One of the first conversations we have with new PhD or master’s students is about the role of models in research where we explain that modelling is a socio-technical endeavour aiming to make sense of the world. And that, given we are imperfect, we must accept that our theories must be, by necessity, also flawed.
During our little monologue at some point, we make this statement (courtesy of George Box) and test their reaction:
All models are wrong, but some models are useful.
Typically, this elicits either shock in many students or feelings of discomfort. And what follows is a rather unsatisfactory conversation that reveals some aren’t really driven by inquisitiveness but are instead motivated by credentialism. Some think research is all about establishing and confirming unassailable facts and others had never been exposed to the idea that science is about error correction and that what constitutes an error depends on a model’s purpose.
However, anyone familiar with the philosophy of science, or with Karl Popper and Thomas Bayes, will be quite comfortable with Box’s statement. In fact, they might, quite reasonably, think that if a simple and obvious statement causes a student intellectual or emotional discomfort then perhaps that student isn’t made of “the right stuff”.
After the student’s initial shock of finding out “all models are wrong”, we then skip to the next stage in the conversation by introducing causality and ‘systems theory’; twin ideas that help us explain and intervene in the world and model reality as interconnected systems with emergent behaviour. Then at blistering pace we discuss subjective probability which, for those students trained in classical statistics, is usually mind-blowing. Next, we argue that the field of statistics has been actively hostile to causality since its inception and that most statisticians or scientists wouldn’t know what a system was if it hit them on the head.
They typically don’t thank us for this sage advice until after they graduate and, we are sure some never learn to forgive us for destroying their comforting certainties!
Context is king
What has all of this to do with excess deaths? Well, most analyses of excess deaths tend to look at what we call bi-variate models involving two variables, like the one shown in the chart below, and argue that one variable is causing the other: in this case because vaccination rates are significantly correlated with excess mortality.
But we know life is not that simple and we all know that proof of correlation does not mean there is causation. If it did, we could say shoe size causes intelligence (as measured by IQ). Life’s more complex than that or some people insist it should be.
Yet in practice virtually every study on excess deaths shows a chart like this, whether its pro or anti any position, and even when the study quotes the mantra “correlation is not causation”, they always go on to make causal statements, in the text of the paper, to support their recommendation that the graph be ignored or to support their argument that the chart proves their point.
There is nothing wrong with this process: it’s natural. But it’s limiting. All this simply goes to show that the model, in the form of the chart or regression equation, must be supplemented by some explanatory text to make sense of it. This is needed to help frame it in some wider real-world context, where the influences of other variables, not shown in the chart, are accounted for, or explained away. Obviously if the model was ‘correct’ there would be no need to engage in this hand waving – it would be self-evident and complete in the model. People will argue that those variables that are not in the model, such as denied treatments, is causing the excess, or it is long covid that is causing the excess or lack of hospital visiting etc. And from then on much of the discussion is about the role of factors that are not in the model.
Context is king when building and interpreting models. It is unavoidable. It is where the assumptions are and where the model limitations and biases hide, and where the pure or impure motivations of researchers might be revealed. It isn’t the details of the models themselves, such as the values of some correlation coefficient, that always interest us, rather it is the controversies behind the modelling process. It’s the bits omitted or exaggerated. And this process of critical analysis reveals how ‘useful’ a model might be for the purpose to which we choose to apply it.
Teaching masters and doctoral students to critically read papers with a sceptical eye is a key part of the apprenticeship process, with which they must be dragged backwards through a hedge before they engage with it and it ultimately becomes reflex.
Blatant plug: some of these perspectives are covered in our book on risk modelling .
Can we do better?
So, is there any way to build a statistical model that might include the all-important context? No, not in an absolute sense because we cannot account for every aspect of reality, but we can do better than bivariate plots and mere correlations by acknowledging that reality is more complex than this and it involves causality where events unfold over time.
Clearly to model excess deaths we need to model a system of interlocking and interdependent factors that, together, give rise to the excess or reveal our assumptions about the causal mechanism that are driving it. Such modelling must take account of the problem of miscategorising (e.g., a pneumonia death as a covid death, a vaccinated deaths as unvaccinated, or a vaccine adverse event as a covid death etc.), ambiguity, obfuscation and malfeasance in measurement.
But, when researchers have presented a coherent ‘systems’ level explanation, such as Rancourt’s brilliant work , they have no choice but to resort to using classical statistics to analyse data in this compartmentalised, rather than integrated, way and then ‘fill in the gaps’ with paragraphs of text supporting narrative analysis. Therefore, the model isn’t really representing the statistics at all, and neither is the text, but something else altogether.
a person's or a group's conception, philosophy, or view of the world; a worldview
In a sense we are all grasping for a weltanschauung: an overarching and complete model of events, where differing and, oftentimes, competing explanations and variables can sit alongside each other. In this article we are trying to present a causal model to explain the various causes of excess deaths, with the benefit that it exposes the complexity of the phenomena and the challenges involved in attempting to model it, and by virtue of this explain, estimate, and judge events and actors participating in those events.
Causal graphs as a map
What we need in our discussion about the causes of excess deaths is a map of some kind that provides an exposition of the theories and suggests how we might test these theories using observational data.
Here we will build up a weltanschauung model in parts and show how the parts might interact. This is our model. It is wrong. You might have your model. It is also wrong but yours or ours might be more-or-less useful in terms of explanations or predictions. But we posit ours to draw threads together.
Our map is represented as a graph where the factors and variables are shown as circles and their causal/functional/statistical interaction by arrows. So, the relationship between a ‘parent’ factor with an arrowhead connected to another ‘child’ factor we consider to be the parent causing or influencing the child. And by “causal’ we mean the common-sense interpretation where the cause occurs before the effect in time and directly affects the other by some identifiable mechanism. Also note that a causal link from a parent to a child factor does not usually mean the child will certainly be true if the parent is, but rather is more likely to be true. The idea is that the strength of connection may be governed by probabilities rather than by deterministic logic. Here we’ve left ALL of the maths out and will concentrate on the shape and content of the causal graph because this is where the action is, but the interested reader can consult our book to find out more about the math if they wish .
Causes of Excess Deaths
We start by assuming there are five main causes hypothesised for the excess deaths observed from 2020 through to 2022 (and beyond?), as shown below. These are:
post viral syndrome mortality, either from influenza-like illness or covid (so-called long covid)
pneumonia mortality (caused by untreated pneumonia, or perhaps because of covid)
societal damage mortality (stress, drugs and poverty mortality including suicide) caused by lockdowns
mortality caused by treatments that were denied during lockdowns (availability of healthcare), and
adverse effects (AE) mortality of the vaccines.
Societal damage and denied treatment
If we look at two of the explanations for the excess – societal damage mortality and denied treatment mortality the theory goes that these are caused by poorer health, which is itself dependent on wealth and age. The less wealthy an individual (or population), and the older an individual (or population) is, the less healthy they will be. The theory here is that lockdowns themselves do not always DIRECTLY cause the extra mortality, but rather if someone is already poor, they are more likely to be unhealthy, stressed and take (prescription or other) drugs, then the lockdowns will impact societal damage mortality.
The quality of the healthcare system in any given locale will be dependent on the wealth of the locale, but when the healthcare system is denied to the population, it is this that causes excess mortality from denied treatment , not the quality of the healthcare system per se (think of empty hospitals with unused but gleaming equipment and nurses doing TikTok dances). Once we factor this in this part of the model gets a little bit more complicated.
Covid or Influenza mortality?
Most people who are seriously ill from a seasonal virus, whether it be an influenza like illness (ILI) or covid-19 ultimately succumb to bacterial pneumonia . It is this that kills them but up until that point there is a ‘complex’ of interactions between viral and bacterial agents, making it sometimes difficult to distinguish the primary causative agent. But we know pneumonia might be successfully treated using antibiotics and that ivermectin and hydroxychloroquine, as well as other drugs, have anti-viral and anti-bacterial properties that can aid recovery if administered early enough. However, it is the failure to administer these drugs that can lead to pneumonia and excess death. Thus, an ILI misdiagnosed as covid-19, as a matter of policy, and refusal to administer treatment, again as a matter of policy, would lead to excess deaths.
Whether antibiotics or alternative anti-viral drugs were administered would also depend on the health of the patient and the policies in place - in the UK antibiotics were prohibited for covid , , especially for the old with comorbidities - but anecdotally we have heard of patients given antibiotics anyway ‘just in case’ (some physicians deliberately circumvented policy mandates and treated their patients correctly).
Deliberate (or accidental?) misattribution and cross reactivity of testing
Covid PCR tests might cross-react with other viruses , including ILIs and other coronaviruses, and the ‘no covid virus’ camp might argue that covid is a deliberate misdiagnosis, when it the respiratory condition is really an ILI. The policy intervention, in the form of the PCR test, might simply have switched the determination of the cause of death to covid from pneumonia and ILI. This pathway can be compared to locales where the covid test was not routinely applied and where the diagnosis of cause of death would likely be pneumonia. This is shown in the graph a) below.
Of course, there are other misattribution problems with covid death classification due to the stipulation that anybody who died ‘within’ 28 days of a positive PCR test was classified as a covid death. Thus ‘normal’, statistically expected, deaths were coded as covid. For a detailed explanation of how this may have been done in practice see .
Unfortunately deliberate changes in cause of death classification have been a problem for a long time and is not new to covid. Mortality code changes by the WHO have always had a huge effect on death attribution with concomitant detrimental effects on the quality of epidemiological data available to researchers . Graph b) below shows what would have been the normal causal pathway before such coding changes.
The stringency of the lockdowns was decided by government fiat and in some countries, they were accompanied by the withdrawal of healthcare. Loneliness and social isolation would have led to more stress, more drug use, suicides, and increased poverty amongst those who lost jobs and businesses. The effects of lockdowns on excess deaths would therefore be revealed in the numbers who died because of denied treatment for health conditions or directly from stress, poverty, and drug use .
Note the possible role of sedatives in hastening or easing death is well documented in  and the process by which this may have occurred described in . In  denial of treatment of the elderly, by moving them out of hospital into the community and applying flowchart tools  to doom some, deemed too frail, to an early death.
Similar concerns have been raised with ventilation and intubation.
Vaccine mortality: adverse events
Turning to the vaccination programme, a possible immediate cause of ‘excess’ mortality would be adverse events (AEs) that occur immediately or soon after vaccination . The amount of excess would obviously be a function of the vaccination rate and the type of vaccine. Many countries used mRNA vaccines but some, such as Hungary, used a mix of Chinese and other vaccines, and these differences might be relevant.
Similarly, the age, and health of the population interact with the vaccine, so those who have serious health problems anyway may develop more immediate adverse events resulting in death.
There are obviously many conjectured mechanisms for AEs and whether they relate to one or more components of the covid mRNA vaccines, including the hypothesis that shortly after vaccination the immune system is depressed, making the recipient more vulnerable to covid as evidenced by the increased probability of a positive PCR test within 14 days of vaccination .
The extent of AEs is again dependent on the vaccination rate and this itself also depends on a personal inclination to vaccinate. This inclination is most positive in wealthier locales or amongst wealthier strata in the locales. Coercion by media, state and public health authorities also has a role in ‘motivating’ people to get vaccinated.
Vaccine scepticism has historically been strong within some ethnic groups who have developed a distrust in government, hence inclination to vaccinate might be mitigated by hesitancy and refusal by certain ethnic groups.
We could, of course, include the number of vaccines and boosters given, assuming a cumulative accumulation of latent damage, which would be later revealed as AE mortality, in the form of cancer or prion disease to take two conjectured possibilities. This hints at a need of a dynamic or temporal version of the model.
Vaccine mortality: ADE and autoimmune disease
There are two causal pathways connecting vaccination and excess mortality: the first, adverse events, we have covered, and the second is a specific kind of AE - antibody dependent enhancement (ADE) (there are others such as original antigenic sin) . Put simply, once vaccinated with an mRNA covid vaccine auto-immune disease may result where the vaccine enhances subsequent infection with the same or related respiratory viruses.
So, someone who is vaccinated, and suffers from ADE, and who subsequently catches a respiratory illness, either an ILI or covid, may then go on to develop bacterial pneumonia and die. We are highlighting this AE because it differs from the others: should it occur, the cause of death would be disguised, and present itself as caused by a subsequent bout of covid or another ILI, rather than as a direct effect of the vaccine.
Other possible AE mechanisms have been hypothesised, such as with cancer, where a depressed immune response, unable to detect and kill cancer cells, might increase the likelihood of death but, again, may be revealed as a ‘normal’ cancer death and one not directly associated with vaccination. Given the spike protein or lipid nano particles (LNPs) can distribute to any part of the body the pathogenetic consequences could be myriad.
Post viral syndrome mortality (and long Covid)
So-called long-covid is touted as the cause of the excess deaths, even though this is a well-recognised kind of post viral syndrome, commonly experienced by those who contracted an ILI. We can model the causal pathway linking ILIs and covid with post viral syndrome mortality as shown below.
There is evidence that the covid virus was probably circulating in late 2019. Given this, we would expect to see non-covid mortality increase in those who suffered post viral pathology. Similarly, the return of influenza in late 2022 would also lead to an uptick in deaths in 2023 and, perhaps beyond.
However, despite the claims that excess deaths are caused by long covid the evidence may be weak .
Iatrogenesis as a matter of policy?
A doctor may find it difficult to identify a single or root cause of death to put on a death certificate since the root causes of death may be multifactorial. Or a doctor might be incentivised to prefer recording a particular root cause rather than another more appropriate proximate cause.
Most statisticians might happily accept that, at first glance, the cause of death is the disease or health condition put on the death certificate as the cause of death. But given what we know about death classification this would be naive, because it is not always as straightforward, accurate or free from negative influence. Accidents and mistakes might be the true cause of death and might be covered up. Such ‘accidents’ aren’t always caused by individuals but may be the product un(intended) side effects of health policy and regulation. After all individuals ‘trapped by the system’ are incentivised to follow instructions.
Hence the “root causes” in our model would include avoidable societal or health policy causes of death such as these and recognise that these might vary by locale, since not every country or region implemented policies uniformly and may vary by kind – different locales may have varied stringency of lockdowns, the availability of healthcare, the extent of vaccine coercion, PCR testing and the administration or banning of alternative therapies such as ivermectin or hydroxychloroquine.
The Weltanschauung causal graph
Put all this together and we get our (BIG) weltanschauung causal graph. This is our map if you like for excess deaths.
However, this graph model has no math. It is simply a graph, a picture, so it is wrong in that way too, especially if we strictly assume all models need be mathematical. To add the math - the statistics and conditional probabilities for this model - we need data, and expert insight (because there is never enough data). Could we then use this to input into a proper Bayesian probabilistic reasoning machine? Currently this is infeasible given the paucity of data and if there is one thing, we’ve learnt it is that the authorities may be unlikely to release such data given its potential self-incriminating nature (if it exonerated them, we’d be tripping over the stuff).
This model is big. It’s complex. But it is more useful than a simple bivariate classical statistical model – if only we could get the data needed to complete it. We hope it usefully shows the challenge ahead in making sense of excess deaths and it shows how we might attribute excess deaths that are happening and how we might express and test hypothetical cause-effect relationships.
Despite it being big it remains incomplete. We could, for example, add changing age structures in the model as an alternative explanation for changes in excess death patterns. All things being equal if the population ages deaths will grow year-on-year leading to a cumulative growth in excess. I’m sure you will be able to imagine other variables that might also be important.
To make hypothesis testing easier we can select subsets of variables and test those separately from the other parts of the model. Divide and conquer. This might only be possible anyway given data constraints. Likewise, some elements of the model are prospective and others retrospective. For example, modelling excess deaths for 2021 might not necessitate any need to consider ADE but will certainly need to consider lockdowns. The worst effects of ADE or vaccine AEs might lie ahead and perhaps affect humanity into the distant future or may be temporary, and the effects of lockdowns may eventually fade. Finally, and obviously, vaccinations will not be relevant to any analysis of excess deaths in 2020 simply because they were not yet launched. What’s relevant and what’s not depends on context.
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Attributed to the British statistician George E. P. Box. Substitute the word theory for model if you like.
This isn't exactly a new argument. Prof John Robison of Edinburgh in the early 1700s argued that an equation's solution set that approximated a data set could be both useful and incorrect. Prof Laplace of Paris insisted contrarily that the equation was always perfect and the measurements were flawed. Euler took the iterative solutions route between the two: For series calculations that converged, we could attain adequate accuracy with enough calculations. Digital computing has made Euler's approach practical for validating models, but three centuries later, those who insist on unknowable levels of certainty, use their imagined certainty to ignore all contradictory facts and impose their beliefs upon the world, by force.
Amazing article. Truly extraordinary. This is what real science and modelling looks like.