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When Our Intuition Fails
Understanding statistics about COVID-19 trends
I have been so grateful during the last 17 months for some parts of my background that are unusual for people who are in clergy and clergy-like positions. First, that I had a career in Information Technology before going back to school, including debuting personal computing in the company I worked for, and later producing and writing for websites, alongside my Ethical Leadership work. So technology doesn’t faze me much. Second, that I worked for almost two years as a video producer of some of the first interactive instructional courses. That included taking distance learning courses in instructional design, equating to about 1/3 of a master’s degree program. So I had a bit of a head start figuring out what might work on video for our Zoom experiences. And now, I’m also glad for my statistics education.
When I was in high school, I was able to spend a summer at a college program, learning computer programming, number theory, and statistics. (And yes, that jump-started my work later in the IT field.) Later, at the University of Chicago, I had to take statistics again, this time with a slant towards how statistics are used in the social sciences. Just before exams that year, I came down with mono, and so I had to take the exams for all my courses during the first weeks of the following quarter. For the statistics class, I finished in about 30 minutes of the offered 90 (it was an open-book test!) and turned my paper in – the professor said, “I’m so sorry, you can take it over if you like. I’ll grade it now so you know what to study for.” To his surprise, and somewhat to mine, I got a 99%. My point? That statistics is one of the areas I can grasp well. And what that means is often that I understand that what seems intuitive is often a mistaken interpretation of what is actually going on.
That’s one reason I approach cautiously many of the stories in the last week or so about the Delta variant infecting those who are vaccinated. I’ve learned to step back from what seems obvious and do a little back-of-the-envelope calculation before coming to conclusions.
Make no mistake. Every rise in the case count, hospitalization count, and death count with this deadly coronavirus is concerning. And yet, looking at the context of statistics is also important.
The main context is this: vaccines were never promised to be 100% effective, even against the original forms of the virus. And yes, the more people who are unvaccinated, the more likely there will be variants on which the vaccines are not effective and which are more infectious. So some “breakthrough” infections and even deaths were always a possibility.
Fewer than 0.001% of those fully vaccinated have had a fatal breakthrough case. Fewer than 0.004% of those fully vaccinated have been hospitalIzed. That’s a lot more effective than I had expected we’d see. And it’s still heart-breaking to know someone in that small percentage.
Yes, New York is seeing a rise in hospitalizations and occupied ICU beds. Most are people who didn’t get vaccinated. We’re still, with many reopenings and with many unmasked especially outside, at about the level we were in the most serious lockdown time in spring of 2020. The news from Florida and Texas and some other states is not as good. New York’s early explosion of cases probably has us more cautious and skittish than some other area (and that helps keep the dangers here lower). Here’s one way to visualize this. (Data from the CDC, regraphed by an anonymous source.)
It’s also true that the more people who are vaccinated, the higher the percent of those who are infected will be among the vaccinated. So we’re going to see more scary stories with headlines like “Outbreak: 50% of those infected were people who were vaccinated!” That’s not the same as saying “50% of those vaccinated were infected,” though our brains may at first react to the news as if that’s the message.
Here’s a drawing making the rounds on Twitter that to explains how, in a population where 95% of the adults are vaccinated, 2/3 of COVID hospitalizations can be of vaccinated people, even with a vaccine with 90% efficacy:
Or this simpler diagram, showing a hypothetical 85% vaccination rate (we're not there for adults yet in NYC), where 50% of the infections are among the vaccinated – yet the vaccines are still highly protective compared to not being vaccinated. This one doesn’t go the next step to how many of those infected in each case end up hospitalized or dying.
A great article with more on the statistics, by an epidemiologist: Why Are Vaccinated People Getting Covid-19? | by Gideon M-K; Health Nerd | Jul, 2021 | Medium
When the vaccines were first being rolled out, the base rate didn’t really matter — if only 10% of the population is immunized, then the majority of cases will be in the unvaccinated population by default. But as more and more people get jabbed, the numbers slowly shift until you have more infections in your vaccinated population. This isn’t some proof that vaccines don’t work, it’s actually simply a numerical certainty given vaccines that don’t provide 100% protection and high immunization rates.
The misunderstandings are easy and that’s why epidemiologists must understand statistics and how to interpret them – in context. My takeaway? It’s time to increase our precautions again, since cases ARE rising and the Delta variant means even the vaccinated may pass along a mild infection. AND it’s not a time to panic, in places like New York state. My condolences to those in hot spots. We New Yorkers know what that's like, from our early experience with this pandemic. I’ll wear a mask indoors when I’ll be close to other people, even though I’m fully vaccinated, because even though vaccinated people are still less likely to have the virus and even less likely to have a serious infection, it is not impossible – and if I have a mild infection that I may not know I have, I could be passing on a deadly virus.
So it’s crucial to remain aware of the trends and vigilant in our goal of keeping others and ourselves as safe as possible.