# COVID-19: The Incredible Shrinking Boost of the Booster Shot

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With COVID-19 after the vaccination is before the vaccination. Now that most people in the developed countries have been vaccinated the question arises of how much boost is in the booster shot. We are here to help you understand the real power (or lack thereof) of the booster, so read on!

Very recently a new study on the matter was published in The New England Journal of Medicine: Protection of BNT162b2 Vaccine Booster against Covid-19 in Israel:

At least 12 days after the booster dose, the rate of confirmed infection was lower in the booster group than in the nonbooster group by a factor of 11.3 […] the rate of severe illness was lower by a factor of 19.5 […].

Wow, 20% risk reduction. That is really impressive, is it not? But 20% of what exactly?

To bring some light into the matter renowned statistician Katharina Schüller did the maths in the article Dritte Covid-19-Impfung – Ein kleiner Boost:

- With two vaccine doses, the risk of infection was around 85 cases per 100,000 person-days and with three doses around 8 cases per 100,000 person-days.
- With two doses, the risk of severe disease was around 6 cases per 100,000 person-days and with three doses around 0.3 cases per 100,000 person-days.

We go one step further here and illustrate the point visually to get an intuitive feel for the situation.

We already talked about the efficacy of the COVID-19 vaccine on this blog and explained the concepts of relative vs. absolute risk reduction (and its dangers): COVID-19 vaccine “95% effective”: It doesn’t mean what you think it means! There we saw that personograph plots (also called Kuiper-Marshall plots) are an excellent way to communicate risks (the `personograph`

package can be installed from CRAN).

Let us start with the risk of infections without and with an additional booster shot, based on 2,500 fully vaccinated people:

library(personograph) ## Loading required package: grImport ## Loading required package: grid ## Loading required package: XML n <- 2500 inf_wo_boost <- 64 / n inf_w_boost <- 6 / n inf_wo_boost / inf_w_boost # rel. risk reduction ## [1] 10.66667 data <- list(first = inf_w_boost, second = inf_wo_boost-inf_w_boost, third = 1-inf_wo_boost) personograph(data, colors = list(first = "red", second = "orange", third = "lightgrey"), fig.title = "Infections w/o booster: < 64/2500, with booster: ~ 6/2500", draw.legend = FALSE, n.icons = n, dimensions = c(25, 100), plot.width = 0.97)

All persons are fully vaccinated, orange and red persons are the unlucky ones who still get an infection (a so-called breakthrough infection), while the orange cases can be prevented by a booster dose.

What is the absolute risk reduction in percentage points?

100 * ((n - inf_wo_boost*n) / n - (n - inf_w_boost*n) / n) # perc. points risk reduction ## [1] -2.32

The initial 11% relative risk reduction became only about two percentage points absolute risk reduction. Now the same analysis for the even more important severe cases:

ev_wo_boost <- 5 / n sev_w_boost <- .25 / n sev_wo_boost / sev_w_boost # rel. risk reduction ## [1] 20 data_2 <- list(first = sev_w_boost, second = sev_wo_boost-sev_w_boost, third = 1-sev_wo_boost) personograph(data_2, colors = list(first = "red", second = "orange", third = "lightgrey"), fig.title = "Severe cases w/o booster: < 5/2500, with booster: < 1/2500", draw.legend = FALSE, n.icons = n, dimensions = c(25, 100), plot.width = 0.97)

The remaining risk of a severe illness after the booster shot is too small to be plotted. We would have to add at least another 7,500 persons to get one red one!

Again, what is the absolute risk reduction in percentage points?

100 * ((n - sev_wo_boost*n) / n - (n - sev_w_boost*n) / n) # perc. points risk reduction ## [1] -0.19

So, the initial 20% relative risk reduction became a meager 0.2 percentage points absolute risk reduction! This is not because the efficacy of the booster is so bad but because the standard vaccination without the booster is already so powerful that it can only add a comparatively small advantage. The huge relative risk reduction shown in the article above is not wrong per se but sure it is misleading.

This squares well with another result I found together with my colleagues Dr. Tobias Krebs and Professor Michael Möckel (both also Technical University Aschaffenburg), where we compared different vaccine regimes. We concluded that “vaccinations of unvaccinated people is more effective than booster vaccinations for already fully vaccinated people”. You can read the full preprint here: COVID-19 scenarios for comparing the effectiveness of age-specific vaccination regimes, exemplified for the city of Aschaffenburg (Germany).

Please share your thoughts on this in the comments and stay tuned for more interesting insights!

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