Pandemic of the vaccinated

The admittedly somewhat provocative title of this article was not chosen without reason. It refers, of course, to the “pandemic of the unvaccinated” announced in many countries at the beginning of September in view of the coming “fourth wave” in autumn. Ms Lenert also made use of this term at the press conference on 1 September: [1]

„De Motto vun der nächster Well […] et sinn di Net-Vaccinéiert déi zueleméisseg dat Ganzt wäerten dreiwen.“

This short quote already describes quite well what it is about: Unvaccinated people would be more likely to become infected and also to pass on the virus. Likewise, the unvaccinated would then also be the main burden on the health system. The vaccinated, on the other hand, would play no more than a negligible role in these contexts. It is almost pointless to mention that this argumentation is equally the conditio sine qua non in legitimizing the CovidCheck as well as the demand for a higher vaccination rate.

Interestingly, any guarantees, black on white, that the vaccination could accomplish this, are hard to find. On the official website of the COVID vaccination, for example, the [2] introduction contains rather general statements, such as saying that vaccination is the most effective way to prevent infectious diseases. The FAQ section does not go much further:

“As with other vaccines, the COVID-19 vaccine does not provide 100% protection even after the second vaccination. It is still possible to become infected. The vaccination helps reduce the symptoms of the disease.”

A member of the Covid-19 task force is also rather pessimistic about the impact of vaccination on the incidence of infection. [3]

„Mir kënnen eng gewësse kollektiv Immunitéit an der Bevëlkerung hunn, mee ob mer wierklech d’Iwwerdroung iwwert d’Immunitéit allgemeng zum Beispill och iwwert d’Impfung kënnen ereechen, dat ass eng vun deene ganz wesentlechen a grousse Froen de Moment.“

In this series of articles, we would like to present some considerations, which, in our opinion, tend to receive insufficient attention by our politicians and the leading media. Many justified points of discussion deserve to be discussed in this context (such as vaccination side effects, alternative treatment methods, etc.), and here we will focus on the efficacy of the Covid-19 vaccines. This concerns, on the one hand, their influence on epidemiological events, i.e., the extent to which they produce a so-called sterile immunity in the vaccinated, and, on the other hand, the extent to which more severe courses of disease can be prevented.

Before we address the caveats of some scientists, in this first part we will look at the bare numbers of the Covid-19 national statistics.  
A vaccine should be highly effective, which, translated into the logic of the current crisis means: unvaccinated people should test positive in PCR tests much more often than vaccinated people, and of course hospitals, especially intensive care units, should be mainly occupied by Covid-19 patients who have not been treated with this gene therapy. Due to the size of Luxembourg, the comparison between vaccinated/unvaccinated with regard to hospitalizations and severe courses is difficult, as the currently (still) very low numbers do not hold sufficient statistical significance. For this reason, we will limit ourselves to examining positive PCR tests.

For some time now, the Ministry of Health has been publishing the number of people who tested positive and those who were hospitalized depending on their vaccination status in its weekly reports [4]. This can thus be seen as an attempt to evaluate, at least roughly, the efficacy of the Covid-19 vaccines. We would like to offer some thoughts on the methodology used below.

A controlled experiment (in which we all participate)

In order to determine the efficacy of a drug in general and a vaccine in particular, it is a well-known fact that a so-called controlled experiment is carried out [5]: an experimental group receiving the active substance is compared with a control group. The principle of ceteris paribus should apply, that is: the same conditions, except for the administration of the vaccine, should apply for both groups. In particular, this implies that all participants will be tested for the virus at a similar frequency and under the same circumstances over time.

In our opinion, the above-mentioned conditions under which a controlled experiment should be carried out are being violated in 3 essential respects, which we will consider in more detail:

  1. Exempting vaccinated persons from contact tracing
  2. Including schoolchildren in comprehensive school
  3. Merging data on unvaccinated and partially vaccinated persons

Exempting vaccinated persons from contact tracing

This was discussed in our report on the amendment of the Covid Act of 12 June.[6] Since vaccinated persons are exempted from the testing obligation following contact with a person who has tested positive as part of contact tracing, and are thus tested much less frequently [7], the ceteris paribus principle has been already violated under this point.

Including schoolchildren in comprehensive school

The experimental group consists of all persons who have been fully vaccinated, i.e. are at least 12 years old. Accordingly, the participants of the control group should also belong to this age group. In the calculations of the weekly reports, however, schoolchildren in comprehensive school are included, who contribute a non-negligible part to those testing positive. After all, some 50,000 people here are tested twice a week for SARS-CoV-2 with self-tests. (Many thanks to the attentive observer who pointed this out to us.)

The effect this has had on the final results can be calculated for calendar weeks 38 and 39, for which, for the first and until now last time, the number of positive PCR tests had been broken down into unvaccinated, partially vaccinated and fully vaccinated. The following image shows the corresponding screenshot of the weekly report for the week from 27 September to 3 October.

The following table summarizes the corresponding data for calendar weeks 37 to 41. In order to estimate the proportion of schoolchildren in comprehensive school among those testing positive, we have also listed the number of positive tests in the age groups 0-9 and 10-19 years.

(2)partially vaccinated194200
(3)fully vaccinated168210217311264494
(5)0-9 years11113114676132141
(6)10-19 years7865104137149165
(7)0-11 years (estimated)127144167103164174
(8)unvaccinated > 12 years (estimated)427

The number of positive PCR tests for individuals up to 11 years of age (7) was estimated simply by adding one fifth of the number of the 10-19 years age group (6) to the 0-9 years category (5).

Since all those testing positive up to 11 years of age are unvaccinated, the estimated number of positive unvaccinated older than 12 years (8) is obtained by subtracting the age group 0-11 years (7) from the total number of unvaccinated people (1).

For calendar week 38, among those tested positive over the age of 12, there are 42 unvaccinated persons compared to 210 vaccinated persons, and for calendar week 39 the ratio is no less than 7 to 217!

Let us convert these numbers to incidence rates.

With a total population of 634,730 and 81,242 people in the 0-11 age group, the 12+ group accounts for 634,730 – 81,242 = 553,488 people.

In week 38, according to the daily report of September 27[8], 403,462 people were fully vaccinated. In the control group, the corresponding figure is 553,488 – 403,462 = 150,026. The incidence rates per 100,000 in the population are thus:

Incidence rate, vaccinated: I_v = 210 \cdot \frac{100.000}{403.462} \approx 52

Incidence rate, unvaccinated: I_u = 42 \cdot \frac{100.000}{150.026} \approx 28

The incidence rate of the vaccinated is thus almost twice as high as that of the unvaccinated!

If one also takes into account that the vaccinated, unlike the unvaccinated, are hardly tested in contact tracing, the actual incidence rate among the vaccinated is certainly even higher.

For calendar week 39, an analogous calculation based on the October 4 daily report leads to:

Incidence rate, vaccinated: I_v = 217 \cdot \frac{100.000}{406.521} \approx 53

Incidence rate, unvaccinated: I_u = 7 \cdot \frac{100.000}{146.967} \approx 5

So vaccinated people tested positive more than 10 times as often as unvaccinated people.

Unfortunately, since calendar week 40, the unvaccinated and partially vaccinated are merged, again, into one category. However, the magnitude of the numbers suggests similar values for the respective incidence rates of vaccinated and unvaccinated.

Merging data on unvaccinated and partially vaccinated persons

With the exception of calendar weeks 38 and 39, unvaccinated and partially vaccinated individuals have been consistently merged into a single statistical category, a practice that interestingly does not appear to be limited to Luxembourg [9].

Apart from the fact that this contradicts the logic of a control experiment (the two relevant groups are the experimental group and the control group), this may bias the evaluation in favor of the vaccine, since in case of negative effects of the vaccination between the first and the second dose, these will be attributed to the unvaccinated.

The fact that this actually plays a role is shown in concrete examples below and has, in fact, already been confirmed in a paper by Dr. Hervé Seligmann: by evaluating the raw data of an extensive Israeli study with 500,000 participants, it could be shown that an increased number of cases occurred immediately after the first dose [10].

For calendar weeks 38 and 39, the incidence rates for the partially vaccinated can be calculated. We need the number of persons who have been vaccinated once with one of the 3 vaccines (BioNTech/Pfizer, Moderna and AstraZeneca) requiring 2 doses. This number can be derived from the data in the corresponding table of daily reports [8]

Thus, for calendar week 38 (as of 27.09.2021), we receive: Vaccinated with one dose: 417,905 – of which fully vaccinated with Janssen: 37,532 – of which vaccinated with the other 3 vaccines: 417,905 – 37,532 = 380,373 Fully vaccinated with 2 doses (other 3 vaccines): 365,930 Partially vaccinated (other 3 vaccines): 380,373 – 365,930 = 14,443

Incidence rate, partially vaccinated: I_p = 194 \cdot \frac{100.000}{14.443} \approx 1.343

Expressed in absolute numbers, this results in a comparable number of persons testing positive (186 to 194) in a group of unvaccinated persons which is about 10 times larger (152,339 to 14,443)!

A word about hospitalizations

As we have pointed out, mostly single-digit numbers associated with Covid-19 hospitalizations are not appropriate for drawing significant statistical conclusions. In addition, a passage in an article already cited  [7] should make us pay attention:

D’Informatiounen iwwert d’Patienten am Spidol wieren awer net sou einfach z’erfaassen, seet sengersäits de Jean-Claude Schmit. “Déi Leit, déi hospitaliséiert sinn, dat variéiert vun Dag zu Dag, et ginn der, déi frësch hospitaliséiert ginn, anerer ginn heem, dat heescht, dat ass eng supplementär Aarbecht fir eis. Mir hunn dat elo a verschiddene Situatiounen extra nogesicht, fir e bëssen en Androck ze hunn, mä wa mer dat routineméisseg wëlle maachen, ass dat relativ vill Aarbecht, fir all Fall nozesichen.”

In our opinion, this statement raises more questions than it answers. Obviously, the vaccination status of a hospital patient is not automatically exchanged between the individual instances involved and thus seems to be determined only in individual cases where circumstances allow this with too much effort. Doubts as to how reliable statistics can be obtained based on such data are therefore justified.

Because what must not be cannot be

The flawed calculation, which [6] simply calculated the percentages of fully vaccinated and un-/partially vaccinated out of the total number of positive tests, was last used for calendar week 40.

The reason for this paradigm shift is probably explained by the fact that even with the methodological errors described above in favor of the fully vaccinated the values calculated in this way hardly justify the use of vaccination for the prevention of infections.

The worst case scenario for the vaccination campaign would certainly be if the values of the incidence rates published from now on (week 41), despite massive “irregularities” in favor of vaccination, would at some point turn out to be higher for the fully vaccinated than for the unvaccinated and partially vaccinated.

We are sure, however, that even then a new statistical “approach” will show vaccination to be the matchless bringer of salvation.

It is hard to find the words to conclude. The sheer audacity with which the foot has been made to fit the shoe beggars belief.

Is this an example of science(-ness) that must – should be trusted?


[1] RTL (01.09.2021): Vum 15. September u keng gratis PCR-Tester méi

[2] Die Luxemburger Regierung – Coronavirus – Impfung

[3] RTL (01.09.2021): Nei Corona-Well am Hierscht/Wanter ass warscheinlech

[4] COVID-19: Rapports hebdomadaires

[5] Khan Academy: Controlled experiments

[6] Expressis Verbis: Die Abrechnung

[7] RTL (07.09.2021): Geimpfte Leit maache manner Aarbecht

[8] COVID-19: Rapports journaliers

[9] Pandemien der Impfdurchbrüche und der Intensivstationen – wie sich das RKI und die Krankenhäuser die Corona-Welt zurechtbasteln

[10] Hervé Seligmann: COVID19 more severe among Pfizer-vaccinated than other Israelis, for 1st, 2nd and 3d injections