# Vaccine Efficacy Estimates

## What does a ‘95% effective’ vaccine mean?

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News reports shared trial findings of different vaccinations against COVID-19. For example, a BBC headline on 16th November was:

Moderna: Covid vaccine shows nearly 95% protection

This article looks at what statements about ‘95% protection’ and similar claims mean. This is another way of phrasing vaccine efficacy. It also shows how to calculate approximate uncertainty around those central estimates.

# What is vaccine efficacy?

Vaccine efficacy is: the relative change in having a disease in the vaccinated group. The comparison is against non-vaccinated people in the trial.

By its nature, researchers estimate vaccine efficacy through trials. The optimal condition is a randomised control trial. This is where trial volunteers are in groups. For example, one group receives the vaccine; the other receives a placebo.

Due to random assignment, researchers can estimate how good the vaccine is. Researchers look at what proportions of people have a disease in each group, and compare them. Different research projects may use different definitions of a case. A case is a person having the disease, or virus. They could use different tests, or confirm in labs after different periods of time.

We can work through an example: the Pfizer & BioNTech phase III study. There were 170 COVID-19 cases. Eight of these were in the vaccine group, and 162 in the placebo group. In this study, there were “over 43,000” participants. For this calculation, assume there were exactly 43,000 participants . These people split into two even groups.

• Attack rate in the vaccinated group (ARV): Eight divided by 21,500 is 0.04%.
• Attack rate in the non-vaccinated group (ARU): 162 divided by 21,500 is 0.75%.

The reduction from 0.75% to 0.04% is then 95%. This is our central estimate of vaccine efficacy.

# What is the uncertainty around this estimate?

In 1988, Hightower, Orenstein and Martin wrote about approximations. These approximations were for vaccine efficacy. In our situation, the approximate intervals may…

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This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.