Meaning of Protective Efficacy from Vaccines

The other day I came across a debate in a vernacular channel where there was a reference to at least 60% protective efficacy from vaccines against COVID-19 even for some new variants of the virus even if one cannot say much about future variants. From the discussion, there seems to be a popular misconception in the understanding of protective efficacy. The purpose of this write-up is to address that misconception.

In popular understanding, 60% of protective efficacy from vaccines could mean that if 100 people take vaccines then 60 of them would be protected from the disease.

In actual practice, protective efficacy refers to relative risk reduction (RRR). Or,

RRR=1-RR.

RR is relative risk, that is, the ratio of the risk in the treatment group (proportion infected from among those who have been administered with the vaccine, R_t) with the risk in the control group (proportion infected from among those who have not been administered with the vaccine, R_c). In other words,

RR=R_t/R_c.

If the proportion of infected is equal in the two groups then a benchmark relative risk, R_tb/R_cb=1. RRR is a reduction from this benchmark. Hence, 60% of protective efficacy in the debate should have been identified with RRR%=RRR*100.

Now, what could this 60% of protective efficacy imply. If the treatment and control groups had 100 people each and if the number of people infected in the two groups are 2 and 5, respectively, or, R_t=2% and R_c=5%, then RRR=60%. This means that if there are 100 people each in the two groups then 2 could be infected from those vaccinated and 5 from those not vaccinated.

But, one would get the same value of RRR=60% with umpteen other possibilities where both the above-mentioned values of R_t and R_c are multiplied by a common factor, k. An extreme situation can be when R_t=40% and R_c=100%, which was the position taken by a panelist in the debate who conveyed that among those vaccinated 40% would be infected and among those unvaccinated everyone would be infected. This is an extreme scenario and in some sense a misrepresentation of facts.

It calls for the relevance of absolute risk reduction, ARR=R_c-R_t. A Lancet Microbe paper (see discussion in earlier blogs here and here), drawing from phase 3 trials of five COVID-19 vaccines indicated that RRR was in the range of 67%-95% while ARR was in the range of 0.84%-1.28%. And, in a population setting for which data was available in one case, ARR comes down to 0.46%.

Based on this, it is quite likely that RRR=60% is to be commensurate with ARR in the range of 0.2%-1.5%, that is, R_t=0.2% and R_c=0.5% where ARR=0.3%, or, if one wants to give some benefit of doubt then R_t=1.0% and R_c=2.5% where ARR=1.5%. By not doing this, the panelist amplified the risk by 40-200 times. This can create panic and fear among the public and should be avoided.

The role of the State in providing vaccination to people by considering it as a public good is a relevant matter. Equally important, in a democratic polity, as conveyed by another panelist in the debate, is the fact that that vaccines being administered are with Emergency Use Authorization and that it is a voluntary act by an individual  who has to weigh the information provided. An informed consent and right to refuse, after being provided with information that leaves questions unanswered, is not the same as hesitancy. For a complex, evolving and uncertain scenario, questions would be the first step for better science.