On November 9, Pfizer and BioNTech announced that their modifed RNA vaccine against Covid-19 had a “90% effective” . That is absolutely a great news in the mid of the third wave of Covid-19 pandemic. However, there have been a lot of misunderstandings of the 90% efficacy. This commentary explains the source and the meaning of that number.
It is unfortunate that the Pfizer’s data have not been peer-reviewed by independent experts or published in a medical journal. And, that is why the data are open to misinterpretation. Many people, including those in the medical community, understand that a vaccine efficacy of 90% means 9 out of 10 people got the jab will not be infected. Indeed, a commentary in the Conversation states that “The Pfizer/BioNTech vaccine reports 90% efficacy, which means that their vaccine prevented COVID-19 symptoms for 90% of volunteers that received the vaccine compared to placebo” . Unfortunately, that explanation is potentially misleading.
Vaccine efficacy (VE) is defined in terms risk (i.e., probability), not the actual number of infected individuals. The standard definition of VE is provided by the CDC  and I rephrase as follows:
VE = 1 — (Rx / R0) ;
where Rx and R0 are the risks of infection among those in the vaccinated group and unvaccinated group, respectively. Risk is determined as the ratio of the number of infected individuals over the number of those at risk of infection.
The crucial question is then: what is the risk of infection among participants in the Pfizer’s study? According to the press release from the company, the trial had enrolled 43,538 participants who had been randomly randomized to receive either the candidate vaccine or placebo in 1:1 allocation ratio (i.e., approx 21769 in each group). The press release also states that 94 participants had been infected with SARS-Cov-2. With those numbers, it can be inferred that the risk of infection among the vaccinated group was 0.037% (or 8 / 21769), and among the placebo 0.39% (or 86 / 21769). Thus, the vaccine efficacy was VE = 1 — (0.037 / 0.39) = 90%.
That is where the number 90% comes from.
As can be seen from the above formulation, a vaccine efficacy of 90% does not in any way mean…