Friday, July 23, 2021

How to Lie While Telling the Truth: This Time on Vaccination Effectiveness

I have had two previous posts on people using a true statement to mislead, one on religion, one on the effects of climate change. This is the third.

99% of COVID deaths are now of unvaccinated people, experts say

And, from a different story:

More than 99% of recent deaths were among the unvaccinated, infectious disease expert Dr. Anthony Fauci said earlier this month on NBC's Meet the Press,

Such claims struck me as implausible. The estimated effectiveness of the vaccines used in the U.S. is about 95%. Since a majority of adults, and a large majority of those most vulnerable, are vaccinated, one would expect more than 5% of those dying to be vaccinated. It might be somewhat lower if more of the unvaccinated are located in areas with higher than average infection rates but it would be surprising if it was that much lower.

The solution appears part way down the story under the headline:

In Texas, 99.5% of people who died from COVID from February through July 14 weren't vaccinated,

As of the beginning of February very few people had been vaccinated and deaths were running about ten times their current level. A calculation for a period starting then can be expected to greatly overestimate the current ratio of unvaccinated to vaccinated deaths. Another story I came across was for a period starting in December.

What the current ratio is I don't know — possibly no one does. Fauci's claim is about the past month, but an AP news story giving the same figure he did (.8%) added:

The CDC itself has not estimated what percentage of hospitalizations and deaths are in fully vaccinated people, citing limitations in the data.

Among them: Only about 45 states report breakthrough infections, and some are more aggressive than others in looking for such cases. So the data probably understates such infections, CDC officials said.

Reading the stories, the consistent theme is the need for more people to get vaccinated. I agree that it would be a good thing if more people got vaccinated, but not that the truth should be stretched to get them to do it.

I don't have current statistics for the ratio of vaccinated to unvaccinated deaths — probably nobody does, judging by the CDC quote — but I note that, according to a recent news story, 20% of recent infections in the LA area are of fully vaccinated persons. The story includes:

Dr. Barbara Ferrer, the department's director, told the Los Angeles Times that if you get COVID-19 after vaccination, "your chances of both ending up in the hospital, ending up in an ICU, ending up intubated are much less than the chances of that happening if you're somebody who is unvaccinated."

According to the published information on vaccine effectiveness, however, protection against hospitalization is about 94%, about the same figure I have seen for protection against infection. I do not know what the figures are for probability of dying. That's a sufficiently rare event so that we probably don't have good data on it from the trials.


DinoNerd said...

While starting the count in February is extremely misleading, you are also falling into a common statistical fallacy. (I gave examples rebutting the fallacy part when you posted this elsewhere, without using the word "fallacy".)

The chance of a random vaccinated individual dying of the virus is unlikely to be the same as the proportion of those who die being unvaccinated.

Now maybe your claim is that newsies and politicians are trying to push people into that fallacy - viewing their own chance of dying of the virus based on this 99% number, to encourage one lot to get vaccinated, and the other lot to avoid all precautions. But it's too easy to read it as "95 % chance of not dying if vaccinatedt, therefore (only) 95% of those who die must be unvaccinated"

David Friedman said...

I don't understand your criticism. Obviously the chances are not the same, if only because there are not the same number of vaccinated and unvaccinated people and the age distribution of the two groups is different.

What did I say that implied the contrary?

I start with a first approximation where vaccinated and unvaccinated get the same exposure, vaccinated and unvaccinated have the same age distribution, and the numbers of two groups were the same. If the vaccine is 95% effective against mortality, then twenty times as many unvaccinated as vaccinated will die.

Now drop the second and third assumptions. There are more vaccinated than unvaccinated adults and they are, on average, older so more at risk. Hence fewer than twenty time as many unvaccinated as vaccinated will die.

We are left with the first assumption, equal exposure. That could be wrong in either direction. On the one hand, getting vaccinated makes one less careful to avoid exposure. On the other hand, the unvaccinated may be in places with many unvaccinated and higher infection rates as a result, and people might remain unvaccinated because they do not take Covid seriously, hence do not take precautions. I find it hard to believe that those effects would be strong enough to reduce the percentage of dead who are vaccinated from more than five to less than one.