Imagine 100 people are ill with Covid-19. “90% efficacy” means if only they’d had the vaccine, on average only 10 would have got ill. Vaccine efficacy is the relative reduction in the risk: whatever your risk was before, it is reduced by 90% if you get vaccinated. There is a lot of confusion about this number: it does not mean there is a 10% chance of getting Covid-19 if vaccinated – that chance will be massively lower than 10%.
Researchers estimate efficacy by comparing numbers of new cases in vaccinated and unvaccinated people, best done through a “randomised control trial”. All volunteers receive an injection but, at random, either the actual vaccine or a placebo.They don’t know which they are getting.
In the Pfizer/BioNTech vaccine trial, there were eight cases in the 22,000 people who got the real vaccine. (So in the trial the risk of getting ill, if you were vaccinated, was only around 8/22,000 = 0.04%.) This compares with 162 cases in the 22,000 people who got the dummy vaccine. Researchers allocated people at random, so we can be sure the vaccine caused this difference. Since 8/162 = 5%, we estimate the efficacy of the vaccine as 95%, but there is some uncertainty around these estimates. The Oxford/AstraZeneca vaccine has an estimated efficacy of 70% for stopping symptomatic disease (30 v 101 cases).
The trials were not about estimating efficacy in preventing severe disease and death. Limited data suggest efficacy may be even higher for these more serious outcomes. These efficacies hold from one or two weeks after two doses have been given. Based on additional data analysis and experience from previous vaccines, the Joint Committee on Vaccination and Immunisation concluded that a single dose provides major protection and approved delaying the second dose up to 12 weeks. This is controversial and is the subject of urgent study.
It remains uncertain how much vaccines reduce the risk of infections without symptoms, so people may still be able to spread the virus. The Oxford/AZ trials estimated 46% efficacy for preventing infection detected by a positive test, but this is being studied further. If you have received one dose, the best advice is to act as if you are not vaccinated. But perhaps allow yourself to feel relieved.
• David Spiegelhalter is chair of the Winton Centre for Risk and Evidence Communication at Cambridge. Anthony Masters is statistical ambassador for the Royal Statistical Society
