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Causal eﬀect of covid vaccination on mortality in Europe"
André Redert, PhD"
Independent researcher"
Rodotti, Netherlands, 24 February 2023"
Abstract
This report investigates shortterm causal vaccinemortality interactions during booster
campaigns in 2022 in 30 European countries (population ~530M). An infectionvaccination
mortality model is introduced with causal aspects of repeatability, random chance, temporal order
and confounding. The model is simple, has few or even zero prior model parameters and is
unbiased in causal mechanisms and strengths. Confounders are taken into account explicitly of
mortalitycaused fear incentivizing vaccinations and four related to covid infections, and
generically for all longterm confounding. Bayesian probabilities quantify all interactions, and from
observed weekly administered vaccine doses and allcause mortality, mortality on shortterm
caused by a vaccination dose is estimated as Vaccine Fatality Ratio (VFR)."
#VFR results are 0.13% (0.05%0.21%, 95% conﬁdence interval) in The Netherlands and 0.35%
(0.15%0.55%) in Europe, subtantially transcending covid IFR. Additionally, sewerviralparticle
experiments suggested vaccination induces covidinfections and/or reactivates latent viral
reservoirs."
#The evidence of a causal relationship from vaccination to both infection and mortality is a very
strong alarm signal to immediately stop current mass vaccination programmes."
Statement of Interest
I declare that this work was done with an interest in science, and personal safety for myself, loved
ones, and humanity. Pro bono, independent, without payroll, not funded. The only competing
interest was time taken from my normal job (indy app developer in entertainment and music). If
you want to support my work, feel free to buymeacoﬀee.com/AndreRedert, or consider one of
the apps at rodotti.nl and qneo.net."
1. Introduction
Since the covid vaccination campaigns, high unexplained excess mortality rates have been
observed worldwide, starting in the second half of 2021. In The Netherlands (population ~18M),
excess mortality rates went up to ~80 people/day (excess ~20%) at end of 2022, before rising
even more due to inﬂuenza. Based on the sparse publicly available Dutch data on mortality and
vaccination, excess mortality was found to correlate positively with vaccination on longterm
[Re1], and shortterm [Mee,Sch,Re2]. Figure 1 illustrates this correlation for weekly 4th/5th
vaccination campaign doses and allcause mortality. Detailed casebased data has still not been
made publicly available, and it remains a scientiﬁc challenge to analyse excess mortality using the
sparse data that is both available, and reliable."
#This report has the same goal as my earlier work [Re2], estimating shortterm Vaccine Fatality
Ratio (VFR) on the basis of weekly administered vaccine doses and allcause mortality; two
integer, countable parameters that do not suﬀer from the subjectivity and ambiguities in PCR
testpolicies, covid diagnoses, cause of death atttributions, and modeling in mortality prognoses."
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"
Figure 1: Left) Weekly rates in the Netherlands for mortality and administered covid vaccine doses
[Src], scaled to illustrate temporal correlations. Right) Pearson correlations are very high. Diﬀerent
regression factors may be related to the campaigns’ target ages (60+ and 12+).
New in this report is explicit causal modeling on the basis of repeatability, temporal order,
handling of infectionbased and generic confounders in a combined infectionvaccinemortality
(IVM) model, and the Bayesian framework to handle randomness and all statistic parameter
estimation. The extraction of shortterm events introduced in [Re2] to remove eﬀects and
confounding on longterm, see Figure 2, will be reused."
"
Figure 2: Same data as in Figure 1, shortterm ﬁltered to extract random weekly variations, easing
a single analysis with multiple campaigns combined."
Infection data will be used of PCR tests and viral particle presence in sewer wastewater [Med],
see Figure 3. As PCR tests are unreliable (false positives/negatives, testwillingness/policy
dependence, arbitrary CTvalues, etc), and sewer data is more objective but less widely available,
the relative performance of a simpliﬁed vaccinemortality (VM) model without infections will be
evaluated to widen the applicability of the method. Experiments will be performed for booster
campaigns in 2022, in The Netherlands as well as 30 European countries (population ~530M)."
"
Figure 3: PCR+ tests and viral particle presence in sewer wastewater, The Netherlands. Sewer
data may be more objective, but lags PCR+ infections by a few weeks, and also lags vaccinations
and mortality as in Figure 1."
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2. Method
In the next sections I will present my method in many highdetailed steps. The ﬁnal result,
however, is simple and contains a bare minimum, or even zero, model parameters."
2.1 Causality
The wellknown “Correlation does not mean causation” is a vague statement that may lead to the
false believe that all correlation is insuﬃcient as evidence of causation. However, correlation is all
one can observe, there is no alternative to determine causality. Pure causality cannot directly be
observed as it is an “abstract philosophical concept that indicates how the world progresses”
[Wik]. One can easily defend that:"
“The origin of all correlation is causality”
The wellknown vague statement means that when A and B are correlating, causation may not be
between A and B (in either direction) but may involve a common cause known as a confounder.
Correlations may also occur by chance, when an “oracle” set of events in the universe conspires
to create the correlation; a confounder that cannot be known by deﬁnition, referred to by
“random”. Theoretically, such a random oracle could exist for every possible A and B, thereby
pulling any practical use of causality out of the scientiﬁc realm ."
1
#Requirements for establishing causality have been studied for epidemiology in particular, listing
consistency and strength of association, confounding, temporality, experiments and plausibility,
based on the famous Bradford Hill criteria [Io1, Shi]. Consistency and strength of association can
be rephrased as strong correlation, which can readily be observed in Figures 1 and 2.
Repeatability, or rechallengable, and random chance are already essential ingredients in
correlation analyses; e.g. covariances are characterizations of commonalities in many repeated
observations, and statistical techniques exist to obtain mean and deviation of such covariances.
Temporality, also known as temporal or causal ordering, and confounding are unique for causality,
the reason to include these in my prior work [Re2] via a causality test involving temporal
correlation and shorttermﬁltered observations to remove all longterm confounding."
#In controlled experiments, one can make event A occur at will, which is very eﬀective for
excluding chance and confounders. Observational studies like in this report can, however, still
accomplish the same goal via additional requirements (see also e.g. [Gia]): natural repeated
occurrence of A, appropriately patterned in time to enable detection of the same pattern later in B
according to temporal order, plus more emphasis on excluding a confounder/chance origin of the
observed pattern. Finally, plausability requires a known mechanism that makes A cause B. For
current covid vaccines, there are plenty of plausible mechanisms that lead to mortality, e.g. acute
myo/pericarditis later followed by sudden cardiac arrest [Sun], and frail elderly for which
vaccination is the last push over the edge [Nor]."
#This report examines causality between observed vaccinations A and mortality B, incorporating
repeatability, temporal ordering, random chance and confounders via several known and unknown
mechanisms. These include a reverse mechanism from mortality to vaccinations and four
mechanisms via infections."
#One cannot keep adding possible confounders indeﬁnitely, as that inevitably leads to
overmodeling. Every possible confounder exhibits random correlations with both A and B, even
unrelated ones such as the weekly number of planetstar eclipses visible from earth. A suﬃcient
number of confounders will swamp any causal eﬀect between A and B at some point. My method
This seems to be the objective of the vague statement when it comes to vaccination and
1
mortality.
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includes shortterm ﬁltering of all observed data, eliminating all confounders that act on a term
longer than several weeks, even those unknown, while preventing overmodeling. As collateral
damage, the method can only measure causal eﬀects that act on short term and is blind to
longerterm eﬀects."
#The random weekly variations in infection, vaccination and mortality rates are used as
repeated, patterned ocurrences to detect temporal order in possible causal directions, while 40+
weeks of data in 2022 are used for statistical repeatability. The Bayesian probability framework is
used to handle random chance."
2.2 InfectionVaccinationMortality model
Figure 4 shows my causal infectionvaccinationmortality (IVM) model. Observables are infections,
vaccinations and mortality, all weekly absolute numbers in a population. Drivers of the
observables are viral waves, campaign dynamics and seasonal baselines. Natural immunity is
lifesaving in the real world but not modeled; it acts via a negative feedback loop on infection,
whose observations already include the full eﬀect of natural immunity."
"
Figure 4: Causal infectionvaccinationmortality (IVM) model. The path of vaccines to mortality has
focus. The other ﬁve causal paths are confounders. Viral waves, campaign dynamics and seasonal
baseline drive the observables and are random sources. As infection data is less reliable, the
relative performance of a vaccinationmortality (VM) model without infections and only two causal
paths will be evaluated also.
Six directed paths, shown as arrows in Figure 4, model the causal interaction from some event in
one observable to events in another observable, either within the same week or in a few future
weeks, but not past weeks. Vaccineinduced immunity and damage are modeled together as a
single net interaction. Interaction strength is measured in units of a ratio such as mortality per
infection (the wellknown Infection Fatality Ratio or IFR), mortality per vaccination (Vaccine Fatality
Ratio or VFR), etc."
#The focus of this report is measuring VFR via the causal path of vaccination to mortality. The
backward confounding path models vaccinations incentivised by fear, caused by observed high
excess mortality. Such confounding may add to a positive correlation as in Figure 1, which can
easily, but falsely, be attributed to vaccine damage in an analysis that does not take temporal
order into account. The four paths connected to infections relate to other confounding
mechanisms, among which the depletion of the reservoir of vulnerable people."
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2.3 VaccinationMortality model without Infections
Infections are the least reliable in the IVM model, not only in terms of data reliability but also by
their origin and role in the model. Ideally, two types of infections are taken into account if reliable
data is available: biological infections which are caused by viral waves and lead to physical
illness/death, and reported infections that are published by by massmedia with main purpose to
induce psychological fear. Two diﬀerent infection observables, however, strongly increases model
dependence on unreliable data, and complexity by number of causal interactions."
#I will simply keep one infection observable: the more objective sewer viral particles scaled to
equivalent PCR+ tests by calibration in the ﬁrst part of 2022. The apparent delay in sewertoPCR
data will be investigated: possibly, compensating the delay may do more harm than good in a
causal context."
#The IVM model can be used when reliable sewer and/or PCR+ infection data are available. To
widen the method’s applicability, a simpliﬁed model without infections will be introduced: the
vaccinemortality (VM) model, as was eﬀectively used in my prior work [Re2]. The VM model does
not suﬀer from unreliable infection data, but cannot compensate explicitly for infectionbased
confounders. Its performance will be evaluated relative to the IVM model."
2.4 Bicausal model for data delays
It may happen that observed data include delays due to a variety of reasons, e.g. testdelays until
symptoms occur and sewer viral particle data lagging PCR data, see Figure 3. Further, it is
common practice to delay vaccination status by several weeks after the “act of vaccination” to
2
account for immunity buildup. Delays are less expected for raw numbers of objectivelydated
events as vaccination doses or mortality, but they are still easily introduced e.g. by accident at
data transfer to 3rd party data aggregators;, or even purposefully for e.g. visualization or
integration of datasets."
#Due to unequal delays in observables, temporal ordering may get mixed up and eﬀects may
migrate between forward and reverse causal paths in the model, see Figure 5 left. For example,
due to a oneweekdelay in data, a severalweeksenduring causal eﬀect in one direction partly
migrates to the causal path in opposite direction. This may not be easily identiﬁable; the migrated
part will also change numerically, as paths in opposite directions have inverted units."
"
Figure 5: The bicausal model combines two oppositelydirected causal paths into a single
bidirectional (“bicausal”) path. All data is simulated for illustration purposes. The green zero means
a zero eﬀect value.
The clarity of the word “vaccination” has eroded substantially in recent years.
2
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For this reason, I will model every causal path pair as a single bicausal path that interacts both
backwards and forward in time using one numerical unit, arbitrarily chosen from original forward
or backward path. Within a bicausal path, data delays manifest simply as a single shift, see Figure
5 at right. Whenever the forward or backward causal path dominates and activity persists for a
few weeks, any delays can be identiﬁed by visual interpretation, using common sense aided by
strength certainty intervals; I will not try to model/automate such an identiﬁcation process. "
#It may appear that the bicausal model causes information loss: in Figure 5, the two causal
paths provide 2x5%=%10 measurements, while one bicausal path provides 9 measurements, one
less. The two instantaneous parts in the two causal paths at get combined into the single
instantaneous measurement of the bicausal path. This information loss, although real, is not due
to the bicausal model, as in the causal model the instantaneous parts get mixed up too, albeit
implicitly. Based on wellknown onset latencies of the six causal paths’ mechanisms, however,
some interactions are zero in the ﬁrst week (see Figure 5), and all measurements will be uniquely
assignable to the six causal mechanisms, both in causal and bicausal model."
2.5 Characteristics of drivers and causal paths
Table 1 shows onset latencies, temporal dynamics, and eﬀect sizes of drivers and causal paths.
All eﬀect sizes are very rough estimates by order of ten, and the expected sign of each of the six
paths is never used. Measurements will thus never be restricted by a priori sign expectations, but
a posteriori inspected for consistency. Free sign modeling is required for vaccineinduced
immunity and damage, as they have opposite signs but reside in the same path. Path interaction
strengths will be modeled both with prior expectations according to listed eﬀect sizes, and
without, that is, completely free of any prior expectation."
#Numerically, covid IFR is in the order of 0.1% [Io2]. The VFR is below ~0.1% given that most of
the population was vaccinated yearly, baseline mortality is yearly ~1% and total observed excess
mortality is in the order of ~10%. VaccineEﬀectivity against infection (VEI) and mortality (VEM)
may start at ~100% but negative VEI (positive damage) is known to possibly occur both in the
the ﬁrst weeks during buildup of immunity, and after several months when immunity wears oﬀ.
The size of vaccinecaused immunity is not plain VaccineEﬀectivity against mortality (VEM), but
scaled by IFR as the paths in my model relate to allcause mortality instead of only infection
attributed mortality, while assuming that ~100% of the population gets infected each year."
#Viral waves, campaign dynamics and seasonal baseline typically evolve on the longer term of
months/years, with random variations acting by deﬁnition on the shortest term of data resolution,
weeks in this report. Vaccinecaused eﬀects have a fast, biological, singlepersion underlying
mechanism, while mortalityinduced fear has a slower, psychological, interpersonal nature, via
fear of death induced by observing deaths of others."
#For this report, the most essential property in Table 1 is the low onset latency of vaccine
damage: adverse systemic events can occur within minutes, with immunity buildup following only
in the next 24 weeks. The path from infection to death, illness, typically takes at least a week,
and slightly above 2 weeks on average [Mar]. The causal path of fear requires data collection,
aggregation, and massmedia reporting of high infection numbers, or high excess deaths that are
above expectation according to some prognosis. While in 2020 it was custom to broadcast fear
inducing infection and mortality numbers daily, in most of 2022 the number of infections was
relatively low, and occurring high excess deaths were not attributable to covid and reported
seldom, late, or not at all."
#Finally, with depletion the reservoir of vulnerable people more susceptible to mortality declines
during periods of excess mortality. Although this eﬀect has zero latency, it acts cumulative and is
thus extremely small on the short term, and dynamical, if at all, only on the long term.
Δt= 0
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Table 1: Time scales, onset latencies and rough order of eﬀect size of drivers and causal paths.
2.6 Confounders
My IVM model handles 5 confounders explicitly, but clearly the list of actual confounders may be
longer and full of unknowns. As stated in the causality section, unlimited adding of possible
confounders leads to overmodeling. Instead, I will review a few known confounders that may have
eﬀect in this model and generic classes of (unknown) confounders."
#First, when closeones (family, friends, neighbours etc) die, shock and mourning may delay
planned vaccinations. This path is the same as the fear path, but with opposite/negative sign, not
delayed/ampliﬁed by massmedia and thus faster/smaller. In most cases, the vaccination will be
catched up shortly after, resulting in a slight delay in a few vaccinations. If present, this will be
measured as minor initial negative fear, with zero net eﬀect after a few weeks."
#Secondly, during vaccination campaigns, typically the smaller group oldest and most
vulnerable get vaccinated ﬁrst, and the broader group of younger and healthier people follow. If
vaccinations do cause mortality on the short term, concentrated in older/vulnerable people, the
order of vaccinations may create a bias towards “mortality ﬁrst” followed by “later vaccinations”,
a temporal order and positivesigned eﬀect equal to that of the fear path. This confounder makes
vaccine damage appear as mortalityinduced vaccinations and thus leads to underestimation of
vaccine damage, an acceptable bias for measurements."
#Many confounders may additionally come into play, known or unknown. All that apply on the
long term will be irrelevant, as this study looks only at shortterm events, as in Figure%2. Whenever
a confounder acts on the shortterm, it may reveal itself in both causal directions with similar
Driver
Onset latency
Time scale
Eﬀect size (10order)
Viral infection waves

month
100% population/year
Vaccination campaigns

month
100% population/year
Seasonal mortality baseline

month
1% population/year
Random ﬂuctations in each
immediate
week*
as observed from data
* zero, limited by source data resolution
Causal path
Onset latency
Time scale
Eﬀect size (10order)
Depletion M to I
>> week
months
Negligible < 0.1%
Illness I to M (IFR)
week or more
2 weeks
0.1%
Damage V to M (VFR)
immediate
months
0.1%
Immunity V to M (~VEM)
24 weeks
months
0.1%
Damage V to I (~VEI)
immediate
24 weeks
100%
Immunity V to I (~VEI)
24 weeks
months
100%
Fear I to V
week or more
week
1
Fear M to V
week or more
week
100
IFR: Infection Fatality Ratio, VFR: Vaccine Fatality Ratio"
VEI: Vaccine Eﬀectivity against infection, VEM: against mortality"
~ the modeled eﬀects are proportional to VE, and involve additional products with IFR or driver eﬀect size
VFR
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strength. In the bicausal measurements in Figure 5, this would appear as a signal without any
speciﬁc temporal order: evidence of confounding, and absence of causal evidence."
#If on the other hand a signiﬁcant vaccine immunity/damage signal is measured, in absence of a
signiﬁcant fear signal, this is evidence that the signal may not originate from a confounder, and
that the measured vaccine eﬀect may be real and causal. Exactly such a signal was found in
[Re2]. Of course, it is possible that an unidentifed, shortterm causally directed confounder exists.
Ignoring alarming evidence by assuming the existence of such a highly characterized but
unidentiﬁed confounder seems unwise."
2.7 Mathematical representation
Mathematically, I present my model ﬁrst in full, longterm causal form, and reduce it subsequently
to the shortterm bicausal model. To start oﬀ:"
#(1)"
#(2)"
# #Time, integer week number, from "
#Total number of analysed weeks in 2022 (typically for weeks 950)"
#Weekly number of infections, administered vaccine doses, and allcause mortality"
#Longterm mortality baseline, captures slow variations over months/years"
#Shortterm weekly variations, uncorrelated zeromean random process"
#Same as mortality baseline, but for viral waves and vaccinations"
#Temporal convolution"
#Causal function from A to B, valued only for "
#Duration of shortterm causal eﬀect (typically weeks)"
#Some prognosis, expected mortality, slowly varying over time (seasonal)"
#Excess mortality with respect to the prognosis/expectation"
#Infection Fatality Ratio, total mortality caused by infection"
#Vaccine Fatality Ratio, total mortality caused by vaccination"
The and are the drivers. The “baselines” vary slowly on the longer
term of a month/year. They capture viral presence waves, overall vaccination campaign dynamics,
and mortality of seasonal waves, othercause waves (covid, NPIs). They also capture confounders
acting between them, on the longterm, such as vaccination campaigns planned during covid
waves. The random processes describe the spread around the baselines, or weekly
variability of infections, vaccination and mortality originating from chance. They are zeromean
I(t) = bI(t) + rI(t) + {V*FV→I} (t) + {MΔ*FM→I}(t)
V(t) = bV(t) + rV(t) + {I*FI→V} (t) + {MΔ*FM→V}(t)
M(t) = bM(t) + rM(t) + {I*FI→M}(t) + {V*FV→M}(t)
MΔ(t) = M(t)−Mex pectat ion(t)
IFR =∑
0≤Δt<ΔT
FI→M(Δt)
VFR =∑
0≤Δt<ΔT
FV→M(Δt)
t
0≤t<T
T
T= 42
I,V,M
bM
rM
bI,rI,bV,rV
*
FA→B
0≤ Δt<ΔT
ΔT
ΔT= 2..5
Mexpectation
MΔ
IFR
VFR
bI,bV,bM
rI,rV,rM
bI,bV,bM
rI,rV,rM
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and uncorrelated over time and with respect to eachother, and nonstationary with variance
changing slowly over the longerterm together with . "
#The six causal functions model the six causal paths in Figure 4, with main focus on
. All operate by temporal convolution, a linear operator. The linearity of is
particularly justifed, as individual biological mechanisms within a population have no direct causal
interaction that could lead to substantial nonlinearities. For fear paths and , linearity
may be less defendable as the underlying psychological mechanism may involve nonlinear
eﬀects, e.g. “100 deaths” causing double the fear of “99 deaths”. For immunity path , and
possibly , one can argue that these should include a product with viral presence/infections
, but this is not taken into account for mathematical simplicity. An argument that justiﬁes this
choice partly is that covid has become endemic and viral waves are less extreme. Also, other
pathogens provide a permanent infectious background and it makes sense to evaluate vaccine
eﬀectivity always and only against allcause mortality [Ben]; ideally infections would represent all
pathogens, or even other mortal threats . Altogether, modeling of and may thus be
3
more accurate than the other paths, which is acceptable regarding the aim of this report."
#The mortality to vaccination and infection functions , have as argument; fear
and depletion are caused by excess mortality or aboveexpectation mortality .
There are other ways expectations may impact , e.g. when a newer expectation is published
that overshadows an older expectation, the newer creates additional fear and it may thus appear
with a positive sign: . For this analysis, it is irrelevant how and
when expectations are constructed, whether or not they include the eﬀects of covid, NPIs,
whether calculated by a national institute or emerged within the minds of individuals, whether their
eﬀect sign is positive or negative. What is important, is that expectations change slowly over time
t, and that the sign of actual, observed mortality is always positive in ."
2.8 Shortterm ﬁlter
As in [Re2], I apply a linear temporal ﬁlter on source data to remove all longterm
events and extract shortterm events in (with a hat), see also Figure 6:"
#(3)"
Applied to (1), this results in:"
#(4)"
bI,bV,bM
FA→B
FV→M
FA→B
FV→M
FM→V
FI→V
FV→I
FV→M
I
I
FV→M
VFR
FM→V
FM→I
MΔ
M−Mexpected
FM→V
Mnewer ex pectat ion −Molder ex pectat ion
M
MΔ
W(Δt)
I,V,M
I,
V,
M
W(Δt) = [−0.05 −0.25 + 0.6 −0.25 −0.05] for Δt∈[−2,2]
I(t) = {W*I}(t)
V(t) = {W*V}(t)
M(t) = {W*M}(t)
I(t) =
rI(t) + {
M*FM→I} (t) + {
V*FV→I} (t)
V(t) =
rV(t) + {
M*FM→V}(t) + {
I*FI→V} (t)
M(t) =
rM(t) + {
I*FI→M} (t) + {
V*FV→M}(t)
Massmedia have suggested vaccination protects against car crashes.
3
of 9 22
"
Figure 6: The temporal ﬁlter W extracts events with a short temporal scale, and removes events
with longer temporal scale.
Importantly, all causal functions are unaﬀected by the shortterm ﬁlter, and subsequently so
is in (2). The shorttime versions of source data are zeromean random
variables, illustrated by Figure 2. All longterm baselines and mortality expectation
have disappeared, also causing excess mortality in (1) to be replaced by plain
shortterm ﬁltered mortality in (4). The ﬁltered versions of drivers have slightly
reduced variance compared to the unﬁltered signals, and are still nonstationary."
#All of this is irrespective of the speciﬁc choice of ﬁlter , as long as it extracts shortterm
events as in Figure 6. The ﬁlter choice (3) in this report is given by ,
where is a Dirac delta function, is a zeromean, deviation Gaussian, one of the smoothest
ﬁlters possible, and is chosen to ensure that is zeromean (sum coeﬃcients is zero). The ﬁlter
choice in [Re2], , was an intuitive approximation of the ﬁlter
in this report."
#As the same ﬁlter is applied to all observables, it does not bias the shortterm measurements
towards any of the causal paths, or towards any direction within any path; the ﬁlter may even be
timeassymetric, e.g. a 3rd derivative ﬁlter [1 +3 3 +1], as possible time delays due to the ﬁlter
do not aﬀect measurements of . The ﬁlter also does not bias measurements by sign. In
combination with zeromean prior expectations on the values of , the ﬁlter may bias
measurements towards zero, with a relative strength growing with event time scale. Aggregates of
such as and will then be biased to zero, or equivalently underestimated in size."
#In the results section, I will illustrate a few alternative ﬁlters as well as absence of the ﬁlter, and
complete relaxation of the prior expectations. For readability: I will leave out all hats from this
point on. In all that follows, observables are shorttermﬁltered."
2.9 Shortterm causal IVM model, prior variances and constraints
The shortterm causal IVM model (4) is here denoted without hats:"
#(5)"
FA→B
VFR
I(t),
V(t),
M(t)
bI,bV,bM
Mexpectation
MΔ
M
rI(t),
rV(t),
rM(t)
W
W(Δt)≈δ(Δt)−KG1(Δt)
δ
Gσ
σ
K
W
[−0.1 −0.25 + 0.7 −0.25 −0.1]
FA→B
FA→B
FA→B
IFR
VFR
I,V,M
I(t) = rI(t) + {M*FM→I} (t) + {V*FV→I} (t)
V(t) = rV(t) + {M*FM→V}(t) + {I*FI→V} (t)
M(t) = rM(t) + {I*FI→M} (t) + {V*FV→M}(t)
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I model all and components of drivers and causal interactions as
independent, normaldistributed (Gaussian) stationary random variables. The original non
stationarity of drivers is remodeled by a slightly higher overall variance, namely that of
the observed :"
#(6)"
For the variances one ﬁnds using the eﬀect sizes in Table 1:"
#(7)"
These values are rough orders, which is accurate enough as they are only used as socalled
“priors” to slightly constrain the model; they bias measurements of to zero in the presence
of insuﬃcient evidence in the observables. The priors’ inﬂuence decreases the more informative
observational data is available. I will alternatively allow for completely free causal
interactions, relaxing prior variance constraints (7), to prevent underestimation of interactions
:"
#(8)"
Using Table 1 one ﬁnds that fear and depletion causal paths have onset latencies beyond a week:"
#(9)"
Although the illness path, death caused by infection , also has an onset latency of a week, I
choose not to take it into account explicitly as a prior restriction. The three restrictions (9) already
suﬃce to disambiguate bicausal interactions at , and it is plausible that a highly vulnerable
person dies within a week after infection due to illness caused."
2.10 Time resolution and onset latency
Figure 7 illustrates how ﬁnite temporal data resolution aﬀects observations and causal functions
. The underlying (inaccessible) timecontinuous causal mechanism (with upper c) translates
to week resolution by a speciﬁc triangularshaped timesymmetric aggregation ﬁlter :"
#(10)"
with continuous (realvalued) time in weeks. The triangular aggregation eﬀect happens always,
no matter how ﬁne the time resolution used. The weekresolution used in this report means that
any event pair separated by 3.5 days or more, is thus captured more by than ."
t
Δt
rI,rV,rM
FA→B
rI,rV,rM
I,V,M
σrI=σIσrV=σVσrM=σM
FA→B
σV→M= 10−3σM→I= 10−3σI→V= 1
σM→V= 102σI→M= 10−3σV→I= 1
FA→B
I,V,M
FA→B
σA→B=∞
FI→V(0) = FM→V(0) = FM→I(0) = 0
FI→M
Δt= 0
F
Fc
Λ
F(Δt) = {Fc*Λ}(Δt) = ∫Δtc
Fc(Δtc)Λ(Δt− Δtc)dΔtc
tc
F(1)
F(0)
of 11 22
"
Figure 7: Resolution eﬀect example for vaccination to mortality. Event pairs separated by 2 days
are captured by and , randomly with probability 5/7 and 2/7 respectively,
depending on location of events within the week. The amounts are described by triangular
function of separation duration."
Most important for this report, any event pair separated by a week or more will under no
circumstance aﬀect , justifying the onset latency constraints (9)."
2.11 Bicausal IVM and simplifed VM model
The bicausal IVM model combines the causal model’s six paths as in Figure 4 into three bicausal
paths, by new functions (note the double arrow):"
#(11)"
Each will be measured and is subsequently uniquely decomposable into and ,
as the latter are both only valued for . Ambiguities at are completely resolved by
onset latency constraints (9). The scale of has the same scale as namely B per A,
and thus ’s scale of A per B is corrected for in (11). Note that the in (11) models the
exact same physical event as in (5), with same accuracy, but with a slightly diﬀerent mathematical
representation. Under expected circumstances where causal path eﬀects are relatively small
compared to the drivers, the diﬀerence is negligibly small."
#The combined functions can be chosen as or for each of the three path pairs in
causal model (5). I choose them to match the biological causal paths, at the same time arriving at
only two equations:"
#(12)"
Variances (7) combine via (11) into:"
#(13)"
From here, the simpliﬁed bicausal VM model without infections is:"
#(14)"
FV→M(0)
FV→M(1)
Λ
F(0)
FA↔B
FA↔B(Δt) = FA→B(Δt) + σ2
B
σ2
A
FB→A(−Δt) , − ΔT<Δt<ΔT
FA↔B
FA→B
FB→A
Δt≥0
Δt= 0
FA↔B
FA→B
FB→A
FB→A
FA↔B
FB↔A
M(t) = rM(t) + {V*FV↔M}(t) + {I*FI↔M}(t)
I(t) = rI(t) + {V*FV↔I} (t)
σV↔M= 10−3σI↔M= 10−3σV↔I= 1
M(t) = rM(t) + {V*FV↔M}(t)
of 12 22
with only one prior from (13). In [Re2], of this bicausal VM model was estimated by a
Pearson correlation trend factor:"
#(15)"
This estimate was suboptimal; next follows an optimal estimation procedure."
2.12 Bayesian probabilities and estimating parameters
The Bayesian probability framework is an ideal, systematic tool to obtain conditional probability
densities of model parameters given observed . From the relevant
statistics as mean and variance of can be extracted. Denoting all drivers by ,
one obtains for the causal IVM model :"
#(16)"
First row: the intermediate roles of drivers are taken into account via integrals, and observations
and model parameters are reversed bringing up additional priors, of which the model parameters
are independent. Second row: prior is expanded in 6 causal paths and all
components. Row 3: prior is split in individal drivers and time . Rows 46: causal IVM
model (5) enters via three Dirac functions plus socalled determinant of Jacobian that
describes the multiple occurences of in the arguments. #The Jacobian is a huge by
σV↔M
FV↔M
FV↔M(Δt)[Re2] ≈COV(V(t), M(t+Δt))
VA R(V(t))
PFI,V,M
F
I,V,M
PFI,V,M
F
r= {rI,rV,rM}
F= {FV→I,FI→V,FI→M,FM→I,FM→V,FV→M}
PFI,V,M=∫r
Pr,FI,V,M=∫r
PI,V,Mr,FPr,FP−1
I,V,M=P−1
I,V,MPF∫r
PrPI,V,Mr,F
=P−1
I,V,M∏
FA→B∈F
∏
Δt
GσA→B(FA→B(Δt))
∫rI,rV,rM
∏
t
GσI(rI(t))⋅GσV(rV(t))⋅GσM(rM(t))⋅
det J(F)⋅δ(I(t)−rI(t)−{V*FV→I}(t)−{M*FM→I}(t))⋅
δ(V(t)−rV(t)−{M*FM→V}(t)−{I*FI→V}(t))⋅
δ(M(t)−rM(t)−{I*FI→M}(t)−{V*FV→M}(t))⋅
=K∏
FA→B∈F
∏
Δt
GσA→B(FA→B(Δt))⋅
∏
t
GσI(I(t)−{V*FV→I}(t)−{M*FM→I}(t))⋅
GσV(V(t)−{M*FM→V}(t)−{I*FI→V}(t))⋅
GσM(M(t)−{V*FV→M}(t)−{I*FI→M}(t))
=Gμ,Σ(F)∼e−1
2{(F−μ)†Σ−1(F−μ)}
r
PF
PF
FA→B
Δt
Pr
0≤t<T
δ
J
I,V,M
δ
J
3T
of 13 22
matrix full of zeros, ones, and (minus the) values of all 6 causal paths . Luckily, this
determinant can be computed analytically:"
#(17)"
where the 2nd equality is due to onset latency constraints (9). At the 3rd equality in (16), the
determinant is gone, prior ’s value is unknown and replaced by constant ; the prior is
constant as are ﬁxed, observed source data. Also, the integrals transfer the causal model
from the functions to the priors of the drivers . As the ﬁnal result contains only Gaussians and a
constant, it must be a simple multivariate Gaussian distribution with mean and
covariance matrix as in the ﬁnal row."
#For the bicausal IVM and VM models, is also 1 and a similar multivariate Gaussian is
obtained. Mean and variance of ’s single components or linear combinations such as can
be obtained analytically. For example, one ﬁnds for the bicausal VM model a socalled least
squares/minimumnorm solution (with for clarity):"
"
#(18)"
where is the identity matrix, is matrix transpose, and ± separates mean and standard
deviation. If the prior variance on is completely relaxed ( ), one gets the so
called leastsquares solution:"
#(19)"
3T
FA→B
det J(F) = {1 −FM→V(0)FV→M(0) −FI→V(0)FV→I(0) −FI→M(0)FM→I(0)
−FI→M(0)FM→V(0)FV→I(0) −FI→V(0)FV→M(0)FM→I(0) }T
= 1
P−1
I,V,M
K
I,V,M
δ
r
Gμ,Σ(F)
μ
Σ
det J(F)
F
VFR
ΔT= 3
V=
V(2) V(1) V(0) 0 0
V(3) V(2) V(1) V(0) 0
V(4) V(3) V(2) V(1) V(0)
.
.
.
V(T−2) V(T−3) V(T−4) V(T−5) V(T−6)
V(T−1) V(T−2) V(T−3) V(T−4) V(T−5)
0V(T−1) V(T−2) V(T−3) V(T−4)
0 0 V(T−1) V(T−2) V(T−3)
,O=
0
0
1
1
1
Σ= (σ−2
MV†V+σ−2
V↔MI)−1
μ=Σσ−2
MV†M
FV↔M=μ±diag(Σ)1
2
VFR =O†μ±(O†ΣO)1
2
I
†
FV↔M
σV↔M=∞
μ= (V†V)−1V†M
Σ= (V†V)−1σ2
M
of 14 22
Bayesian approaches are ideal to obtain probabilistic answers to hard, binary questions such as
whether “vaccination has a net mortal eﬀect in the ﬁrst few weeks” (hypothesis ), or not
( ). With mean and variance from (18), one ﬁnds:"
#(20)"
This is a true probability, not a socalled likelihood ratio between two hypotheses: As the set of
hypotheses is complete in all possible outcomes, there are no other (unknown)
competing hypotheses possible."
#Any prior belief in any of the two hypotheses has already been accounted for in the calculation
of . If one has a strong prior belief in , one should incorporate this by a negative
mean expectation of in the ﬁrst few weeks, which is counter to commonly accepted
knowledge that protective eﬀects of vaccines do not occur in the ﬁrst few weeks. Logically, one
cannot ﬁrst accept the computation of , and subsequently reject (20) on the basis that it
does not incorporate an additional explicit prior biasing towards reﬂecting one’s beliefs."
3 Results
I apply the bicausal model to booster campaigns during 2022 in The Netherlands (population
~18M). Infection, vaccination and mortality data are unstratiﬁed, weekly, total absolute numbers
from public national sources [Src]. With PCR+ and sewer viralparticlebased infection data
available, the IVM model is used to determine the usability of sewer data and relevance of
infection confounders, all compared to the relative performance of the infectionless VM model.
With the VM model, a few additional experiments are performed with diﬀerent shortterm ﬁlters
and periods, mortality age groups, and relaxation of prior variances on causal interactions ."
#Finally, I apply the bicausal VM model to 30 European countries (~530M people) with data from
aggregation sources [Eur, Owi] in 2022 during weeks 1043 (limited by data availability)."
3.1 Sewer data for infections in the IVM model
Sewer viral particle data are publicly available for The Netherlands, see Figure 3. In weeks 120 of
2022, PCR tests were performed in higher volumes; I use this period to compute a scale constant
of PCR+ tests per sewer viral particle, and convert the more objective sewer data over entire 2022
to PCRequivalent infections ."
#Figure 8 shows results of the bicausal IVM model, with PCR and sewer infection data, weeks
950 during the vaccination campaigns. Although few measurements are signiﬁcant, a few
observations can be made. PCRbased infectiontomortality suggests a peak at ,
matching the expected average time from infection to death. The sewerbased curve peaks just
signiﬁcantly at , suggesting sewerbased measurements lag by a twoweek time delay.
Applying a minustwoweekshift in sewer data to compensate the delay brings the sewerbased
infectiontomortality peak also at ."
#The individual PCRbased vaccinationtomortality measurements of and 5weeknet
result 9±7% after vaccination are just signiﬁcant, and the probability that the vaccine protects
against infection (hypothesis ) is 91%. The original unshifted sewerbased measurements
suggest that vaccination causes infections with a probability 83%. The 2weeks shifted sewer
Hmortal
¯
Hmor ta l
VFR
Pr{Hmortal} = Pr{V FR > 0} = 1
2+1
2erf(μVFR
2σVFR
)
{Hmortal,¯
Hmor ta l}
VFR
¯
Hmor ta l
FV→M
VFR
¯
Hmor ta l
F
I
FI→M(2)
FI→M(0)
FI→M(2)
FV→I
H−
of 15 22
measurements solve this uncomfortable ﬁnding, but bring up a logical, causal issue: the shift
brings the peak towards , infectioninducedvaccinations via fear. This is, however, not
causally possible as the original unshifted sewer data cannot cause fear before being measured.
As can be seen in Figure 3, PCR+ testing was quite low for most of 2022, and its mediareporting
seem unable to have simultaneously produced the same required fear, as is also visible in Figure 8
by with 5weeknetresult 0.53±2.67."
"
Figure 8: Results for bicausal IVM model, infectionmortality and vaccinationmortality interactions,
with PCR+ and sewer measurements, weeks 950 of 2022 in The Netherlands. Black dotted lines
indicate week is assigned to right, biological causal path according to onset latencies. Y
axis has biological path scale. Grey areas"indicate"±1 sigma interval. Pr indicates Bayesian
probability of the biological path to be net positive or negative (hypotheses and ).
FI→V(1)
FI→V
Δt= 0
H+
H−
of 16 22
These results suggest that sewer data should not be backshifted in time, and that the viral
particles in the sewer are caused by vaccination. The possibility that sewer data is measuring
spike (S) particles created directly by vaccinations can be excluded, as there is no overlap
between viral genes used for sewer measurements (N/E) and vaccination (S) [Med]. Recent
research did ﬁnd evidence that infections correlate strongly with vaccinations [Shr]."
#Using , a PCRequivalent ratio of infections/reactivations per vaccination is found as
justnotsigniﬁcant 0.35±0.37, see Figure 8 rightcenter. Figure 9 shows the same result with
: with more than 99% probability, vaccination causes viral particles to increase ( ) in
the ﬁrst three weeks since vaccination. The amount of equivalentPCRinfections per vaccination
is 0.50±0.21 (95%%CI%0.080.92). This number is very high; possibly the equivalent PCR+/sewer
particle scale factor is not well estimated or applicable. An additional explanation is that besides
triggering infections, vaccinations may reactivate latent viral (particle) reservoirs."
"
Figure 9: The causal eﬀect of vaccinations on infections as measured eﬀectively by sewer viral
particles."
3.2 IVM versus VM model
Figure 10 shows and obtained via the IVM model via PCR+, plain and 2weeks
backshifted sewerbased infections, and the VM model without infections, in weeks 950 in The
Netherlands. In all four cases a causal temporal order eﬀect can clearly be seen, with mortality
insigniﬁcant before vaccination and signiﬁcant after. Also in all four cases, equals
0.09±0.03%, that is, vaccineinduced mortality in the same week of vaccination is near 0.1%, with
3sigma conﬁdence. Finally, again in all 4 cases, over 5 weeks is just insigniﬁcant at ca
0.07±0.09%."
#Apparently, infections did not confound mortality and vaccination in The Netherlands in 2022,
in a signiﬁcant way measurable by the IVM model. Based on these results, I conclude that the IVM
model does not oﬀer substantially diﬀerent or better results compared to the simpler VM model
without infection confounders."
#The insigniﬁcance of appears caused by a negative after two weeks and an
increasing sigma when aggregating over weeks. The positivenegativedynamics
of are consistent with vaccination being the last push to mortality for highly vulnerable
people. The probability that vaccination causes net mortality over the entire 5 weeks after
vaccination ( ) remains however ca 75%80% in all cases. The found is lower but order
comparable to that of my prior work [Re2], which found ~0.18% in weeks 934 of 2022, using
agecorrection in vaccinationmortality data, and a suboptimal estimation procedure."
ΔT= 5
ΔT= 3
H+
FV→M
VFR
FV→M(0)
VFR
VFR
FV→M
FV→M
ΔT= 5
FV→M
H+
VFR
of 17 22
"
Figure 10: Results for and with bicausal IVM and VM models, with and without
infection confounder, weeks 950, The Netherlands."
3.3 Shortterm ﬁlter, period, relaxation of prior, age groups
Table 2 shows using the VM model, for diﬀerent shortterm periods , ﬁlters and
relaxation of prior variance . It shows that shorter periods lead to better/lower
result variances, and that varying ﬁlter has marginal inﬂuence. Most importantly, relaxing the
prior from zeromean Gaussian with to a uniform unbiased prior with
has no signiﬁcant inﬂuence."
#Figure 11 illustrates a few results: the signiﬁcant result with without prior, an isolated
central peak in with , and the erratic eﬀect of not using any shortterm ﬁlter.
Figure 12 shows a result for age groups: signiﬁcant is concentrated at ages 65+."
Table 2: and ( ) with bicausal VM model for several diﬀerent shortterm
periods, ﬁlters, and relaxation of prior variance.
FV→M
VFR
VFR
ΔT
W
σV→M=∞
ΔT
W
σV→M= 10−3
σV→M=∞
ΔT= 2
FV→M
ΔT= 16
FV→M
default VM model
0.12±0.04% (99.9%)
0.09±0.05% (97%)
0.07±0.08% (80%)
0.13±0.04% (99.9%)
0.10±0.05% (98%)
0.07±0.09% (79%)
0.14±0.04% (99.9%)
0.11±0.05% (97%)
0.07±0.09% (80%)
0.14±0.07% (97.7%)
0.13±0.10% (89%)
0.06±0.16% (66%)
ΔT= 5
ΔT= 3
ΔT= 2
= [1 +3 3 +1]
W
Relaxed prior
σV→M=∞
= [0.25 +0.5 0.25]
W
VFR
Pr{V FR ≥0}
of 18 22
"
Figure 11: A few results with shortterm periods , and without shortterm ﬁlter.
"
Figure 12: Results with bicausal VM model for several age groups (mortality data agestratiﬁed,
vaccination data is allages). is concentrated at ages 65+."
3.4 Europe
I applied the bicausal VM model on 30 European countries using data from aggregators [Eur,Owi]
in weeks 1043. Countries include Austria, Belgium, Bulgaria, Croatia, Czechia, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and United Kingdom."
#Figure 13 shows results for The Netherlands, with data from the same national source used in
previous sections and the aggregation sources. Clearly, aggregator data has been processed.
This may involve smoothing or small accidental/deliberate data shifts in time, e.g. to align data
sets or optimize visualization for their online services. In this study, however, it negatively aﬀects
the signiﬁcance of measurements."
"
Figure 13: Results with bicausal VM model for The Netherlands, weeks 1043, data from three
diﬀerent sources [Src,Eur,Owi].
Figure 14 shows results for a selection of European countries. Clearly, the individual results lack
signiﬁcance.
ΔT= 2
ΔT= 16
VFR
of 19 22
"
Figure 14: Results for several individual countries, weeks 1043 (data from [Eur], UK data was
available only at [Owi]).
Signiﬁcant results are obtained when data from all 30 countries are combined. Table 3 shows
results for , with/without relaxation of prior expectations. Figure 15 shows a result with
: all are signiﬁcantly diﬀerent from zero, and all are not, evidence for a
signiﬁcant mortality eﬀect caused by vaccination, not involving a confounder. In absence of any
prior expectation, a of 0.35% ±0.10% is obtained according to Table 3 in the ﬁrst 3 weeks."
Table 3: and ( ) of all countries combined, at , per data source, with
and without prior model."
ΔT= 3
ΔT= 5
FV→M
FM→V
VFR
Data source [Eur]
Data source [Owi]
0.26±0.08% (99.9%)
0.01±0.03% (59%)
0.35±0.10% (99.98%)
0.01±0.03% (60%)
Prior model variance
σV→M
10−3
∞
VFR
Pr{V FR ≥0}
ΔT= 3
of 20 22
"
Figure 15: Results for 30 European countries combined, weeks 1043.
4 Conclusions and discussion
This report presents a causal model of infections, vaccinations and mortality (IVM), with main goal
to estimate Vaccine Fatality Ratio on the shortterm of a few weeks. The model has few to
zero prior model parameters, which are unbiased in terms of causal eﬀect direction (from A to B or
vice versa), sign (enforcing or supression, protection or damage), and even strength (strong or
weak). Bayesian probabilities are used to quantify all interactions. Five confounders are explicitly
taken into account, plus all longterm confounding using a ﬁlter that extracts shortterm events
only. A simpeler VM model without infections and only one “bicausal” interaction is shown to
provide essentially the same results, indicating that during the analysis period, infections did not
play a signiﬁcant confounding role. "
#Evidence was found of a causal eﬀect from vaccination to mortality during booster campaigns
in the Netherlands (2022 weeks 950) and Europe (weeks 1043 due to data limtations). A positive
Vaccine Fatality Ratio was found within 23 weeks after vaccination of 0.13%
(0.05%0.21%, 95% CI) for The Netherlands, and 0.35% (0.05%0.55%) for Europe. These s
transcend the of covid substantially [Io2]."
#The high on the shortterm was found to be partially compensated a few weeks later. A
single, partially agestratiﬁed experiment did indicate that vaccineinduced mortality focuses on
the 65+ age group. This supports the mechanism of very frail elderly whose death is accelerated
12 weeks due to vaccination, associated with a low loss of QALYs (Quality Adjusted Life Years). If
present, this mechanism is only partial; over 5 weeks still has 6880% probability of being
net positive."
#Additionally, experiments using the IVM model with sewerviralparticle data in The Netherlands
suggested vaccination induces covidinfections and/or reactivates latent viral reservoirs, at a rate
scaled to equivalentPCRinfections per vaccination of 0.50 (0.080.92). Recent research reported
that infections strongly correlate with vaccinations [Shr]."
#This study was limited in many ways. The available source data was not casebased but
national weekly overall rates. The shortterm ﬁlter approach is insensitive to all longterm eﬀects.
Signiﬁcance levels were very low for many measurements. The method used is very sensitive for
preprocessing that data aggregators may apply, e.g. smoothing or small accidental/deliberate
data shifts in time, e.g. to align data sets or optimize visualization. Infection data was of low
reliability, by nature. Finally, my method has all kinds of ﬂaws unknown to me, to all [Bre]. Despite
all this:"
#The evidence of a causal relationship from vaccination to infections and mortality is a very
strong alarm signal to stop the current mass vaccination programs."
VFR
VFR
VFR
IFR
VFR
VFR
of 21 22
References
[Ben]#C.S. Benn and F. SchaltzBuchholzer, “Randomised Clinical Trials of COVID19 Vaccines:
Do AdenovirusVector Vaccines Have Beneﬁcial NonSpeciﬁc Eﬀects?”, The Lancet
preprint, papers.ssrn.com/sol3/papers.cfm?abstract_id=4072489"
[Bre]#N. Breznau et al., “Observing Many Researchers Using the Same Data and Hypothesis
Reveals a Hidden Universe of Uncertainty”, doi.org/10.31222/osf.io/cd5j9"
[Eur]#Source data for European vaccinations and mortality, europe.eu (ECDC and EuroStat)"
[Gia]#E.A.L.Gianicolo et al., “Methods for Evaluating Causality in Observational Studies”,
ncbi.nlm.nih.gov/pmc/articles/PMC7081045/"
[Io1]#J.P.A. Ioannidis, “Exposurewide epidemiology: revisiting Bradford Hill”, doi.org/10.1002/
sim.6825"
[Io2]#J.P.A. Ioannidis, “Infection fatality rate of COVID19 inferred from seroprevalence data”,
dx.doi.org/10.2471/BLT.20.265892"
[Mar]#I.C. Marschner, “Estimating agespeciﬁc COVID19 fatality risk and time to death by
comparing population diagnosis and death patterns: Australian data”,
bmcmedresmethodol.biomedcentral.com/articles/10.1186/s1287402101314w"
[Med]#G. Medema et al., “Presence of SARSCoronavirus2 RNA in Sewage and Correlation
with Reported COVID19 Prevalence in the Early Stage of the Epidemic in The
Netherlands”, ACS Publications, pubs.acs.org/doi/10.1021/acs.estlett.0c00357"
[Mee]#R. Meester et al., “COVID19 vaccinations and mortality  a Bayesian analysis”,
dx.doi.org/10.13140/RG.2.2.34443.21285, and “Bayesian analysis of shortterm
vaccination eﬀects”, dx.doi.org/10.13140/RG.2.2.21276.16001"
[Nor]#Norwegian review, “Covid19: PﬁzerBioNTech vaccine is likely responsible for deaths of
some elderly patients”, doi.org/10.1136/bmj.n1372"
[Owi]#Source data for European vaccinations and mortality, ourworldindata.org"
[Re1]#A. Redert, “Covid19 vaccinations and allcause mortality  a longterm diﬀerential
analysis among municipalities”, dx.doi.org/10.13140/RG.2.2.33994.85447"
[Re2]#A. Redert, “Shortterm Vaccine Fatality Ratio of booster and 4th dose in The
Netherlands”, dx.doi.org/10.13140/RG.2.2.29841.30568"
[Sch]#T. Schetters, “Prof. dr. Theo Schetters: analyse van oversterfte is reden tot zorg over
veiligheid mRNAvaccins”, artsencollectief.nl/profdrtheoschettersanalysevan
oversterfteisredentotzorgoverveiligheidmrnavaccins/"
[Shi]#M. Shimonovich et al., “Assessing causality in epidemiology: revisiting Bradford Hill to
incorporate developments in causal thinking”, doi.org/10.1007/s10654020007037"
[Shr]#N.K. Shrestha et al., “Eﬀectiveness of the coronavirus disease 2019 (covid19) bivalent
vaccine”, doi.org/10.1101/2022.12.17.22283625"
[Src]#Source data for infections (PCR+ and sewerviral particles), vaccinations and mortality in
The Netherlands, cbs.nl (Central Bureau for Statistics) and rivm.nl (Dutch national
institute for health and environment)"
[Sun]#C.L.F. Sun et al, “Increased emergency cardiovascular events among under40
population in Israel during vaccine rollout and third COVID19 wave”, www.nature.com/
articles/s4159802210928z"
[Wik]#Wikipedia, “Causality”, en.wikipedia.org/wiki/Causality, accessed Jan 2023"
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