Vaccine Efficacy and the Immunity Time Spans
Vaccine efficacy numbers mean a very specific thing and it's not what many people think.
Visualizing Vaccine Efficacy Numbers
The Rhetoric of Immunity Time Limits
Looney Tunes: High Diving Hare
Visualizing Vaccine Efficacy Numbers
There have been more examples of innumeracy over the last year than we could possibly count (get it!) but as we’re racing toward the end of this crisis, we get to fight our way through some persistent misunderstandings around COVID, the vaccines, and the ways that public health officials talk about data that doesn’t consistently match how the public understands that rhetoric.
Let’s start with the concept that vaccines are 95% effective. This is an idea completely misunderstood from the moment we started talking about vaccines.
It is clear to me at this point that any writer who has not studied mathematics past a certain level should simply have their math card revoked and required to filter any numerical writing past an approved authority.
We gotta back way up on this one to get it right. Vaccine efficacy is based on observing a large population of people and watching how infection patterns impact both the vaccinated and the placebo group.
Let’s refer back to the Pfizer study submitted to the FDA. In that study, 18,555 people were vaccinated and 18,533 people received the placebo injection. In these groups, 7 days after the second dose was administered, we saw that the vaccinated group got infected at only 5% the rate that the placebo group was infected.
Furthermore, this is the number of cases we see over the course of a two month study. So those 9 people out of 18,555 were not symptomatic and infectious that whole time, but only for a few weeks.
So, to take CNN’s example and re-imagine it for the reality we have with this data.
Let’s say 1 million people are travelling. If everyone is unvaccinated (and the window of infection is roughly one week), there will be about 1,100 infected travelers.
If, however, everyone is vaccinated, there will be about 60 infected travelers and their chance of infecting you (my dear vaccinated friend) is reduced substantially.
A Boeing 747 carries 366 passengers, so assuming the risk is distributed evenly (which is never is, but let’s ignore that for now) and that your plane is completely packed (which it probably isn’t) that means:
with no one vaccinated, there is about a 43% chance that even a single person on your plane has COVID
with everyone vaccinated, there is only a 2% chance anyone on your plane has COVID
The media presentation that one in ten travelers has COVID is so unspeakably incorrect, it makes me daydream about what constitutional provisions we can implement that can get these people to shut the hell up for one goddamn minute and talk to someone before they hit the “publish” button. The idea that 10% of all vaccinated travelers at a given time have COVID is about 20,000% higher than the reality. I pondered trying to visualize it, but the absurdity of it would give me a larger task than I’m willing to apply to this problem.
(I’m only half-way comfortable with that proposed way of looking at the numbers b/c everything is so variable. The Pfizer vaccine study was not done during a major COVID surge, so it’s not really representative of the likelihood of infection during a surge. On the other hand, as vaccines help pull the numbers down, it becomes even less likely that you’ll catch COVID because even fewer people will have it. So the 0.05% chance a vaccinated person had of catching COVID at some point during this study will go down even further as more people people get vaccinated.)
Here is the bottom line: Travel is relatively safe. Airplanes really do have excellent filtration systems. Masks increase the safety but vaccines increase the safety far more. We are very close to having 50% of the entire adult population vaccinated and that will make a huge difference.
The Rhetoric of Immunity Time Limits
Oh man, this one is driving me up a wall and it took me days to figure out why.
I was an early adopter for florescent bulbs and for LED lights. My initial excitement was the description on the packaging, that they would last “up to 7 years”. Imagine my frustration and disappointment when I’m still replacing bulbs every 2-3 months because when they say “up to 7 years”, they mean “these bulbs may burn out with in 6 months or they may last up to 7 years”. To be fair, I was in my 20’s when I learned this lesson, so I may perhaps be forgiven my youthful optimism.
But this is something that has been established in our cultural consumer memory: when someone says “up to X months”, they are referring to an upper limit. It could be that a product that works “up to 8 months” will break around 3 months. On the other hand, if we hear that something will last “at least 8 months”, we interpret that phrase as a time limit. We hear that we are guaranteed 8 months of functionality but all bets are off after that. This is our cultural understanding based on our experiences with commercial products judged against the rhetoric of marketing firms.
But that is not how the terminology works when we start talking about the length of COVID immunity.
In the FDA study I linked to earlier, the time frame for immunity that is consistently referenced is “two months”. The reason the reference such a short time frame is because the study was done very quickly. They couldn’t study the effects over 3 months because, when they published the paper, verifying 3 months of immunity meant looking into the future.
That is the case for most studies of re-infection. This virus has been such an omnipresent force over the last year that we often forget how recent this disease is. Studies that look at re-infection can’t see any further than the runway of the past. What we have found so far is that natural antibodies for COVID protect people right up until the end point of the study. Most scientists are not comfortable making projections into a future they cannot observe, so when they say that a vaccine or COVID infection produces antibodies that protect up to 7 months, what they mean is that it protects until 7 months at a minimum and we don’t have a way to time-travel into the future to know more.
Antibody immunity and vaccine immunity currently last as long as we have been able to measure them. Every month adds another month to how long we know that immunity lasts. It could go on forever or it could wane over time. We simply do not know.
My personal view in this is that speculating about the future of COVID is borrowing trouble. I will complete my vaccine series this week and continue on, unconcerned about the future of this disease in my own life, but I’m not going to spend time worrying about the unknowable.
Looney Tunes: High Diving Hare
In High Diving Hare, Bugs is running a vaudeville show that includes Fearless Freep, a high-diving act. For some reason, Yosemite Sam is a huge Freep fan and, when Freep is delayed, Sam demands that Bugs perform the high-dive himself. This leads Bugs to trick Sam into doing the high-dive about a dozen times.
Yosemite Sam versus Bugs Bunny has some of the same energy as the Wile-E-Coyote shorts. Sam’s persistence would be laudable if it wasn’t so mean-spirited. There is a delightfully manic quality in this short and I can see the big difference between Disney (where jokes typically have an origin or at least a logical connection to the action) and Looney Tunes.
Here, the only thing that matters is the joke. If it get’s a laugh, it’s worth doing. How did Sam get confused and walk out onto the plank on the upside-down side? Doesn’t matter, it gets a laugh.
Fun side-note: There is a moment when Sam pounds on a door Bugs constructed on the plank and shouts “Open that door”, the turns to the audience and says “You notice I didn’t say Richard” that has confused me since I was a child. Today I learned that “Open the Door Richard” was an enormously popular vaudeville act and song about a drunk who can’t get into the bar. Mystery solved!
I might be missing something, but you may have a typo --or math error-- when you say there is a "43% chance that even a single person on your plane has COVID".
Shouldn't it be 1 - (1 - 1100/1x10^6)^366 which is about 33% ?
Not to defend the CNN paragraph in the slightest, but it seems to me the mistake they're making is somewhat different then how you put it.
They said "for every million vaccinated people who fly, 100,000 could still become infected." That sounds to me like they're understanding 90% efficacy as something like, "90% of people are entirely immune, 10% of people the vaccine just doesn't work for some reason so are still vulnerable."
Which to my understanding is also wrong, but not ludicrous like "10% of all travelers have Covid." Of course then the problem is that they put it in such a way that it's easy to misunderstand it as "10% of all travelers have Covid," because they foregrounded the big number to make it sound alarming and didn't explain it further.