# Category Archives: epidemiology

## Let’s clear up what efficacy means when we talk about vaccine efficacy

## What does 95% efficacy even mean?

The Pfizer Covid-19 vaccine has an efficacy rate of 95%. The Moderna Covid-19 vaccine has an efficacy of 94.1%. The Johnson and Johnson Covid-19 vaccine has efficacy of 66.3%.

But what does this MEAN?

In my casual observation, it seems to me that there are a lot of people who see these numbers and think, quite reasonably, that 95% effective means that 5% of the people who get the vaccine will get Covid-19. Or, if you were to get the Johnson and Johnson vaccine, there is still a 33.7% chance that you’ll get Covid-19. So, they then make the argument that if there is still about a 1 in 3 chance that you’ll get Covid even AFTER the vaccine, why even bother getting the vaccine?

Well, that’s not a correct interpretation of efficacy rate.

I will illustrate this with some simple examples.

**Example 1 **

Let’s say that we find 10,000 people and we inject them with a placebo. And we find another 10,000 people and we inject them with a vaccine. We follow all 20,000 for 90 days to see if they develop the disease of interest (in this case Covid-19).

Let’s say that 5,000 people who received the placebo get the disease while only 250 of the vaccinated group get the disease. In this case we have the following quantities:

Incidence rate UNvaccinated: 5,000 / 10,000 = 0.5 (or 50%)

Incidence rate vaccinated: 250 / 10,000 = 0.025 (or 2.5%)

(Note: Incidence rates are also known as “attack rates”. I didn’t know that until this morning. I’ve always just called these incidence rates).

Now using these incidence rates, we can calculate something called relative risk (RR):

RR = Incidence rate vaccinated / Incidence rate UNvaccinated = 0.025 / 0.5 = 0.05

The efficacy is then defined as 1 – RR = 1 – 0.05 = 0.95 (or 95%).

So in this scenario the vaccine was “95% effective” while 2.5% of the vaccinated group developed the disease.

*(Note: You can also calculate efficacy this way and get the exact same answer: *

*Efficacy = (Incidence rate UNvaccinated – Incidence rate vaccinated) / Incidence rate UNvaccinated = (0.5 – 0.025) / (0.5) = 0.95*

*It’s exactly the same result.)*

**Example 2 **

let’s look at a second example with the same initial set up: we find 10,000 people and we inject them with a placebo. And we find another 10,000 people and we inject them with a vaccine. We follow all 20,000 for 90 days to see if they develop the disease of interest (in this case Covid-19).

Let’s say that 100 people who received the placebo get the disease while only 5 of the vaccinated group get the disease. In this case we have the following quantities:

Incidence rate UNvaccinated: 100 / 10,000 = 0.01 (or 1%)

Incidence rate vaccinated: 5 / 10,000 = 0.0005 (or 0.05%)

Now using these incidence rates, we can calculate something called relative risk (RR):

RR = Incidence rate vaccinated / Incidence rate UNvaccinated = 0.0005 / 0.01 = 0.05

The efficacy is then defined as 1 – RR = 1 – 0.05 = 0.95 (or 95%).

So in this scenario the vaccine was ALSO “95% effective” while only 0.05% of the vaccinated group developed the disease.

**Takeaways**

- In the first example given here, 2.5% of the vaccinated group developed the disease, and in the second example, 0.05% of the vaccinated group developed the disease, but in BOTH EXAMPLES the efficacy was 95%.
- Vaccine efficacy is a RELATIVE reduction in risk when compared to a placebo group.
- There are many different incidence rates that will result in a 95% efficacy.
- This is why a vaccine that has efficacy of 50% is really an incredible vaccine. It doesn’t mean that 50% of the people who get the vaccine will get the disease; it means that the relative risk has been reduced by 50%! Which is a ton!
- Someone should get on national television and explain this to the American people.

Further reading:

- https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(21)00075-X/fulltext
- https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section6.html
- https://www.medicalnewstoday.com/articles/what-is-vaccine-efficacy
- https://www.medicalnewstoday.com/articles/what-is-vaccine-efficacy

Cheers.