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Causal effect of covid vaccination on mortality in Europe


Abstract and Figures

This report investigates short-term causal vaccine-mortality interactions during booster campaigns in 2022 in 30 European countries (population ~530M). An infection-vaccination-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 mortality-caused fear incentivizing vaccinations and four related to covid infections, and generically for all long-term confounding. Bayesian probabilities quantify all interactions, and from observed weekly administered vaccine doses and all-cause mortality, mortality on short-term 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, sewer-viral-particle experiments suggested vaccination induces covid-infections 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.
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Causal eect of covid vaccination on mortality in Europe"
André Redert, PhD"
Independent researcher"
Rodotti, Netherlands, 24 February 2023"
This report investigates short-term causal vaccine-mortality interactions during booster
campaigns in 2022 in 30 European countries (population ~530M). An infection-vaccination-
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
mortality-caused fear incentivizing vaccinations and four related to covid infections, and
generically for all long-term confounding. Bayesian probabilities quantify all interactions, and from
observed weekly administered vaccine doses and all-cause mortality, mortality on short-term
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, sewer-viral-particle
experiments suggested vaccination induces covid-infections and/or reactivates latent viral
#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, or consider one of
the apps at and"
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 long-term
[Re1], and short-term [Mee,Sch,Re2]. Figure 1 illustrates this correlation for weekly 4th/5th
vaccination campaign doses and all-cause mortality. Detailed case-based 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 short-term Vaccine Fatality
Ratio (VFR) on the basis of weekly administered vaccine doses and all-cause mortality; two
integer, countable parameters that do not suer 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. Dierent
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 infection-based and generic confounders in a combined infection-vaccine-mortality
(IVM) model, and the Bayesian framework to handle randomness and all statistic parameter
estimation. The extraction of short-term events introduced in [Re2] to remove eects and
confounding on long-term, see Figure 2, will be reused."
Figure 2: Same data as in Figure 1, short-term 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, test-willingness/policy-
dependence, arbitrary CT-values, etc), and sewer data is more objective but less widely available,
the relative performance of a simplified vaccine-mortality (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 high-detailed steps. The final result,
however, is simple and contains a bare minimum, or even zero, model parameters."
2.1 Causality
The well-known “Correlation does not mean causation” is a vague statement that may lead to the
false believe that all correlation is insucient 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 well-known 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 ."
#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 short-term-filtered observations to remove all long-term confounding."
#In controlled experiments, one can make event A occur at will, which is very eective 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 planet-star eclipses visible from earth. A sucient
number of confounders will swamp any causal eect 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
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includes short-term 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 eects that act on short term and is blind to
longer-term eects."
#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 Infection-Vaccination-Mortality model
Figure 4 shows my causal infection-vaccination-mortality (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 eect of natural immunity."
Figure 4: Causal infection-vaccination-mortality (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 vaccination-mortality (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. Vaccine-induced 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 Vaccination-Mortality 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 mass-media with main purpose to
induce psychological fear. Two dierent 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 sewer-to-PCR
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
vaccine-mortality (VM) model, as was eectively used in my prior work [Re2]. The VM model does
not suer from unreliable infection data, but cannot compensate explicitly for infection-based
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. test-delays 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
account for immunity build-up. Delays are less expected for raw numbers of objectively-dated
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 eects may
migrate between forward and reverse causal paths in the model, see Figure 5 left. For example,
due to a one-week-delay in data, a several-weeks-enduring causal eect 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 oppositely-directed causal paths into a single
bidirectional (“bicausal”) path. All data is simulated for illustration purposes. The green zero means
a zero eect value.
The clarity of the word “vaccination” has eroded substantially in recent years.
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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 well-known 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 eect sizes of drivers and causal paths.
All eect 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 vaccine-induced
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 eect 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%. Vaccine-Eectivity against infection (VE-I) and mortality (VE-M)
may start at ~100% but negative VE-I (positive damage) is known to possibly occur both in the
the first weeks during build-up of immunity, and after several months when immunity wears o.
The size of vaccine-caused immunity is not plain Vaccine-Eectivity against mortality (VE-M), but
scaled by IFR as the paths in my model relate to all-cause 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. Vaccine-caused eects have a fast, biological, single-persion underlying
mechanism, while mortality-induced fear has a slower, psychological, inter-personal 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 build-up following only
in the next 2-4 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 mass-media 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 eect 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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Onset latency
Time scale
Eect size (10-order)
Viral infection waves
100% population/year
Vaccination campaigns
100% population/year
Seasonal mortality baseline
1% population/year
Random fluctations in each
as observed from data
* zero, limited by source data resolution
Causal path
Onset latency
Time scale
Eect size (10-order)
Depletion M to I
>> week
Negligible < 0.1%
Illness I to M (IFR)
week or more
2 weeks
Damage V to M (VFR)
Immunity V to M (~VE-M)
2-4 weeks
Damage V to I (~VE-I)
2-4 weeks
Immunity V to I (~VE-I)
2-4 weeks
Fear I to V
week or more
Fear M to V
week or more
IFR: Infection Fatality Ratio, VFR: Vaccine Fatality Ratio"
VE-I: Vaccine Eectivity against infection, VE-M: against mortality"
~ the modeled eects are proportional to VE, and involve additional products with IFR or driver eect size
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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 eect may be real and causal. Exactly such a signal was found in
[Re2]. Of course, it is possible that an unidentifed, short-term 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, long-term causal form, and reduce it subsequently
to the short-term bicausal model. To start o:"
# #Time, integer week number, from "
#Total number of analysed weeks in 2022 (typically for weeks 9-50)"
#Weekly number of infections, administered vaccine doses, and all-cause mortality"
#Long-term mortality baseline, captures slow variations over months/years"
#Short-term weekly variations, uncorrelated zero-mean 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 short-term causal eect (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, other-cause waves (covid, NPIs). They also capture confounders
acting between them, on the long-term, 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 zero-mean
I(t) = bI(t) + rI(t) + {V*FVI} (t) + {MΔ*FMI}(t)
V(t) = bV(t) + rV(t) + {I*FIV} (t) + {MΔ*FMV}(t)
M(t) = bM(t) + rM(t) + {I*FIM}(t) + {V*FVM}(t)
MΔ(t) = M(t)Mex pectat ion(t)
T= 42
0 Δt<ΔT
ΔT= 2..5
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and uncorrelated over time and with respect to eachother, and non-stationary with variance
changing slowly over the longer-term 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
eects, 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
eectivity always and only against all-cause mortality [Ben]; ideally infections would represent all
pathogens, or even other mortal threats . Altogether, modeling of and may thus be
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 above-expectation 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 eects of covid, NPIs,
whether calculated by a national institute or emerged within the minds of individuals, whether their
eect 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 Short-term filter
As in [Re2], I apply a linear temporal filter on source data to remove all long-term
events and extract short-term events in (with a hat), see also Figure 6:"
Applied to (1), this results in:"
Mnewer ex pectat ion Molder ex pectat ion
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*FMI} (t) + {
V*FVI} (t)
V(t) =
rV(t) + {
M*FMV}(t) + {
I*FIV} (t)
M(t) =
rM(t) + {
I*FIM} (t) + {
Mass-media have suggested vaccination protects against car crashes.
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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 unaected by the short-term filter, and subsequently so
is in (2). The short-time versions of source data are zero-mean random
variables, illustrated by Figure 2. All long-term baselines and mortality expectation
have disappeared, also causing excess mortality in (1) to be replaced by plain
short-term filtered mortality in (4). The filtered versions of drivers have slightly
reduced variance compared to the unfiltered signals, and are still non-stationary."
#All of this is irrespective of the specific choice of filter , as long as it extracts short-term
events as in Figure 6. The filter choice (3) in this report is given by ,
where is a Dirac delta function, is a zero-mean, -deviation Gaussian, one of the smoothest
filters possible, and is chosen to ensure that is zero-mean (sum coecients 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 short-term measurements
towards any of the causal paths, or towards any direction within any path; the filter may even be
time-assymetric, e.g. a 3rd derivative filter [-1 +3 -3 +1], as possible time delays due to the filter
do not aect measurements of . The filter also does not bias measurements by sign. In
combination with zero-mean 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 short-term-filtered."
2.9 Short-term causal IVM model, prior variances and constraints
The short-term causal IVM model (4) is here denoted without hats:"
[0.1 0.25 + 0.7 0.25 0.1]
I(t) = rI(t) + {M*FMI} (t) + {V*FVI} (t)
V(t) = rV(t) + {M*FMV}(t) + {I*FIV} (t)
M(t) = rM(t) + {I*FIM} (t) + {V*FVM}(t)
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I model all and components of drivers and causal interactions as
independent, normal-distributed (Gaussian) stationary random variables. The original non-
stationarity of drivers is remodeled by a slightly higher overall variance, namely that of
the observed :"
For the variances one finds using the eect sizes in Table 1:"
These values are rough orders, which is accurate enough as they are only used as so-called
“priors” to slightly constrain the model; they bias measurements of to zero in the presence
of insucient 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
Using Table 1 one finds that fear and depletion causal paths have onset latencies beyond a week:"
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
suce 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 aects observations and causal functions
. The underlying (inaccessible) time-continuous causal mechanism (with upper c) translates
to week resolution by a specific triangular-shaped time-symmetric aggregation filter :"
with continuous (real-valued) time in weeks. The triangular aggregation eect happens always,
no matter how fine the time resolution used. The week-resolution used in this report means that
any event pair separated by 3.5 days or more, is thus captured more by than ."
σVM= 103σMI= 103σIV= 1
σMV= 102σIM= 103σVI= 1
FIV(0) = FMV(0) = FMI(0) = 0
Δt= 0
F(Δt) = {Fc*Λ}(Δt) = Δtc
Fc(Δtc)Λ(Δt Δtc)dΔtc
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Figure 7: Resolution eect 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 aect , 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):"
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 dierent mathematical
representation. Under expected circumstances where causal path eects are relatively small
compared to the drivers, the dierence 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:"
Variances (7) combine via (11) into:"
From here, the simplified bicausal VM model without infections is:"
FAB(Δt) = FAB(Δt) + σ2
FBA(−Δt) , ΔT<Δt<ΔT
Δt= 0
M(t) = rM(t) + {V*FVM}(t) + {I*FIM}(t)
I(t) = rI(t) + {V*FVI} (t)
σVM= 103σIM= 103σVI= 1
M(t) = rM(t) + {V*FVM}(t)
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with only one prior from (13). In [Re2], of this bicausal VM model was estimated by a
Pearson correlation trend factor:"
This estimate was sub-optimal; 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 :"
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 4-6: causal IVM
model (5) enters via three Dirac functions plus so-called determinant of Jacobian that
describes the multiple occurences of in the arguments. #The Jacobian is a huge -by-
FVM(Δt)[Re2] COV(V(t), M(t+Δt))
VA R(V(t))
r= {rI,rV,rM}
det J(F)δ(I(t)rI(t){V*FVI}(t){M*FMI}(t))
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matrix full of zeros, ones, and (minus the) values of all 6 causal paths . Luckily, this
determinant can be computed analytically:"
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 so-called least-
squares/minimum-norm solution (with for clarity):"
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 least-squares solution:"
det J(F) = {1 FMV(0)FVM(0) FIV(0)FVI(0) FIM(0)FMI(0)
FIM(0)FMV(0)FVI(0) FIV(0)FVM(0)FMI(0) }T
= 1
det J(F)
ΔT= 3
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(T2) V(T3) V(T4) V(T5) V(T6)
V(T1) V(T2) V(T3) V(T4) V(T5)
0V(T1) V(T2) V(T3) V(T4)
0 0 V(T1) V(T2) V(T3)
Σ= (σ2
VFR =Oμ±(OΣO)1
μ= (VV)1VM
Σ= (VV)1σ2
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Bayesian approaches are ideal to obtain probabilistic answers to hard, binary questions such as
whether “vaccination has a net mortal eect in the first few weeks” (hypothesis ), or not
( ). With mean and variance from (18), one finds:"
This is a true probability, not a so-called 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 eects 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 viral-particle-based 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 infection-less VM model.
With the VM model, a few additional experiments are performed with dierent short-term 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 10-43 (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 1-20 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 PCR-equivalent infections ."
#Figure 8 shows results of the bicausal IVM model, with PCR and sewer infection data, weeks
9-50 during the vaccination campaigns. Although few measurements are significant, a few
observations can be made. PCR-based infection-to-mortality suggests a peak at ,
matching the expected average time from infection to death. The sewer-based curve peaks just
significantly at , suggesting sewer-based measurements lag by a two-week time delay.
Applying a minus-two-week-shift in sewer data to compensate the delay brings the sewer-based
infection-to-mortality peak also at ."
#The individual PCR-based vaccination-to-mortality measurements of and 5-week-net-
result -9±7% after vaccination are just significant, and the probability that the vaccine protects
against infection (hypothesis ) is 91%. The original unshifted sewer-based measurements
suggest that vaccination causes infections with a probability 83%. The 2-weeks shifted sewer
Hmor ta l
Pr{Hmortal} = Pr{V FR > 0} = 1
Hmor ta l}
Hmor ta l
Hmor ta l
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measurements solve this uncomfortable finding, but bring up a logical, causal issue: the shift
brings the peak towards , infection-induced-vaccinations 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 media-reporting
seem unable to have simultaneously produced the same required fear, as is also visible in Figure 8
by with 5-week-net-result -0.53±2.67."
Figure 8: Results for bicausal IVM model, infection-mortality and vaccination-mortality interactions,
with PCR+ and sewer measurements, weeks 9-50 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 ).
Δt= 0
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These results suggest that sewer data should not be back-shifted 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 PCR-equivalent ratio of infections/reactivations per vaccination is found as
just-not-significant 0.35±0.37, see Figure 8 right-center. 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 equivalent-PCR-infections per vaccination
is 0.50±0.21 (95%%CI%0.08-0.92). 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 eect of vaccinations on infections as measured eectively by sewer viral
3.2 IVM versus VM model
Figure 10 shows and obtained via the IVM model via PCR+, plain and 2-weeks-
backshifted sewer-based infections, and the VM model without infections, in weeks 9-50 in The
Netherlands. In all four cases a causal temporal order eect can clearly be seen, with mortality
insignificant before vaccination and significant after. Also in all four cases, equals
0.09±0.03%, that is, vaccine-induced mortality in the same week of vaccination is near 0.1%, with
3-sigma confidence. Finally, again in all 4 cases, over 5 weeks is just insignificant at ca
#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 oer substantially dierent 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 positive-negative-dynamics
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 9-34 of 2022, using
age-correction in vaccination-mortality data, and a suboptimal estimation procedure."
ΔT= 5
ΔT= 3
ΔT= 5
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Figure 10: Results for and with bicausal IVM and VM models, with and without
infection confounder, weeks 9-50, The Netherlands."
3.3 Short-term filter, period, relaxation of prior, age groups
Table 2 shows using the VM model, for dierent short-term 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 zero-mean 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 eect of not using any short-term filter.
Figure 12 shows a result for age groups: significant is concentrated at ages 65+."
Table 2: and ( ) with bicausal VM model for several dierent short-term
periods, filters, and relaxation of prior variance.
σVM= 103
ΔT= 2
ΔT= 16
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]
Relaxed prior
= [-0.25 +0.5 -0.25]
Pr{V FR 0}
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Figure 11: A few results with short-term periods , and without short-term filter.
Figure 12: Results with bicausal VM model for several age groups (mortality data age-stratified,
vaccination data is all-ages). 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 10-43. 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 aects
the significance of measurements."
Figure 13: Results with bicausal VM model for The Netherlands, weeks 10-43, data from three
dierent sources [Src,Eur,Owi].
Figure 14 shows results for a selection of European countries. Clearly, the individual results lack
ΔT= 2
ΔT= 16
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Figure 14: Results for several individual countries, weeks 10-43 (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 dierent from zero, and all are not, evidence for a
significant mortality eect 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
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
Pr{V FR 0}
ΔT= 3
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Figure 15: Results for 30 European countries combined, weeks 10-43.
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 short-term of a few weeks. The model has few to
zero prior model parameters, which are unbiased in terms of causal eect 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 long-term confounding using a filter that extracts short-term 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 eect from vaccination to mortality during booster campaigns
in the Netherlands (2022 weeks 9-50) and Europe (weeks 10-43 due to data limtations). A positive
Vaccine Fatality Ratio was found within 2-3 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 short-term was found to be partially compensated a few weeks later. A
single, partially age-stratified experiment did indicate that vaccine-induced mortality focuses on
the 65+ age group. This supports the mechanism of very frail elderly whose death is accelerated
1-2 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 68-80% probability of being
net positive."
#Additionally, experiments using the IVM model with sewer-viral-particle data in The Netherlands
suggested vaccination induces covid-infections and/or reactivates latent viral reservoirs, at a rate
scaled to equivalent-PCR-infections per vaccination of 0.50 (0.08-0.92). Recent research reported
that infections strongly correlate with vaccinations [Shr]."
#This study was limited in many ways. The available source data was not case-based but
national weekly overall rates. The short-term filter approach is insensitive to all long-term eects.
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."
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[Ben]#C.S. Benn and F. Schaltz-Buchholzer, “Randomised Clinical Trials of COVID-19 Vaccines:
Do Adenovirus-Vector Vaccines Have Beneficial Non-Specific Eects?”, The Lancet
[Bre]#N. Breznau et al., “Observing Many Researchers Using the Same Data and Hypothesis
Reveals a Hidden Universe of Uncertainty”,"
[Eur]#Source data for European vaccinations and mortality, (ECDC and EuroStat)"
[Gia]#E.A.L.Gianicolo et al., “Methods for Evaluating Causality in Observational Studies”,"
[Io1]#J.P.A. Ioannidis, “Exposure-wide epidemiology: revisiting Bradford Hill”,
[Io2]#J.P.A. Ioannidis, “Infection fatality rate of COVID-19 inferred from seroprevalence data”,"
[Mar]#I.C. Marschner, “Estimating age-specific COVID-19 fatality risk and time to death by
comparing population diagnosis and death patterns: Australian data”,"
[Med]#G. Medema et al., “Presence of SARS-Coronavirus-2 RNA in Sewage and Correlation
with Reported COVID-19 Prevalence in the Early Stage of the Epidemic in The
Netherlands”, ACS Publications,"
[Mee]#R. Meester et al., “COVID-19 vaccinations and mortality - a Bayesian analysis”,, and “Bayesian analysis of short-term
vaccination eects”,"
[Nor]#Norwegian review, “Covid-19: Pfizer-BioNTech vaccine is likely responsible for deaths of
some elderly patients”,"
[Owi]#Source data for European vaccinations and mortality,"
[Re1]#A. Redert, “Covid-19 vaccinations and all-cause mortality - a long-term dierential
analysis among municipalities”,"
[Re2]#A. Redert, “Short-term Vaccine Fatality Ratio of booster and 4th dose in The
[Sch]#T. Schetters, “Prof. dr. Theo Schetters: analyse van oversterfte is reden tot zorg over
veiligheid mRNA-vaccins”,
[Shi]#M. Shimonovich et al., “Assessing causality in epidemiology: revisiting Bradford Hill to
incorporate developments in causal thinking”,"
[Shr]#N.K. Shrestha et al., “Eectiveness of the coronavirus disease 2019 (covid-19) bivalent
[Src]#Source data for infections (PCR+ and sewer-viral particles), vaccinations and mortality in
The Netherlands, (Central Bureau for Statistics) and (Dutch national
institute for health and environment)"
[Sun]#C.L.F. Sun et al, “Increased emergency cardiovascular events among under-40
population in Israel during vaccine rollout and third COVID-19 wave”,
[Wik]#Wikipedia, “Causality”,, accessed Jan 2023"
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... This evidence was assumed universally valid. Later research [26,27] including 2022 data from the second period (see Figure 1) effectively exposed some of the lagged effects of the injections. Their findings contradict those of the earlier published papers and would likely be rejected for journal publication because they do not suit the official narrative. ...
Full-text available
Background: Conflicting findings in correlation studies between COVID-19 injections and excess deaths have been published. Negative correlations with 2021 data appear to justify the official claim that COVID-19 injections reduce illness and death and therefore should be prioritized for vulnerable elderly (over-75s) Australians. This claim needs to be reviewed including 2022 data. Method: Simpson's Paradox is illustrated to explain how the negative correlations, supporting injection effectiveness can come from 2021 data, while positive correlations, suggesting injection ineffectiveness, have come from inclusion of 2022 data. Excess deaths of Australian elderly in the COVID pandemic are analysed in detail for their statistical significance. Results: Negative correlations from 2021 data are refuted in this paper as false causality, because the results have insufficient temporal separation between cause and effect. Strong positive correlation (69 to 74 percent) in Australian data is confirmed when the effects of excess mortality are lagged optimally by 21 weeks after COVID-19 injections [1]. A strong statistical signal (2.5 standard deviations) is shown in this paper in the mortality of elderly Australians, who suffered the greatest relative harm from the injections, even when adjusted for age-dependent high expected mortality. Conclusions: Earlier epidemiological evidence that COVID injections reduce illness and death is now methodologically invalidated, and the claim that the injections are beneficial for the vulnerable is refuted. The injections explain the mystery of significant numbers of non-COVID excess deaths. The Australian pandemic is shown to be iatrogenic particularly for the elderly, who have suffered disproportionate harm. Deliberately ignoring this clear evidence is tantamount to iatrogenic geronticide.
Full-text available
Nyström and Hammarström (2022) found 7 segments in the bio-active SARS-CoV-2 spike protein that can produce abnormal proteinaceous (fibrinaloid) clots according to the Waltz algorithm. In vitro results confirmed the Waltz predictions. If the spike coding sequence was captured in the BNT162b2, Moderna, and other injectables, as claimed by the manufacturers, the clot producing segments are present in them too. Mainstream medical publications claim that SARS-CoV-2 infection can cause abnormal clotting, especially in “long COVID”. Telling evidence from Medicare data shows a decreasing life expectancy with each dose of COVID-19 “vaccine” — 1 dose is worse than 0, and 2 worse than 1, etc. In Connecticut, 26,091 Medicare participants who died before December 31, 2022, but never took a COVID injection, on the average, survived 428 days after the middle of the pandemic period (July 27, 2020). By then nearly all of them must have been exposed to and/or infected by some SARS-CoV-2 variant — hence, the CDC urging to take the “vaccines”. By contrast, 108,156 Medicare patients across the US who died before January 1, 2023, after just 1 dose of COVID-19 “vaccine”, survived only 308 days — a loss of 119.9 days on the average. Connecticut participants, 23,248 of them, who received 2 to 5 doses, on the average, lost an additional 62 days of life-expectancy with each booster. It follows that 5 boosters times 62 days reduces the average remaining 308 days left-to-live after dose 1 by 310 days. So, nearly all the Medicare participants will have been dead for 2 days by booster 4 (dose 5). The upshot is that 5 doses, on the average, will kill all the Medicare participants who accept the advice of the CDC.[1] For 157,495 of the 65 and older Medicare population studied here — people supposedly most apt to benefit from COVID-19 injectables — days-left-to-live shrinks by 74 days, on the average, with each dose. It is also likely that the COVID-19 injectables are partly, maybe wholly, responsible for the unnatural clots found by treating physicians, pathologists, and embalmers in living and dead recipients of the experimental injectables. It is certain is that the injectables are increasing all-cause mortality across the globe. [1] In the dataset from Connecticut, only 7 of 57,261 Medicare participants (7/57261 = 0.000122), or about 1.22 persons in 10,000 survived 5 doses during the experimental pandemic in order to take a 6th dose. Those who did so died, on the average, in 34 days. Only 1 participant survived 6 doses to receive a 7th and died within 69 days at the age of 68.
Full-text available
Background. The purpose of this study was to evaluate whether a bivalent COVID-19 vaccine protects against COVID-19. Methods. Employees of Cleveland Clinic in employment on the day the bivalent COVID-19 vaccine first became available to employees, were included. The cumulative incidence of COVID-19 was examined over the following weeks. Protection provided by vaccination (analyzed as a time-dependent covariate) was evaluated using Cox proportional hazards regression. The analysis was adjusted for the pandemic phase when the last prior COVID-19 episode occurred, and the number of prior vaccine doses received. Results. Among 51011 employees, 20689 (41%) had had a previous documented episode of COVID-19, and 42064 (83%) had received at least two doses of a COVID-19 vaccine. COVID-19 occurred in 2452 (5%) during the study. Risk of COVID-19 increased with time since the most recent prior COVID-19 episode and with the number of vaccine doses previously received. In multivariable analysis, the bivalent vaccinated state was independently associated with lower risk of COVID-19 (HR, .70; 95% C.I., .61-.80), leading to an estimated vaccine effectiveness (VE) of 30% (95% CI, 20-39%). Compared to last exposure to SARS-CoV-2 within 90 days, last exposure 6-9 months previously was associated with twice the risk of COVID-19, and last exposure 9-12 months previously with 3.5 times the risk. Conclusions. The bivalent COVID-19 vaccine given to working-aged adults afforded modest protection overall against COVID-19, while the virus strains dominant in the community were those represented in the vaccine.
Full-text available
This report proposes a new and simple method to measure vaccination-mortality correlation, test for causality, and if passed, obtain Vaccine Fatality Ratio (VFR), in the short-term of 0-4 weeks after vaccination. Only data of weekly administered number of doses and weekly all-cause-deaths are required, without reference to e.g. mortality prognoses, covid-labeled deaths or excess mortality. This report presents evidence of a short-term causal relation from 4th-dose covid-vaccination to mortality in The Netherlands, with a VFR of 0.18% corresponding to ca. 4400 vaccine-related deaths, in the order of magnitudes of covid IFR and observed excess mortality.
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We analyse the relation between covid-19 vaccinations and all-cause-mortality in N=340 Dutch municipalities (17.3M people, ~99% of population), during the entire pandemic period. We do not use covid-19-attributed mortality, mortality predictions and excess mortality, thereby bypassing the ambiguities of case-identification and mortality-modeling. Municipal demographics such as age, culture and population density are strong confounders of mortality and vaccine-uptake. We account for these by normalizing results to prepandemic year 2019, where covid was absent but demographics were highly representative for later years. Normalized to 2019, we found no correlation between municipal mortality in 2020 with vaccination uptake in 2021, which shows the effectiveness of our confounder accounting. We could not observe a mortality-reducing effect of vaccination in Dutch municipalities after vaccination and booster campaigns. We did find a 4-sigma-significant mortality-enhancing effect during the two periods of high unexplained excess mortality. Our results add to other recent findings of zero mRna-vaccine effectiveness on all-cause mortality, calling for more research on this topic.
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Cardiovascular adverse conditions are caused by coronavirus disease 2019 (COVID-19) infections and reported as side-effects of the COVID-19 vaccines. Enriching current vaccine safety surveillance systems with additional data sources may improve the understanding of COVID-19 vaccine safety. Using a unique dataset from Israel National Emergency Medical Services (EMS) from 2019 to 2021, the study aims to evaluate the association between the volume of cardiac arrest and acute coronary syndrome EMS calls in the 16–39-year-old population with potential factors including COVID-19 infection and vaccination rates. An increase of over 25% was detected in both call types during January–May 2021, compared with the years 2019–2020. Using Negative Binomial regression models, the weekly emergency call counts were significantly associated with the rates of 1st and 2nd vaccine doses administered to this age group but were not with COVID-19 infection rates. While not establishing causal relationships, the findings raise concerns regarding vaccine-induced undetected severe cardiovascular side-effects and underscore the already established causal relationship between vaccines and myocarditis, a frequent cause of unexpected cardiac arrest in young individuals. Surveillance of potential vaccine side-effects and COVID-19 outcomes should incorporate EMS and other health data to identify public health trends (e.g., increased in EMS calls), and promptly investigate potential underlying causes.
Full-text available
Findings from 162 researchers in 73 teams testing the same hypothesis with the same data reveal a universe of unique analytical possibilities leading to a broad range of results and conclusions. Surprisingly, the outcome variance mostly cannot be explained by variations in researchers’ modeling decisions or prior beliefs. Each of the 1,261 test models submitted by the teams was ultimately a unique combination of data-analytical steps. Because the noise generated in this crowdsourced research mostly cannot be explained using myriad meta-analytic methods, we conclude that idiosyncratic researcher variability is a threat to the reliability of scientific findings. This highlights the complexity and ambiguity inherent in the scientific data analysis process that needs to be taken into account in future efforts to assess and improve the credibility of scientific work.
Full-text available
Objective: To estimate the infection fatality rate of coronavirus disease 2019 (COVID-19) from seroprevalence data. Methods: I searched PubMed and preprint servers for COVID-19 seroprevalence studies with a sample size ≥ 500 as of 9 September 2020. I also retrieved additional results of national studies from preliminary press releases and reports. I assessed the studies for design features and seroprevalence estimates. I estimated the infection fatality rate for each study by dividing the cumulative number of COVID-19 deaths by the number of people estimated to be infected in each region. I corrected for the number of immunoglobin (Ig) types tested (IgG, IgM, IgA). Findings: I included 61 studies (74 estimates) and eight preliminary national estimates. Seroprevalence estimates ranged from 0.02% to 53.40%. Infection fatality rates ranged from 0.00% to 1.63%, corrected values from 0.00% to 1.54%. Across 51 locations, the median COVID-19 infection fatality rate was 0.27% (corrected 0.23%): the rate was 0.09% in locations with COVID-19 population mortality rates less than the global average (< 118 deaths/million), 0.20% in locations with 118-500 COVID-19 deaths/million people and 0.57% in locations with > 500 COVID-19 deaths/million people. In people younger than 70 years, infection fatality rates ranged from 0.00% to 0.31% with crude and corrected medians of 0.05%. Conclusion: The infection fatality rate of COVID-19 can vary substantially across different locations and this may reflect differences in population age structure and case-mix of infected and deceased patients and other factors. The inferred infection fatality rates tended to be much lower than estimates made earlier in the pandemic.
Full-text available
The nine Bradford Hill (BH) viewpoints (sometimes referred to as criteria) are commonly used to assess causality within epidemiology. However, causal thinking has since developed, with three of the most prominent approaches implicitly or explicitly building on the potential outcomes framework: directed acyclic graphs (DAGs), sufficient-component cause models (SCC models, also referred to as ‘causal pies’) and the grading of recommendations, assessment, development and evaluation (GRADE) methodology. This paper explores how these approaches relate to BH’s viewpoints and considers implications for improving causal assessment. We mapped the three approaches above against each BH viewpoint. We found overlap across the approaches and BH viewpoints, underscoring BH viewpoints’ enduring importance. Mapping the approaches helped elucidate the theoretical underpinning of each viewpoint and articulate the conditions when the viewpoint would be relevant. Our comparisons identified commonality on four viewpoints: strength of association (including analysis of plausible confounding); temporality; plausibility (encoded by DAGs or SCC models to articulate mediation and interaction, respectively); and experiments (including implications of study design on exchangeability). Consistency may be more usefully operationalised by considering an effect size’s transportability to a different population or unexplained inconsistency in effect sizes (statistical heterogeneity). Because specificity rarely occurs, falsification exposures or outcomes (i.e., negative controls) may be more useful. The presence of a dose-response relationship may be less than widely perceived as it can easily arise from confounding. We found limited utility for coherence and analogy. This study highlights a need for greater clarity on BH viewpoints to improve causal assessment.
Fifty years after Bradford Hill published his extremely influential criteria to offer some guides for separating causation from association, we have accumulated millions of papers and extensive data on observational research that depends on epidemiologic methods and principles. This allows us to re-examine the accumulated empirical evidence for the nine criteria, and to re-approach epidemiology through the lens of exposure-wide approaches. The lecture discusses the evolution of these exposure-wide approaches and tries to use the evidence from meta-epidemiologic assessments to reassess each of the nine criteria and whether they work well as guides for causation. I argue that of the nine criteria, experiment remains important and consistency (replication) is also very essential. Temporality also makes sense, but it is often difficult to document. Of the other six criteria, strength mostly does not work and may even have to be inversed: small and even tiny effects are more plausible than large effects; when large effects are seen, they are mostly transient and almost always represent biases and errors. There is little evidence for specificity in causation in nature. Biological gradient is often unclear how it should it modeled and thus difficult to prove. Coherence remains usually unclear how to operationalize. Finally, plausibility as well as analogy do not work well in most fields of investigation, and their invocation has been mostly detrimental, although exceptions may exist. Copyright © 2015 John Wiley & Sons, Ltd.