Contextualizing Scale & Probability
By: Mike Flanagan
Tags: Data Science, Vaccines, Covid 19, Probability, Risk

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Recently, a friend got a call from her local pharmacy, informing her that she could come in early to get her COVID-19 vaccine, though there was a catch—she had originally arranged to receive the Pfizer mRNA vaccine, but the pharmacy only had the Johnson & Johnson’s Janssen vaccine available for the early slot.

She really wanted the Pfizer, but with J&J’s Janssen only being single dose, she decided to move forward with the offer, hoping that she would feel immediate relief and security with the understanding that she would be fairly well covered after a single shot. She would be one step closer to feeling like she was living free, unburdened by the menace that we have all been living with this past year.

One note about this friend before I continue—she is a class-A worrier, especially when it comes to her health. Her concerns and anxieties can be crippling, and she is persistently in need of reassurance.

So when the CDC and FDA called for pause on Johnson & Johnson brand vaccinations the following week, she commenced to panic.

Federal health officials advised the pause after six woman who had received the J&J Janssen vaccine had developed potentially fatal blood clots, with one incidence of death among them. At the time, roughly 7 million people had received the shot.

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Fortunately, with my recently acquired probability capabilities, I was well equipped to understand why the clot risk was negligible, and nothing to worry about.

Unfortunately, I overestimated a person who has not studied statistics’ ability to comprehend scale (and, consequently, I discovered a newfound appreciation for how difficult it was to teach concepts such as probability).

Here is substantially a snippet from our conversation:

“Don’t worry—the incidents of concern only occurred in six people of the over

seven million that have received the vaccine. Therefore, at the moment, our best estimation of such an event occurring to you is less than one in a million.” “Please don’t use one-in-a-large-number odds when trying to ease my concerns… When my dad had his health trouble, we were told his risk was only one in a hundred.”

Her concerns in the moment were deeply personal, but I would like to point out something to the reader, in the hope that were you to find yourself in a similar circumstance that provokes concern for your own wellbeing, you would be able to realize and embrace a sense of security.

One in a hundred is significantly more frequent than one in a million.

So much so, that were you to discover (due to some solar storm activity or whatever) that the likelihood that you would get struck by lighting in a given year were one in a hundred, it would be almost certain that you would get struck by lightning in your lifetime. Lightning would become one of the most haunting presences known to man, and not just in Zeus times.

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It would be up there with cancer, neurodegenerative diseases, and heart disease as a severe, lifelong concern that the most brilliant minds in the world would be attempting to remedy with endless effort every day. Healthy practices would still include exercise, but while outfitted in rubber instead of spandex.

On the other hand, if the likelihood of getting struck by lightning in a given year were one in a million, you would almost certainly live several hundred lifetimes before ever being struck.

Estimating based on an 80 year average lifespan, you would have a 7% chance of being struck within 875 lifetimes. Being struck within 6,250 lifetimes would be the chance outcome of a coin flip—50%. Were you to live in such a world, you would hopefully be less concerned about getting struck by lightning than you are now, in the world with the particular atmospheric electrodynamics that we happen to bear, because, well…

The odds of getting struck by lightning in a given year are around 1 in 500,000, per the CDC—that’s twice as likely as one in a million. I did the math.

Bonus terrifying note: also according to the CDC, 32% of lightning injuries occur indoors. You can’t hide.

Hopefully my digression for the J&J Jansenn vaccine illustrates my point well enough—keeping a sense of proportion when you hear numbers in a certain circumstance is useful. It is not, however, very well intuitive; it is learned.

I would also like to note that surely any risks and (substantial) benefits of any of the developed COVID-19 vaccines may vary among the alternatives. In the context of the Jansenn clotting, we had only seen fatalities among women who had received a particular anticoagulant, heparin. So, at the time, a person would only be at risk under those conditions, which was the reason that the FDA and CDC called for pause, to ensure that heparin would not be used to treat those vaccinated with the Jansenn.

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Since this all happened, the accounting of total incidents of potentially life-threatening clots have gotten modestly worse. Other actions have also since been taken to avoid continued issues with both the J&J and AstraZeneca vaccines.

And a final thought for your loved ones—in times of crisis or severe distress, the numbers will not always help. Often we just need to be heard—to feel embraced and emboldened with care, to be built up in a world that makes us feel small.

In the moment, this may not be intuitive to some of us—I’m still trying to learn this, myself.