Vaccines more effective than raw Israeli hospitalization data would seem to indicate

There's been some reporting recently of vaccines not protecting against severe infection as well as expected, based on looking at the number of hospitalized people who are vaccinated vs not. "60% of people with severe COVID-19 in the hospital had been vaccinated!" Here's an article explaining why this analysis is complete junk:

https://www.covid-datascience.com/post/israeli-data-how-can-efficacy-vs-severe-disease-be-strong-when-60-of-hospitalized-are-vaccinated

If you're familiar with Simpson's paradox, it's another case of that. TL;DR: Vaccination status is highly correlated with age, and if you actually slice up the cases by age, you see that efficacy against severe disease is 80–100%, depending on age. And yes, this is in the context of the Delta variant (or other current strains).

(But also see the article for some additional confounding factors.)