Significant proportions of people admitted to hospital, or dying from covid-19 in England are vaccinated—this doesn’t mean the vaccines don’t work

More vaccinated people are dying of the delta variant of covid than unvaccinated people, according to a recent report from Public Health England. The report shows that 489 of 742 people (65.9%) who died of the delta variant within 28 days of a positive covid test between 1 February 2021 and 2 August 2021, had received at least one dose of the vaccine. 54.1% (402 of 742) had received both doses. This seems like an alarming set of statistics, but with an imperfect vaccine and high vaccination coverage, it is exactly what we would expect.

Here’s a simple thought experiment: imagine everyone is now fully protected with covid vaccines—which are excellent, but not 100% effective at preventing death. Some people who get infected with covid will still die, although far fewer than without vaccinations. With complete vaccination coverage all of these people will be fully vaccinated—100%. That doesn’t mean vaccines aren’t effective at reducing death—the overall number of people dying from covid will have been reduced dramatically.

The risk of dying from covid doubles roughly every seven years older a patient is. The 35-year difference between a 45-year-old and a 80-year-old means the risk of death between the two patients has doubled five times—equivalently it has increased by a factor of 32. An unvaccinated 70-year-old might be 32 times more likely to die of covid than an unvaccinated 35-year-old. This dramatic variation of the risk profile with age means that even excellent vaccines don’t reduce the risk of death for older people to below the risk for some younger demographics.

Data from Public Health England suggest that being double vaccinated reduces the risk of hospital admission with the now-dominant delta variant by around 96%. Even conservatively assuming the vaccines are no more effective at preventing death than hospital admission (actually, they are likely to be more effective at preventing death) this means the risk of death for double vaccinated people has been cut to less than one-twentieth of the value for unvaccinated people with the same underlying risk profile.

However, the 20-fold decrease in risk afforded by the vaccine isn’t enough to offset the 32-fold increase in underlying risk of death of a 80-year-old compared to a 45-year-old. Given the same risk of infection, we would still expect to see a higher proportion of double-vaccinated 80-year-olds die from covid than unvaccinated 40-year-olds. There are caveats to that simple calculation. The risk of infection is not the same for all age groups. Currently, infection rates are higher in the young and lower in older age groups.

However, given the UK’s vaccination strategy (vaccinate older, more vulnerable people first) and uptake profile (higher uptake in older groups), you would expect high proportions of the people who die from covid to have been vaccinated. And that is exactly what we see in the data.

A similar sort of story holds true when it comes to hospital admissions. Imagine a hypothetical population of 1000 people who would have been admitted to hospital with covid before the vaccines were available. At the time of writing, vaccine coverage among adults in the UK (at least one dose) is around 90%, so 900 of our 1000 potential hospital patients are vaccinated. The remaining 100 unvaccinated people would still end up in hospital. If the vaccine is 96% effective against hospital admission with delta (this figure is for two doses, but let’s assume it holds for anyone vaccinated for simplicity) then 4% of our 900—or 36—vaccinated individuals will join the unvaccinated in hospital. 36 of the 136 (26%) people who end up in hospital will have been vaccinated. Again, this doesn’t mean the vaccines don’t work. If they had no effect, then we would expect all 1000 individuals to be hospitalised — 90% of them vaccinated. Vaccination has, in fact, meant that the overall number of hospitalisations has fallen dramatically from 1000 to 136. Of course, even with highly effective vaccines, such a high uptake rate means a significant proportion of hospitalised patients will have been vaccinated. That proportion will only get higher, the higher the uptake rate becomes.

Seatbelts help to prevent serious injury and death on the roads, but they are not perfect. 27% of car occupants who died on Britain’s roads in 2017 were not wearing seatbelts, despite the fact that around 95% of all car occupants in Britain wear seatbelts. This means that the 5% of people who don’t wear seatbelts account for over a quarter of the deaths. A disproportionately high number. If seatbelts didn’t do anything then we would expect to see only 5% of the deaths to come from the 5% non-seatbelt wearers. In fact, it is much higher, illustrating how dangerous it is not to wear a seatbelt. The parallels with the protective effect of vaccination are powerful.

The fact that more vaccinated people are dying than unvaccinated people, or that a higher proportion of people in hospital with covid have been vaccinated than we might expect, does nothing to undermine vaccine safety or effectiveness. In fact, it’s exactly what we’d expect from the excellent vaccines that have already saved hundreds of thousands of lives around the world.

Kit Yates, Senior Lecturer, University of Bath, UK.

Twitter: @Kit_Yates_Maths

Competing interests: none declared.