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Revised: The Importance of a Correct Infection Pool Estimation when
Making a Comparison Between COVID-19 Injury Rates and COVID-19
Vaccine Injury Rates
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:
Cerebral venous sinus thrombosis
Electronic health records
COVID-19
Portal vein thrombosis
SARS-CoV-2
S U M M A R Y
On July 31, 2021 the above article, Cerebral Venous Thrombosis and Portal Vein Thrombosis: A
Retrospective Cohort Study of 537,913 COVID-19 Cases, was published in EClinicalMedicine.
Unfortunately, the study includes two method errors which make the comparisons 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 a highly adequate infection pool estimation when conducting such a comparative study is of
utmost importance. I'll also carry out a more correct calculation of th is infection pool, based on official
infection rate figures.
Introduction and Review
On July 31, 2021 the above article, Cerebral Venous
Thrombosis and Portal Vein Thrombosis: A Retrospective
Cohort Study of 537,913 COVID-19 Cases, authored by
Taquet et al from Oxford University, was published in
EClinicalMedicine [2]. The title of the article describes its
content very well, although in addition to investigating the
occurence of cerebral venous thrombosis, CVT, and portal
vein thrombosis, PVT, following COVID-19 diagnosis it also
investigates the occurence of these conditions following
influenza diagnosis and following administration of an mRNA
vaccine (BNT162b2 or mRNA-1273) against COVID-19.
I've now gone through and reviewed this article and I'm
sorry, but this study is not correct. That is, to begin with, the
pool of people used as denominator when calculating the
percentage of COVID-19 infected people who developed
CVT and PVT is greatly inadequate. I'll explain what I mean.
On page 2 of the study, it's stated:
"COVID-19 increases the risk of CVT and PVT compared
to patients diagnosed with influenza, and to people who have
received a COVID-19 mRNA vaccine."
However, when comparing the risk of developing medical
condition X from infectious disease Y with the risk of
developing condition X from something else, e g vaccine Z,
you first and foremost need to make a correct assessment of
how how large the pool of people infected with Y is. And to
do that, you need to make an estimate. Merely counting the
number of people who've sought out primary or secondary
care for their symptoms won't do. Not even if you include all
the people who were asymptomatic but sought out the care
center anyway in order to take a test to see if they were
infected (simply because they wanted to know) and then tested
positive.
No, you need to include all infected persons in the total
pool of people belonging to the health care facility/facilities in
question, including the ones 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 being into alternative
medicine, or of lacking interest/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 who develops condition X from
infection Y becomes incorrect.
A study measuring the risk of developing condition X from
infection Y using a smaller denominator than one including
everyone infected may be useful at times, but it can not be
used for comparison with a correctly calculated vaccine risk.
I’ll use the study Estimation of the Lethality for COVID-19
in Stockholm County published by the Swedish Public Health
Agency [3] as an example of a correctly calculated risk, based
on an adequately defined denominator. The fact that this is a
calculation of the lethality percentage from COVID-19 and
not the CVT and PVT percentage is irrelevant, the point is
that the same mathematics used in this study should've been
applied in the present Oxford study. From page 13 in 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 the first part of their calculation but they
didn't. From their text:
"Using a retrospective cohort study based on electronic
health records primarily in the USA, the absolute risks of
CVT and portal vein thrombosis (PVT) in the two weeks
following a diagnosis of COVID-19 (made between January
20, 2020 and March 25, 2021) were calculated. (--) A total of
537,913 patients with a COVID-19 diagnosis were included."
This excluded a considerable amount of infected persons in
the total pool of 81 million people belonging to all of these
primary and secondary care centers, who didn't go test
themselves because of a number of reasons (being
asymptomatic, being alternative medical, 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.
If they'd used an adequate figure in the denominator, the
percentage of people established to've developed CVT and
PVT from COVID-19 would've gotten vastly lower. However,
the percentage of people determined to've developed CVT and
PVT from the COVID-19 vaccine was fully correctly carried
out since there are no unregistered vaccinated cases and
therefore the registered figure is to be used. Towards the end
of the text the possibility is mentioned of a number of people
having received their vaccination elsewhere and therefore not
being included in the vaccinee pool, but that figure is likely
to’ve been very low.
Via the determined COVID-19 CVT and PVT risks in the
study along with the online verson’s Figure 2 [4], I calculated
the following figures: First time CVT cases diagnosed after
administration of the COVID vaccine amounted to 6.6 per
million and first time PVT cases diagnosed after vaccination
amounted to 10.7 per million. As for the infection derived
forms of the diseases, the study’s figures were 35.3 per million
for first time CVT and 175.0 per million for first time PVT.
Now, the study looked at the time period from January 20,
2020 to to March 25, 2021, and what we need for a first step
in determining the correct denominator is to estimate how
many people in the US were infected at least once during these
14 months in question. For the calculation to be really
accurate, we need the total, accumulated estimated number of
infected people.
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 the United States [5]. If we
download the file and look at the figures, we find that the total
number of estimated infections in the country during these 14
months amounted to 83 098 301. Prevalence studies of the
latter part of this period indicate that the adequate estimate to
use here is the upper one [6].
If we then look at the data for confirmed infections in the
country during this period, we see that they amounted to 29
562 445. This means that the estimated number of infections
was 2.8 times higher than the number of confirmed. And this,
in turn, means that we have to multiply the incorrect
denominator of 537 913 used in the study by 2.8 to get the
correct denominator, which should've been used instead. That
multiplication gives us the figure of 1 506 156 estimated
COVID-19 infections.
Further, the study says that first time CVT was found in 19
of the patients following COVID-19 diagnosis and first time
PVT in 94. This means that in reality, the rates of CVT and
PVT elicited by COVID-19 were much lower than the present
study claims. Infection elicited CVT cases, correctly
calculated, amounted to 12.6 per million and the PVT cases
amounted to 62.4 per million; far from the study’s 35.3 per
million and 175.0 per million for CVT and PVT, respectively.
Now to the second part of the risk calculation, a part which
the authors of the present study didn’t miscalculate but simply
left out.
Let me first clarify what this study by Taquet et al makes a
comparison of. It makes a comparison between the CVT and
PVT risks among [confirmed] COVID-19 infected people and
the CVT and PVT risks among COVID-19 vaccinated people.
However, when referring to this paper within the context of
making a risk/benefit assessment regarding decisions about
administration of the COVID-19 vaccine, these risk figures
among infected people cannot be used in their "raw" form, not
even if you correct the numbers from confirmed cases to total
cases as I did above.
The reason why these "raw" figures cannot be used is that
the alternative to taking a vaccine is to not take the vaccine,
the alternative isn't to get the infection. 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 risk which is much lower.
And as we’ve seen, in the US during the analysis period in
question, the accumulated number of estimated COVID-19
infections in the end of the study period was 83 098 301.
According to same source, Our World in Data, the
accumulated number of estimated infections in the beginning
of the period was 510. 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 0.00015%
in the beginning of the study period and 25% towards the end
of it. Thus, the average infection risk during this period was
12,5%.
This means that we have to multiply the recalculated
infection derived CVT and PVT risk figures in the study by
0.125 to get the correct risks for people of acquiring COVID-
19 derived forms of these conditions if they stayed
unvaccinated. We thus get a risk of 1.6 per million for CVT
and a risk of 7.8 per million for PVT. And this means, that
taking the COVID-19 vaccine during this time period entailed
a 4.1 times (310%) higher risk of developing CVT and a 1.4
times (40%) higher risk of developing PVT than if you
abstained from taking it.
Conclusion
In the Introduction of the Taquet et al study, it's stated:
"Here, using an electronic health records network primarily
based in the USA, we estimated the incidence of CVT and
PVT occurring in confirmed COVID-19 cases (both
hospitalized and non-hospitalized) and compared this
incidence to two other groups: people who received a COVID-
19 mRNA vaccine (i.e. the BNT162b2 or mRNA-1273
vaccine), and a cohort of patients with influenza."
And the final passage of the Discussion states:
"In summary, COVID-19 is associated with a markedly
increased incidence of CVT compared to patients with
influenza, people who have received BNT162b2 or mRNA-
1273 vaccines and compared to the best estimates of the
general population incidence."
Well, I've now shown that when making a truly correct
comparison, i e not between vaccinees and [confirmed]
infected but between vaccinees and unvaccinated individuals,
we can see that taking the vaccine actually entailed a much
greater risk for aquiring virus/mRNA derived forms of these
conditions vs if you abstained from taking it. Both of the
above quotes from the present study imply that it's
methodically correct to compare vaccinees to infected
individuals in a risk/benefit context. But it's not, in fact it's
hugely incorrect.
At the very least the authors should've included a longer
passage in which they carefully explained the importance of
comparing vaccinees to unvaccinated individuals in such
contexts, instead of using the "raw" form from their study, but
they didn't. Unfortunately, this has led to references to this
paper by both laymen and medical professionals over the
world in texts contending that the benefits of COVID-19
vaccinating the population outweigh the risks connected to it.
Because apparently it's not obvious to everyone that this
recalculation including infection rate figures needs to be done.
In this particular case, there's a reason why the method
inadequacies discussed above have especially serious
consequences. That is, the Centers for Disease Control and
Prevention (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 [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 in regard to CVT and PVT, the
risks of vaccinating are far greater than abstaining.
Interestingly though, with their work including these
method errors, these authors have actually provided scientific
validation of the growing suspicion that the COVID-19
vaccinated state gives rise to thrombocytic complications to a
greater extent than does the unvaccinated (which is the
opposite of the message of the paper), because even if the 537
913 figure is inadequate, the other figures in the study are
most likely not.
Finally, I'd like to recommend a reading through of 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 CDC, 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.
References
1. Stahel, A (2021) The Importance of a Correct Infection
Pool Estimation when Making a Comparison Between
COVID-19 Injury Rates and COVID-19 Vaccine Injury Rates:
Peer Review of Cerebral Venous Thrombosis and Portal Vein
Thrombosis: A Retrospective Cohort Study of 537,913
COVID-19 Cases ScienceOpen DOI: 10.14293/S2199-
1006.1.SOR-UNCAT.A8324974.v1.RUJZBA
https://www.scienceopen.com/document/review?
review=44831b83-8336-4642-9d1d-
bfef514960ec&vid=02c7c05a-485d-4666-9c5c-e1dcc93fabc4
2. Taquet, M, Husain, M, Geddes, J R, Luciano, S &
Harrison, P J (2021) Cerebral Venous Thrombosis and Portal
Vein Thrombosis: A Retrospective Cohort Study of 537,913
COVID-19 Cases EClinicalMedicine
https://www.thelancet.com/action/showPdf?pii=S2589-
5370%2821%2900341-2
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. Taquet, M, Husain, M, Geddes, J R, Luciano, S &
Harrison, P J (2021) Cerebral Venous Thrombosis and Portal
Vein Thrombosis: A Retrospective Cohort Study of 537,913
COVID-19 Cases EClinicalMedicine
https://www.thelancet.com/journals/eclinm/article/PIIS2589-
5370(21)00341-2/fulltext
5. Our World in Data, Global Change Data Lab (2021)
Daily New Estimated COVID-19 Infections from the IHME
Model, United States https://ourworldindata.org/grapher/daily-
new-estimated-covid-19-infections-ihme-model?
country=~USA
6. Wiegand, R E, Deng, Y, Deng, X, Lee, A, Meyer, W A
3rd, Letovsky, S, Charles, M D, Gundlapalli, A V, MacNeil,
A, Hall, A J, Thornburg, N J, Jones, J, Iachan, R & Clarke, K
E N (2023) Estimated SARS-CoV-2 Antibody Seroprevalence
Trends and Relationship to Reported Case Prevalence from a
Repeated, Cross-sectional Study in the 50 States and the
District of Columbia, United States - October 25, 2020 -
February 26, 2022 Lancet Reg Health Am 18: 100403
https://www.sciencedirect.com/science/article/pii/S2667193X
22002204?via%3Dihub
7. Trading Economics (2023) United States Population
(2021) https://tradingeconomics.com/united-states/population
8. Centers for Disease Control and Prevention, Advisory
Committee for Immunization Practices [ACIP Workgroup
Presentation] ACIP Meeting, Atlanta, GA, United States
(2021, April 23) Risk/Benefit Assessment of Thrombotic
Thrombocytopenic Events after Janssen COVID-19 Vaccines
https://www.cdc.gov/vaccines/acip/meetings/downloads/slides
-2021-04-23/06-COVID-Oliver-508.pdf
9. Centers for Disease Control and Prevention (2021) CDC
Library: COVID-19 Science Update May 21
https://www.cdc.gov/library/covid19/pdf/public_pdfs/05-21-
2021-Science-Update-Final-public.pdf
