On efficacy

1 minute read


The term efficacy is not new for the drug industry people, but of course it has now entered the public consciousness thanks to the vaccine efforts. As Carl Zimmer pointed out, our intuitive understanding of “95% effectiveness” is that 95 out of 100 people who get the vaccine will be immune.

As you might already know, it’s not exactly that. That number means that out of certain number of symptomatic, PCR-positive participants, the placebo arm has 95% more than the vaccinated arm, where vaccine:placebo population is 1:1. Taking the numbers from the NY Times article, Pfizer waited until they had 170 cases (for statistical power): 162 in placebo, 8 in vaccine. If vaccine:placebo populations are exactly 1:1, the denominators all cancel out and efficacy = (162-8)/162 = 95%. Even if it is not exactly 1:1, usually it is close to that, so this is a good shortcut for quick calculation. For exact figure, just replace the absolute numbers as fraction in that arm instead – see how the denominators cancel out when a=b :

\Large \text{Efficacy}=\frac{\frac{162}{a}-\frac{8}{b}}{\frac{162}{a}}}

So, efficacy is a proxy for the eventual effectiveness. The former is in controlled clinical trial setting, while the latter is in messy real word setting. Some points on why there will be discrepancy between the 2:

  • Clinical trial population is biased – only certain kind of people would volunteer for the trial. You can expect that they usually are healthy and do not have underlying conditions. Behaviour-wise, they would tend to be more cautious as well.
  • Blinding is imperfect. Some people get mild reactions from the vaccine, which sort of tell you that you are in the vaccine arm.
  • Asymptomatic cases are not accounted for. The participants are not tested regularly. Instead, they are only tested when they self-report symptoms. This is the case for Moderna trials. AZ-Oxford does weekly swabs so they have data about asymptomatic cases as well.

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