1. If a large share of hospitalised people are vaccinated, that’s a sign of success. It has been common to see headlines noting that a substantial minority of people who have been hospitalised or even killed by Covid have been fully vaccinated. These numbers suggest vaccine failure is alarmingly common. The fallacy only becomes clear at the logical extremes: before vaccines existed, everyone in hospital was unvaccinated; if vaccines were universal, then everybody in hospital would be vaccinated. Neither scenario tells us whether the vaccines work.
So try this. Imagine that 1 per cent of the unvaccinated population will end up in hospital with Covid over a given time period. In a city of a million people, that would be 10,000 hospital stays. Now let’s say that 950,000 people get fully vaccinated, that the vaccine is 95 per cent effective against hospitalisation, and that the vaccine doesn’t reduce transmission (although it does). Here’s the arithmetic: 500 of the 50,000 unvaccinated people end up in hospital. A total of 9,500 of the vaccinated people would be at risk of a hospital visit, but the vaccine saves all but 5 per cent of them. These unlucky 475 still go to hospital. The hospital contains 500 unvaccinated and 475 vaccinated people — almost half and half — which makes it seem as though the vaccine barely works. Yet when 95 per cent of people take a 95 per cent effective vaccine, hospital visits fall from 10,000 to fewer than 1,000.
Author(s): Tim Harford
Publication Date: 19 August 2021
Publication Site: TimHarford.com