Lost in vaccination

Ezekiel 45:10

Trigger warning: there be element’ry arithmeticks (and not much else).

In Germany, the Robert Koch-Institut (RKI) is responsible for monitoring the pandemic. The minions there are producing weekly reports in which they elaborate, among other stuff, on vaccine efficacy. The report that came out on December 30, 2021, is a kind of flash report, presumably written under the influence of Christmas goose and mulled wine. It contains a few interesting bits about Omicron but not much more. The report as of December 23, 2021, on the other hand, has been the first to distinguish between “simply” vaccinated and boostered cases. Of interest regarding vaccine efficacy are pages 21 (for definitions), 25 (for the tables reproduced below, the yellow parts showing my incredible Paint SkillZ) and 26 (for interpretation of the tables).

The world according to the RKI is divided into five camps:

1. The unvaccinated

2. Those that received one or two injections but are less than 14 days past the second injection (or the only injection, in the case of J&J)

3. Those that received two injections (or one, in the case of J&J) more than 14 days ago, and have not been boostered

4. Those that have been boostered less than seven days ago

5. Those that have been boostered seven days ago or earlier

I am going to refer to the proportions of those five groups in the population as U (unvaccinated), L (limbo), V (vaccinated), P (purgatory) and B (boostered). Of course, we have:

U + L + V + P + B = 100%

In the following we will concentrate on the 60+ age cohort, and on symptomatic cases (as indicated in yellow in the tables). Be reminded that the data are junk, and garbage in, garbage out. But that does not mean that you can’t make it worse by processing them.

The RKI’s new strategy is to compare cases numbers for U with those for V, and case numbers for U with those for B (in previous reports, it was comparison of U with V+P+B). Whenever vaccination rates are mentioned in this section of the report, they have been rescaled by the respective sub-sample size. The vaccination rates given therefore have to be interpreted as follows:

• 85.1% = V / ( U + V ), which means V = U * 85.1% / 14.9% = U * 5.71

• 70.9% = B / ( U + B ), which means B = U * 70.9% / 29.1% = U * 2.44

Vaccine efficacy (against symptomatic illness) is computed as

• 1 – ( 35,494 / 85.1% ) / ( ( 54,019 – 35,494 ) / ( 100% - 85.1% ) ) = 66%

• 1 – ( 2,720 / 70.9% ) / ( ( 21,245 – 2,720 ) / ( 100% - 70.9% ) ) = 94%

Note that the text on p. 26 claims 69% instead of 66%, a mistake probably due to manual copying of figures.

If presented that way, vaccine efficacy still looks pretty reassuring. However, uncertainty lurks both in the case numbers and in the vaccination rates. In particular, what about cases in limbo (L) and in purgatory (P)? Even if we had L = P = 0, we would compute

100% = U + V + B = U * ( 1 + 5.71 + 2.44 ) = U * 9.15,

and therefore U = 10.9%. However, the official figure reported elsewhere is 11.8% as of December 26, 2021; a contradiction (U can only decrease with time). With realistic estimates of L = 1% and P = 10% (cf. the diagram on p. 19 of the RKI report; note the slope of “60+ Jahre (Auffrischimpfung)”) we even get U = 9.7%. And what are the case numbers observed in limbo and purgatory? Would we detect some Fenton/Neil type of effect due to the hot-running booster campaign? Hint: with the data at hand, efficacy of B versus V is 82%. Does this mean that it makes more sense to booster the vaccinated than to vaccinate the unvaccinated?

What has become of the country of Gauss and Hilbert, of Virchow and Koch, of Zuse and Nixdorf? Why are we unable to collect and present data in a meaningful way? Is it a wonder that politicians are meandering between headlessness and authoritarianism?

Please, RKI, show us the raw data (case numbers and vaccination rates) for all categories. Or would this damage the carefully pampered narrative?

Addendum: what I called “Fenton/Neil type of effect” has been termed “Bayesian datacrime” by el gato malo. Please read this (and its predecessor):

new data on vaccine efficacy from scotland and more evidence on bayesian datacrime