdotes, right? Anecdotes are selected from the wild, and they make it through the overwhelming din of informational noise because they:
So we cannot extrapolate from anecdotes. We cannot generalise from them. Nor can we conclude much from them at all. Right?
Actually, this is wrong, and I’m going to show why in this post. In fact, a single case can do a lot more than people realise.
First of all, a single case can definitively reject that something doesn’t occur. When we find clear evidence that there was a massive extinction 66 million years ago, we can reject with certainty that such extinctions do not happen.
Second, a single case can provide information about how often these events occur. We know, for example, that major extinctions are rare, because have not found one in the last 66 million years.
Third, it can illuminate underlying causal effects that later research can investigate systematically. Why would such an extinction occur? Well, it seems there’s a massive indentation in the earth, coupled with a layer of iridium in geological deposits, and evidence of massive tidal waves 66 million years ago. Hmm, sounds like a massive asteroid collided with the earth just when the extinctions can occur.
So a single case can be enormously information-rich.
The Case of Maddie de Garay
This brings us to Maddie de Garay. Last November, as part of Pfizer’s trial of their COVID-19 vaccine for 12 - 15 year olds, Maddie de Garry, a healthy, normal 12 year-old girl, suffered a catastrophic reaction to the Pfizer vaccine. Within hours after her vaccination, her bodily systems began to shut down. She became paralyzed from the waist down, unable to eat food, and now requires a wheelchair.
These effects commenced immediately after the administration of the vaccine, and it is obvious that no similar events were observed in the placebo arm. There can be no doubt that the vaccine is the causal agent.
Her case demonstrates that we cannot assume the vaccine is universally safe. In fact, rejecting that the vaccine cannot do catastrophic systemic harm—everything in the body gone wrong in one fell swoop—requires only a single case of such harm.
The case of Maddy de Garay has special properties that make it even more relevant. Her experience was not selected from the wild by media biases. It was, in fact, embedded in a systematic set of data, Pfizer’s randomized controlled trial of its mRNA vaccine. For that reason, it conveys a lot more information. We know for example that there were only 2,000 12 - 15 year olds in this trial, with about 1,000 getting the vaccine and 1,000 getting placebo.
Because there were only 1,000 children who got the vaccine in the trial, and Maddie de Garay’s adverse effect was among them, we have some basis for establishing the parameters for such catastrophic events. Using a Bayesian estimate—assuming a uniform prior (which just means that we have no a prior estimate of the likelihood of such an event)—we know that the most likely (posterior) probability of such catastrophic events is 1 in 500. Using binomial assumptions, this has a 95% confidence interval of between I in 182 and 1 in 4082. In other words, under these assumptions, such an event could be as likely as 1 in 182 children experiencing such an event.
But I grant that this is unlikely to be the true prevalence. Let’s use a more conservative estimate and see how that fares. If we assume the true prevalence of these catastrophic effects is 1 in 100,000, then what is the chance we would observe this adverse effect in a sample of 1,000. It is only 1 in 100. The conventional probability value in such research is 1 in 20 (p = .05). This means that we can reject the possibility that such effects occur at a population level of 1 in 100,000 and therefore are more likely to be more frequent.
We can play the same game with 1 in 50,000. We can reject that as well, because we would only get the result 1 in 50 times, substantially more than the conventional probability of 1 in 20. Although this requires some additional assumptions (that the Pfizer trial sample is representative of the larger population), only an estimate of 1 in 20,000 would be within the bounds of statistical probability.
In other words, an estimated probability of a reaction as severe as Maddie de Garay’s is somewhere between 1 in 182 and 1 in 19,999, depending on your prior assumptions. And yet children from 12 - 15 face a risk of harm from COVID that is statistically indistinguishable from zero.
I recommend everyone listen to Maddie de Garay’s mother’s testimony about her daughter here (around 2:10). Her tragic story has been in my head ever since. Indeed, I am unlikely ever to forget it.
Source: wearyprof.substack.com
- are sensational
- flatter our prejudices
- conveniently support a preferred narrative
- confirm pre-existing beliefs (e.g., confirmation bias).
So we cannot extrapolate from anecdotes. We cannot generalise from them. Nor can we conclude much from them at all. Right?
Actually, this is wrong, and I’m going to show why in this post. In fact, a single case can do a lot more than people realise.
First of all, a single case can definitively reject that something doesn’t occur. When we find clear evidence that there was a massive extinction 66 million years ago, we can reject with certainty that such extinctions do not happen.
Second, a single case can provide information about how often these events occur. We know, for example, that major extinctions are rare, because have not found one in the last 66 million years.
Third, it can illuminate underlying causal effects that later research can investigate systematically. Why would such an extinction occur? Well, it seems there’s a massive indentation in the earth, coupled with a layer of iridium in geological deposits, and evidence of massive tidal waves 66 million years ago. Hmm, sounds like a massive asteroid collided with the earth just when the extinctions can occur.
So a single case can be enormously information-rich.
The Case of Maddie de Garay
This brings us to Maddie de Garay. Last November, as part of Pfizer’s trial of their COVID-19 vaccine for 12 - 15 year olds, Maddie de Garry, a healthy, normal 12 year-old girl, suffered a catastrophic reaction to the Pfizer vaccine. Within hours after her vaccination, her bodily systems began to shut down. She became paralyzed from the waist down, unable to eat food, and now requires a wheelchair.
These effects commenced immediately after the administration of the vaccine, and it is obvious that no similar events were observed in the placebo arm. There can be no doubt that the vaccine is the causal agent.
Her case demonstrates that we cannot assume the vaccine is universally safe. In fact, rejecting that the vaccine cannot do catastrophic systemic harm—everything in the body gone wrong in one fell swoop—requires only a single case of such harm.
The case of Maddy de Garay has special properties that make it even more relevant. Her experience was not selected from the wild by media biases. It was, in fact, embedded in a systematic set of data, Pfizer’s randomized controlled trial of its mRNA vaccine. For that reason, it conveys a lot more information. We know for example that there were only 2,000 12 - 15 year olds in this trial, with about 1,000 getting the vaccine and 1,000 getting placebo.
Because there were only 1,000 children who got the vaccine in the trial, and Maddie de Garay’s adverse effect was among them, we have some basis for establishing the parameters for such catastrophic events. Using a Bayesian estimate—assuming a uniform prior (which just means that we have no a prior estimate of the likelihood of such an event)—we know that the most likely (posterior) probability of such catastrophic events is 1 in 500. Using binomial assumptions, this has a 95% confidence interval of between I in 182 and 1 in 4082. In other words, under these assumptions, such an event could be as likely as 1 in 182 children experiencing such an event.
But I grant that this is unlikely to be the true prevalence. Let’s use a more conservative estimate and see how that fares. If we assume the true prevalence of these catastrophic effects is 1 in 100,000, then what is the chance we would observe this adverse effect in a sample of 1,000. It is only 1 in 100. The conventional probability value in such research is 1 in 20 (p = .05). This means that we can reject the possibility that such effects occur at a population level of 1 in 100,000 and therefore are more likely to be more frequent.
We can play the same game with 1 in 50,000. We can reject that as well, because we would only get the result 1 in 50 times, substantially more than the conventional probability of 1 in 20. Although this requires some additional assumptions (that the Pfizer trial sample is representative of the larger population), only an estimate of 1 in 20,000 would be within the bounds of statistical probability.
In other words, an estimated probability of a reaction as severe as Maddie de Garay’s is somewhere between 1 in 182 and 1 in 19,999, depending on your prior assumptions. And yet children from 12 - 15 face a risk of harm from COVID that is statistically indistinguishable from zero.
I recommend everyone listen to Maddie de Garay’s mother’s testimony about her daughter here (around 2:10). Her tragic story has been in my head ever since. Indeed, I am unlikely ever to forget it.
Source: wearyprof.substack.com