It seems like lately there's been a big push for people to respond to the disappointing outcomes for the vaccines in places like Israel and Iceland with "Simpson's paradox!" or "base rate fallacy!" as a way of ignoring what the actual data is saying. The other day NPR had a segment about Iceland where they said "67% of cases being in vaccinated people might sound like a disappointing number, but you have to remember that 71% of the country is vaccinated" which still seems pretty underwhelming?

These calculations aren’t stratified by age / prior risk, so you can’t really infer the efficacy this simply.

> so I might be missing something

You're surely calculating a useful number, but it's not the "vaccine efficacy". Definition from the CDC website:

    Vaccine efficacy/effectiveness is interpreted as the proportionate reduction in disease among the vaccinated group. So a VE of 90% indicates a 90% reduction in disease occurrence among the vaccinated group, or a 90% reduction from the number of cases you would expect if they have not been vaccinated.

Your calculation looks at the number of hospitalised people not in the people who got the disease.

So, on a first glance it seems you're computing a useful number: how effective is the vaccine from preventing your to get hospitalised assuming that you would have been hospitalised if you caught covid. Surely that's a useful number, it just shouldn't be confused with the >90% vaccine efficacy number, which measures a different thing.

Now, I do also have some qualms with your calculation of the "hospitalisation prevention efficacy" rate.

Let me rewrite your calculation symbolically:

    "Israelis >12 years are v/(100-v) vaccinated/not vaccinated. Among the hospitalised h/(100-h) are vaccinated/not vaccinated. So you have h/v = x and (100-h)/(100-v) = y Therefore the ratio of risks is x/y = z. Which gives you (1-z) as I mentioned."

Let's make a little thought experiment. Let's imagine that 98% of people were vaccinated with a vaccine with 90% efficacy. Since the efficacy is not 100%, some people will still get the disease and some will still get hospitalised. Since very few people in this scenario are unvaccinated, most of the people who end up in hospitals will be vaccinated. Let's imagine that 50% of those who get the disease get hospitalised. Since only 10% of those vaccinated that get infected contract the disease, only 5% of the vaccinated population will get hospitalized. OTOH (in this scenario) 50% of the infected unvaccinated people get hospitalized, but since only 2% of the people are unvaccinated, this means only 1% of the infected unvaccinated population get hospitalized; 99% of the hospitalized people are thus vaccinated.

    v = 98
    h = 99

    "People from our scenario are 98/2 vaccinated/not vaccinated. Among the hospitalised 99/1 are vaccinated/not vaccinated. So you have 99/98 = 1.01 and 1/2 = 0.5 Therefore the ratio of risks is 1.01/0.5 = 2.02. Which gives you -1.02 as I mentioned."

That formula doesn't seem to make sense.

The israeli data has issues because it was during the initial surge of delta which was predominantly in cities with high vaccination rates, which drives the VE down if you compare it against the population-wide ratio of vaccinated to unvaccinated.

Most studies of VE also do statistical modelling of how many of the unvaccinated have been infected and are actually recovered. This was the case of the CDC study from yesterday which had the headline number of only 66% efficacy against delta, but if you dig into the data they didn't test for antibodies or anything but modeled viral spread and had a 95% CI on that number of 26% to 84%.

That is literally garbage data.

The actual value could be closer to the higher end due to them underestimating community spread (pretty plausible) and due to selection effects where their unvaccinated population was higher risk for prior infection than they thought.

I thought that study might change my mind on the situation since they had done a much better job than the Israeli data on controlling for age, comorbidities, etc. But when you get down to it the VE data was still crap. And the mention of waning immunity seemed to be just tacked on with no supporting evidence other than the lower number VE number against delta.

Similarly, its now been found that the studies which equated similar Ct values to viral load are bad because there's less culturable virus in vaccinated individuals, and the Ct values drop faster which indicates vaccinated individuals are producing more viral debris at peak Ct and clearing the virus faster. So they would therefore be expected to have less transmission. Since they're staying out of the hospital and Ct values correlate somewhat with symptom severity that also suggests less transmission (the people who wind up hospitalized most likely transmit more before they get there).

Then there's that silly study out of China which found the odd result that viral-load-as-measured-by-Ct where 1,000 times higher against delta than against original Wuhan strain data from the pandemic when measured at the onset of symptomology (so not peak data, not average data, and compared against the earliest PCR results against the original pre-D614G virus). That quietly disappeared from scientific discussions, but the media keeps on citing it as the truth without any qualifications.

We know that vaccination reduced actual transmission and attack rates against Alpha and its very likely that it does the same against Delta. No data has contradicted that yet.

And I can't explain why so many scientists are so eager to undermine the message of vaccine efficacy. I guess they think it'll be easier to get vaccinated people to mask up than it is to get the unvaccinated to get vaccinated, and some of them are presumably just as addicted to bad news on facebook and twitter as the rest of the population is.