Have you heard people saying that “hospitals have as many jabbed as non-jabbed patients” to suggest that vaccines are ineffective? Soon you may hear that there are “more vaccinated covid patients than unvaccinated ones in hospital wards”. What I’m seeing around me is that such misleading arguments can make smart folks otherwise confident in the power of science and modern medicine doubt the rationale for vaccination.
Let us be clear. What is wrong in this argument is not the statistics. But the conclusion anti-vaxxers pretend to draw. As with many things about the pandemic, you don’t need a degree in epidemiology to figure out why. All that is required is logic. The curve I’ve plotted here correctly shows that the proportion of vaccinated patients among people admitted to hospital for a covid infection should go up as the vaccination campaign progresses. You’ve read correctly: it should go UP, not down. I’ve drawn the curve assuming that non-vaccinated people are 9 times more likely to develop a form of the disease leading to hospitalisation, which is a good approximation of what we know about the efficacy of jabs authorised in Western countries (see analysis in Nature).
How can this be? The first thing to remember is that vaccinated and unvaccinated patients are drawn from changing populations. As more people get inoculated, the population of vaccinated people grows whereas the population of unvaccinated people shrinks. The other thing is that 90 per cent efficacy is not the same as 100 per cent efficacy. So, although the efficacy of the Pfizer/Biontech and Moderna jabs is very high, a more or less constant share of those who have been jabbed will catch the virus and end up in hospital care. As the inoculated population grows thanks to the progress of the vaccination campaign, this constant share represents a larger group in absolute terms (holding virus circulation and mitigating measures constant). Meanwhile, the unvaccinated population follows the same dynamic in reverse. Relative to the unvaccinated population, the share of people requiring hospital care is bigger, but this constant share applies to a population that gets smaller and smaller as more people get inoculated — thus moving them from unvaccinated to vaccinated status.
Counter-intuitive as it may first sound, the proportion of vaccinated people among covid patients will be lowest at the start and highest at the end of the vaccination campaign, when nearly everyone has been inoculated. But again, given what we know about vaccine efficacy, this is the conclusion that logic dictates. So don’t be fooled by anti-vaxxers and conspiracy theorists, use logic to debunk their flawed reasoning!