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Revised: The Importance of Correct Infection and Exposure Pool
Estimations when Making a Comparison Between COVID-19 Vaccine
Injury Rates Among Vaccinees and COVID-19 Injury Rates Among
Unvaccinated Individuals
Anette Stahel, MSc
Email: anette.stahel@yahoo.com
A R T I C L E I N F O
Article history:
Post-Publication Peer Review, Revision of [1]
Published 13 April 2023
Keywords:
BNT162b2 mRNA vaccine injury rates
Clalit Health Services
COVID-19
SARS-CoV-2
S U M M A R Y
On August 25, 2021 the above paper, Safety of the BNT162b2 mRNA COVID-19 Vaccine in a Nationwide
Setting, was published in New England Journal of Medicine. Unfortunately, the study includes two method
errors which make the comparison between COVID-19 vaccine injury rates and COVID-19 injury rates in it
incorrect. More specifically, the vaccine injury rates among vaccinees are compared to disease injury rates
among confirmed infected people when instead they should be compared to disease injury rates among the
total pool of unvaccinated people. I'll here explain how come using highly adequate infection and exposure
pool estimations when conducting such a comparative study is of utmost importance. I'll also carry out a more
correct calculation of the total pool of unvaccinated people, based on official infection rate figures.
Introduction
On August 25, 2021 the above paper, Safety of the
BNT162b2 mRNA COVID-19 Vaccine in a Nationwide
Setting, authored by Barda et al from the Israeli Clalit
Research Institute (CRI), was published in New England
Journal of Medicine [2]. The title of the paper describes its
content very well, although in addition to investigating the
occurence of various injuries following BNT162b2 mRNA
COVID-19 vaccination, it also made a comparison between
injury rates among vaccinees and COVID-19 injury rates
among infected individuals.
I've now gone through and reviewed this paper and I'm
sorry, but this study is not correct. That is, it contains two
major method errors. First of all, the pool of people used as
denominator when calculating the percentage of COVID-19
infected people who developed certain conditions due to the
infection is greatly inadequate. Second, the vaccine injury
rates among vaccinees were compared to disease injury rates
among infected people when instead they should’ve been
compared to disease injury rates among the total pool of
unvaccinated people. These method inadequacies have serious
consequences. I'll explain what I mean.
Correct estimation of infection pool
When calculating the risk of developing a medical
condition from an infectious disease, you need to make a
correct assessment of how how large the pool of infected
people is. And to do that, you need to make an estimate.
Merely counting the number of people who've tested positive
in a certain area isn't enough, as you need to include people
who don't go test themselves because of being asymptomatic,
or of not having the energy to do it due to their symptoms, or
of lacking interest or knowledge about the infection et c. There
may be many different reasons. This means you need to make
an estimate, otherwise the denominator in the calculation of
the percentage of infected people who develops the condition
becomes incorrect.
I'll use the study Estimation of the Lethality for COVID-19
in Stockholm County published by the Swedish Public Health
Agency as an example of a correctly calculated risk, based on
an adequately defined denominator [3]. The fact that this was
a calculation of the lethality percentage from COVID-19 and
not the percentage of infection complications is irrelevant, the
point is that the same mathematics used in this study should've
been applied in the present CRI study. From the Swedish
study, in translation:
"Recruitment was based on a stratified random sample of
the population 0-85 years. In the survey we use, the survey for
Stockholm County was supplemented with a self-sampling kit
to measure ongoing SARS-CoV-2-infection by PCR test. The
sampling took place from March 26 until April 2 and 18 of a
total of 707 samples were positive. The proportion of the
population in Stockholm County which would test positive
was thus estimated at 2.5%, with 95% confidence range 1.4-
4.2%."
For a complex reason, which I won't go into but is
described in the study text, one sometimes needs to use a
slightly higher percentage when multiplying it with the total
number of people in the pool, but that's of minor importance.
Anyway, in this study they had to use the figure 3.1169% and
when they multiplied it with the number of people in
Stockholm County, 2 377 000, they got 74 089. This estimate
was then the correct denominator to use when calculating the
percentage of people who died from COVID-19 in Stockholm
County during this time period.
The numerator was the number of people who died in
Stockholm County with a strong suspicion of COVID-19 as a
cause, which was 432, no incorrectness there either, as long as
a suspected cause number, not a diagnosed cause number, is
also used as the numerator when calculating the lethality from
the COVID-19 vaccine when the infection lethality and
vaccine lethality rates are compared.
So, what they found was that the lethality from COVID-19
in Stockholm County was 0.58%. This was a correct figure, as
long as we keep in mind the fact that some of the suspected
COVID-19 deaths may later have become diagnosed as
unrelated to the infection.
The above is thus how the authors of the present study
should've carried out their calculations but they didn't. From
their text:
"Each day in this SARS-CoV-2 analysis, persons with a
new diagnosis of SARS-CoV-2 infection were matched to
controls who were not previously infected. As in the vaccine
safety analysis, persons could become infected with SARS-
CoV-2 after they were already matched as controls on a
previous day, in which case their data would be censored from
the control group (along with their matched SARS-CoV-2–
infected person) and they could then be included in the group
of SARS-CoV-2–infected persons with a newly matched
control. Follow-up of each matched pair started from the date
of the positive PCR test result of the infected member and
ended in an analogous manner to the main vaccination
analysis, this time ending when the control member was
infected or when either of the persons in the matched pair was
vaccinated."
I e, the selection pool for their SARS-CoV-2 analysis
merely consisted of confimed infected persons. This excluded
a considerable amount of infected persons in the total pool of
roughly 3 million people of relevant age during the study
period belonging to Clalit Health Services (CHS), the health
care organization in question, who didn't go test themselves
because of a number of reasons (being asymptomatic, not
having the energy or interest for it, et c). In short, the pool of
participants should've been added with a vast amount of both
symptomatic and asymptomatic SARS-CoV-2 positive people
who didn't develop these medic care necessitating conditions.
How large then, exactly, should the denominator have
been? Well, the present study looked at the time period from
March 1, 2020 to to May 24, 2021. What we need to do first,
is to look at the official statistics of how many estimated new
infections arose in Israel during these 15 months in question.
And this figure is found by means of the statistical online
resource Our World in Data, via the page presenting daily new
estimated COVID-19 infections in Israel [4]. If we download
the file and look at the figures, we find that the total number of
estimated infections in the country during these 15 months
amounted to 2 099 453. Prevalence studies of this period
indicate that the adequate estimate to use here is the upper one
[5].
If we then look at the data for confirmed infections in the
country during this period, we see that they amounted to 839
689. This means that the estimated number of infections was
2.5 times higher than the number of confirmed. And this, in
turn, means that we have to multiply the incorrect
denominator in the study by 2.5 to get the correct
denominator, which should've been used instead.
Further, in the CRI study's Figure 4, eleven adverse events
after vaccination are chosen for comparison with the
occurence of these after infection, and we find the following
excess risk numbers associated with COVID-19: Arrhythmia
0.166%, acute kidney injury 0.125%, pulmonary embolism
0.062%, deep-vein thrombosis 0.043%, myocardial infarction
0.025%, pericarditis 0.011%, myocarditis 0.011%, intracranial
hemorrhage 0.008%, appendicitis 0.004% and
lymphadenopathy 0.003%. As for herpes zoster infection, the
study found that COVID-19 reduced instead of increased the
risk of acquiring it, with 0.009%.
Now, if we apply the laws of mathematics and recalculate
these numbers, taking into account that the pool of participants
should've been 2.5 times larger, we get the following, more
correct figures: Arrhythmia 0.066%, acute kidney injury
0.050%, pulmonary embolism 0.025%, deep-vein thrombosis
0.017%, myocardial infarction 0.010%, pericarditis 0.004%,
myocarditis 0.004%, intracranial hemorrhage 0.003%,
appendicitis 0.002%, lymphadenopathy 0.001% and herpes
zoster infection -0.013%.
I'd here like to interpose a recommendation of reading
through the Swedish COVID-19 lethality study that I took up
in the beginning of my text as a correct, comparative example
[3]. The PDF is easily translated into any language via Google
Translate. This is the main paper that the Swedish equivalent
to the Centers for Disease Control and Prevention, the Public
Health Agency (Folkhälsomyndigheten), refers to when
talking about COVID-19 lethality here and it's put up on one
of the major information pages of their website. I really
recommend reading all of it, because it explains so well and in
such detail how come this model of denominator calculation
without exception must be used in studies like these, which
aim to investigate the rate of injuries/complications arising
from an infectious illness.
Correct estimation of exposure pool
Let's continue to the second method error of the CRI paper.
The vaccine injury rates among vaccinees were in the study
compared to disease injury rates among infected people, when
instead they should’ve been compared to disease injury rates
among the total pool of unvaccinated people (the
unvaccinated pool in the first part of the study is irrelevant as
it merely constituted a COVID-19 negative control group,
incomparable to a real life pool of unvaccinated people). From
the paper:
"To place the magnitude of the adverse effects of the
vaccine in context, we also estimated the effects of SARS-
CoV-2 infection on these same adverse events during the 42
days after diagnosis."
Also, in the study's Figure 3 and Figure 4, injury rates
among vaccinees and injury rates among infected people are
directly compared. The problem is, this type of comparison
simply cannot be done, i e, it's an incorrect comparison. This
is because the alternative to taking a vaccine is to not take the
vaccine, the alternative isn't to get the infection. Also, when
comparing vaccinees to infected instead of unvaccinated, the
risk/benefit assessment derived from these figures becomes
greatly inadequate. I'll explain what I mean.
Let me start by taking the potentially crippling condition
myocarditis as an example, a COVID-19 vaccine injury which
has been extra noted in media lately since it primarily affects
very young adults and teenagers, among which the increased
risk after vaccination is around 0.02% [6]. According to the
present study's data, there was a 0.003% increased risk of
getting myocarditis after the vaccine, and since older
individuals were included here, that's a correct figure. Further,
according to the study's data, the increased risk of developing
the condition after a confirmed COVID-19 infection was
0.011%. Since we in accordance with the laws of mathematics
have corrected that figure though, it's now narrowed down to
0.004%.
However, when comparing the risk of developing medical
condition X from taking vaccine Y with the risk of developing
condition X from not taking vaccine Y, you can't compare a
pool of vaccinees with a pool of infected people. Because
when you take a vaccine, there's a 100% risk of getting the
"infection" (in this case with viral RNA), while in the case of
not taking the vaccine, it doesn't imply a 100% risk of getting
the infection (with the virus), but a much lower risk.
And as we’ve seen, in Israel during the analysis period of
the present paper, the accumulated number of estimated
COVID-19 infections towards the end of the study period was
2 099 453. According to same source, Our World in Data, the
accumulated number of estimated infections in the beginning
of the period was 661. Based on the size of the country’s
population in 2021 [7] and in accordance with the laws of
mathematics, this means that the infection risk was 0.007% in
the beginning of the study period and 22% towards the end of
it. Thus, the average infection risk during this period was 11%.
This means that we have to multiply the figure 0.004% by
0.11 to get the correct risk increase for people of acquiring
myocarditis if they stayed unvaccinated. And this in turn
means that the risk increase for COVID-19 derived
myocarditis for people who didn't get the vaccine was as low
as 0.0004%. Now we're suddenly in a whole different
ballpark, as 0.003, the vaccine myocarditis risk increase
figure, is 7.5 times as much as 0.0004. And this means that as
for myocarditis, the risk of acquiring it was 7.5 times higher if
you got vaccinated as opposed to if you abstained.
Further, we have to apply this recalculation to all the other
recalculated COVID-19 related injury data in the study as
well, given that the unvaccinated didn't have a 100% risk for
infection but only 11%. What we then find, is that if you were
unvaccinated, the correct COVID-19 derived risk increase
figures for the eleven mentioned conditions were:
Arrhythmia 0.007%, acute kidney injury 0.006%,
pulmonary embolism 0.003%, deep-vein thrombosis 0.002%,
myocardial infarction 0.001%, pericarditis 0.0004%,
myocarditis, as said, 0.0004% also, intracranial hemorrhage
0.0003%, appendicitis 0.0002%, lymphadenopathy 0.0001%
and herpes zoster infection -0.014%.
Let’s now look at the risk increase figures for COVID-19
vaccinated individuals according to the study. These were
fully correctly calculated since there are no unregistered
vaccinees and therefore the registered figure is to be used. For
appendicitis, the vaccine generated risk increase was 0.005%,
for myocardial infarction, it was 0.001%, for pericarditis, it
was 0.001% as well, for myocarditis, it was, as mentioned,
0.003%, for herpes zoster infection, it was 0.016% and for
lymphadenopathy, it was as high as 0.078%. For acute kidney
injury, arrhythmia, deep-vein thrombosis, intracranial
hemorrhage and pulmonary embolism, the vaccine related
effect was slightly negative: -0.005%, -0.006%, -0.001%, -
0.003% and -0.001%, respectively.
Now, what we find if we add all eleven vaccine related risk
figures together and then compare that sum to the sum of all
eleven risk figures for the unvaccinated group, is that the
aggregated risk increase for the vaccinated individuals was as
much as 14.7 times higher than the corresponding risk
increase for the unvaccinated. For the vaccinated, the
aggregated risk increase was 0.088%, while the figure for the
unvaccinated was 0.006%, and it's worth underlining that
these are all very serious afflictions (or, as for
lymphadenopathy, can point to such).
Let me emphasize: The risk increase of acquiring a SARS-
Cov-2 derived form of one or more of the eleven serious
conditions focused on in this large study was 14.7 times
higher for vaccinees than for unvaccinated individuals.
One may object here and say that even if the vaccine
increased the risk of developing a number of conditions, it
also reduced the risks of developing a number of them. From
the paper:
"The BNT162b2 vaccine appears to be protective against
certain conditions such as anemia and intracranial
hemorrhage. These same adverse events are also identified in
this study as complications of SARS-CoV-2 infection, so it
appears likely that the protective effect of the vaccine is
mediated through its protection against undiagnosed SARS-
CoV-2 infection, which may be undiagnosed either because of
a lack of testing or because of false negative PCR results."
In the study's abstract, this is commented as well:
"In this study in a nationwide mass vaccination setting, the
BNT162b2 vaccine was not associated with an elevated risk
of most of the adverse events examined."
Well, that's something of a play with words, because if we
look at Table 2 in the paper, where the entirety of adverse
events associated with the vaccine is listed, we find that in
total, the risk reduction for serious conditions generated by the
vaccine was 0.04%, while the total risk increase for serious
conditions generated by it was 0.14%; that is, a whole 3.5
times larger.
Conclusion
Interestingly, with their work including the
abovementioned errors, these authors have actually provided
scientific validation of the growing suspicion that the COVID-
19 vaccinated state gives rise to various serious injuries to a
much greater extent than does the unvaccinated (which is the
opposite of the message of the paper) because even if the
figures used for comparison with the vaccine injury figures
are inadequate, the other figures in the study are most likely
not.
Towards the end of the study, one of the problems
discussed above is briefly mentioned:
"When a person decides to become vaccinated, this choice
results in a probability of 100% for the vaccination, whereas
the alternative of contracting SARS-CoV-2 infection is an
event with uncertain probability that depends on the person,
place, and time."
However, since omitting to include a calculation example
with an adequate exposure pool, based on a correct infection
pool and official infection rate figures has such a large impact
on the main message of this paper - changing it from defining
the COVID-19 vaccinated state as less injurious than the
unvaccinated, to the opposite - merely briefly mentioning it
towards the end like this, as one among several limitations of
the study, is so greatly misleading that it constitutes an error in
itself.
Finally, and most importantly, there's a reason why the
method inadequacies discussed here have especially serious
consequences in this particular case. That is, CDC, the major
public health organization in the US and an organization with
profound influence on public health officials worldwide, refers
to this study and its figures in their documents as a source to
support their view that the benefits of COVID-19 vaccinating
the population outweigh the risks connected to it [8, 9]. Of
course, had the present study been correctly performed, it
would've pointed the CDC in the direction of determining the
opposite; that the risks of vaccinating are far greater than
abstaining.
References
1. Stahel, A (2021) The Importance of Correct Infection
and Exposure Pool Estimations when Making a Comparison
Between COVID-19 Vaccine Injury Rates Among Vaccinees
and COVID-19 Injury Rates Among Unvaccinated Individuals
ScienceOpen DOI: 10.14293/S2199-1006.1.SOR-
UNCAT.A8427535.v1.ROECQS
https://www.scienceopen.com/document/review?
review=da097d27-a5ea-48ff-9b4f-
30aa6731e9d6&vid=c68bbc3f-7990-41aa-b86c-
d947b7537386
2. Barda, N, Dagan, N, Ben-Shlomo, Y, Kepten, E,
Waxman, J, Ohana, R, Hernán, M A, Lipsitch, M, Kohane, I,
Netzer, D, Reis, B Y & Balicer, R D (2021) Safety of the
BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Setting
N Engl J Med 385(12): 1078-1090
https://www.nejm.org/doi/10.1056/NEJMoa2110475
3. Svenska Folkhälsomyndigheten (2020) Skattning av
Letaliteten för Covid-19 i Stockholms Län
https://www.folkhalsomyndigheten.se/contentassets/da0321b7
38ee4f0686d758e069e18caa/skattning-letalitet-COVID-19-
stockholms-lan.pdf
4. Our World in Data, Global Change Data Lab (2021)
Daily New Estimated COVID-19 Infections from the IHME
Model, Israel https://ourworldindata.org/grapher/daily-new-
estimated-infections-of-covid-19?country=~ISR
5. Bassal, R, Keinan-Boker, L, Cohen, D, Mendelson, E,
Lustig, Y & Indenbaum, V (2022) Estimated Infection and
Vaccine Induced SARS-CoV-2 Seroprevalence in Israel
among Adults, January 2020 - July 2021 Vaccines (Basel)
10(10): 1663
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9609359/
6. Vogel, G & Couzin-Frankel, J (2021) Israel reports link
between rare cases of heart inflammation and COVID-19
vaccination in young men Science, American Association for
the Advancement of Science
https://www.science.org/news/2021/06/israel-reports-link-
between-rare-cases-heart-inflammation-and-covid-19-
vaccination
7. Trading Economics (2023) Israel Population (2021)
https://tradingeconomics.com/israel/population
8. Lee, G M & Hopkins, Jr, R H, Centers for Disease
Control and Prevention, Advisory Committee for
Immunization Practices [ACIP Workgroup Presentation]
ACIP Meeting, Atlanta, GA, United States (2021, August 30)
COVID-19 Vaccine Safety Updates: COVID-19 Vaccine
Safety Technical (VaST) Work Group Assessment
https://www.cdc.gov/vaccines/acip/meetings/downloads/slides
-2021-08-30/05-COVID-Lee-508.pdf
9. Lee, G M (2021) The Importance of Context in Covid-
19 Vaccine Safety N Engl J Med 385(12): 1138-1140
https://www.nejm.org/doi/10.1056/NEJMe2112543