Spot the flaw in this argument — I didn’t

The following sentence appeared in an article in the latest (24 September ’21)  Science.   ” In mid-August, after vaccine efficacy had started to wane and before the effects of boosters had taken hold, 59% of severe patients were fully vaccinated.”

This is far worse than ’started to wane’, given the following sentence from the same article “Israel’s vaccination rate—64% of its population has received at least two doses”

Put the two together (which the article really didn’t do) and you see that at most the vaccine was giving at most 5% protection against severe infection, which is really no protection at all.

The null hypothesis is that the rates of severe COVID19 in the vaccinated and unvaccinated should be the same, and the percentages cited above seems to bear that out.  

What’s wrong?  Something called the Simpson paradox —

Start by assuming 100% of the population vaccinated, then all breakthrough hospitalizations will be in the vaccinated group, which means nothing. The point is that the vaccinated groups of Israeli’s are much different than the unvaccinated.    Note the unstated assumption in the above paragraph in bold type — we’re assuming that vaccination in the Israeli population is a random event.

But of course vaccination was never random.  Those at higher risk (the elderly, the immunodeficient for whatever reason) were vaccinated first.  So there are a lot of them to have breakthroughs, and they will have more breakthroughs because their immune systems aren’t as strong.

“Among Israeli adults under 50, as of Aug. 15, 3.5 million were vaccinated and 1.1 million were not. That’s still a considerable number of vaccine holdouts. Among those 3.5 million vaccinated younger people, just 11 were hospitalized — about three per million. Meanwhile, of the unvaccinated in this age range, 43 were in the hospital, or 39 per million.

Note that hospitalizations of young people for both the vaccinated and unvaccinated are low, because younger people rarely suffer the severest illness from covid-19. (Their immune systems are stronger)l Still, vaccination reduced the rate of hospitalization more than 10-fold in the population under 50.

Now look at the population 50 and older. There are 2.1 million vaccinated Israelis over 50, and 290 were in the hospital Aug. 15. That’s 136 per million, a rate that dwarfs anything younger people are experiencing. And unvaccinated older Israelis? There are very few people in that category: just 186,000. But of that group, 171 were hospitalized — a grievously higher rate of 919 per million. In the older population, vaccinated people were less than one-sixth as likely to be hospitalized as the unvaccinated.”

I thank a friend for pointing out the error of my ways.

Even so only in the under 50 group can vaccination be said to provide > 90% protection against severe infection.  In the over 50 group the protection is 84% — still not bad

Post a comment or leave a trackback: Trackback URL.


  • Peter Shenkin  On September 27, 2021 at 12:38 pm

    Does Israel routinely test COVID patients for Delta? I wonder what the results look like if restricted to Delta victims.

  • luysii  On September 27, 2021 at 4:45 pm

    Not sure, but apparently all the infections in the USA are delta.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: