Israel, 50% of infected are vaccinated, and base rate bias

Delta has arrived in Israel, and with its arrival, cases are increasing (albeit relatively small). And, this is expected. We’ve seen it in the UK. and India. and Indonesia. And South Africa. And Russia. No country is 100% vaccinated. And this coupled with Delta being more transmissible and preliminary evidence suggesting its ability to escape natural immunity, unvaccinated people and populations are in trouble.

The statistic that’s concerning most (and that’s in the news) is a detail the Director General of the Health Ministry of Israel (Professor Chevy Levy) said during a radio interview. When asked how many of the new COVID19 cases had been vaccinated, Levy said that, “we are looking at a rate of 40 to 50%”.

This must mean the Delta variant is escaping our vaccines, right? When I started digging into the numbers, though, this might not be as alarming as it seems.

Base rate bias

This is likely an example of base rate bias in epidemiology (it’s called base rate fallacy in other fields). Professor Levy said that “half of infected people were vaccinated”. This language is important because it’s very different than “half of vaccinated people were infected”. And this misunderstanding happens all. the. time.

The more vaccinated a population, the more we’ll hear of the vaccinated getting infected. For example, say there’s a community that’s 100% vaccinated. If there’s transmission, we know breakthrough cases will happen. So, by definition, 100% of outbreak cases will be among the vaccinated. It will just be 100% out of a smaller number.

Cue Israel. They are one of the global leaders in vaccinations; 85% of Israeli adults are vaccinated. So, say we have the following scenario:

  • 100 adult community

  • 4 COVID19 cases

  • 50% of cases were among the vaccinated

It would look something like this:

With an infection rate among the vaccinated of 2% and infection rate of 13% among the unvaccinated, this would give us an efficacy rate of 85%. This is pretty darn close to the clinical trial efficacy rate, meaning the Pfizer vaccine is still working against Delta.

Unfortunately, this gets more complicated. We know the original Israeli outbreaks were in two schools. Because the vast majority of kids in Israel are not vaccinated (only 2-4% because they were just approved), imbalance is introduced. But, I ran the numbers and as long as at least 90% of the adults in the original outbreak were vaccinated, we know the vaccine is still working against Delta. 91% isn’t a farfetched number as teachers (at least in the US) are vaccinated at a much higher rate than the general public.

We need other fundamental details before we start to worry too. Like…

  1. What did these outbreaks look like? How many people were at risk? How many people infected? What proportion of the infected were adults vs. kids?

  2. How were the cases caught? Was there surveillance testing at the schools? In other words, were these asymptomatic cases? If not, what was the severity of the cases? What was the severity of the vaccinated cases?

  3. Were vaccinated cases fully or partially vaccinated? We know 1 dose of vaccines doesn’t work well against Delta.

Bottom Line: I have more questions than answers. And we will (hopefully) get answers to these questions soon. But, there’s a strong possibility that this is a textbook example of base rate bias. Which means I’m optimistic that this is just further evidence the vaccine works against Delta on an individual level. However, this does NOT mean that we shouldn’t worry about Delta on a population-level.

Stay tuned.

Love, YLE