## Wednesday 1 December 2021

### The impact of misclassifying deaths in evaluating vaccine safety: the same statistical illusion

In a previous post we showed that if there was a one-week delay in reporting deaths then a vaccine that was a placebo would be seen to have a decreased mortality rate for the vaccinated compared to the unvaccinated. In other words, an illusion of effectiveness is created by the one-week delay in reporting. This is shown in Figure 1 with our hypothetical example comparing the correct figures to the reported figures based on a one-week delay. The example assumes that in this population of 10 million people there is a (constant) weekly mortality rate of 50 deaths per 100,000 people. Each week the population reduces by the number of deaths the previous week. All death numbers (which are simply the relevant population multiplied by 50/100000) are rounded to whole numbers.

Figure 1: Hypothetical example of a placebo vaccine introduced into a population. A) shows correct results; B) shows results reported if there isa one-week delay in reporting deaths

It turns out that, under the same hypothetical assumptions, the same results arise if, instead of a one-week delay in death reporting there is a misclassification of newly vaccinated deaths; specifically, any death of a person occurring in the same week as the person is vaccinated is treated as an unvaccinated, rather than vaccinated, death.

Table 1: Reported deaths and mortality rate if newly vaccinated deaths are reported as unvaccinated

A proof of why the results are equivalent (except for week 1) is provided below.

The plot resulting from either reporting error is shown in Figure 2.

Figure 2 Plot of weekly mortality rates under either the delayed death reporting or death misclassification scenarios

It shows the apparently clear life-saving benefit of the ‘vaccine’.

But there is an obvious indication that these results are not real. If they were, why would the mortality rate in the unvaccinated peak at about the same time as the vaccine programme reaches its peak?

It turns out that the plots for mortality rates from the ONSreport (weeks 1-38) for the Covid-19 vaccination programme in each of the older age categories look remarkably similar to the plot in Figure 2, i.e. with the same peaks in unvaccinated mortality coinciding with when the vaccination programme reached its peak for this age group. For example, Figure 3 shows the 60-69 age group (for which vaccination peak was reached in week 11) and Figure 4 shows the 80+ age groups (for which vaccination peak was reached in week 6).

Figure 3 Plot of weekly mortality rates for Covid19 vaccinated v unvaccinated (this is all-cause mortality but the plots are have hesame shape even if deaths classified as Covid are removed)

Figure 4 Plot of weekly mortality rates under either the delayed death reporting or death misclassification

Why are the theoretical results important? Because they at least partly explain how the strange observed ONS results could occur even if the mortality rate of the vaccinated was the same (or even higher) than that of the unvaccinated. While it seems that deaths in the ONS report are being reported by date of death (hence are not delayed), newly vaccinated deaths are being classified as unvaccinated. Indeed, it is likely that any death within the first 14 days of vaccination may be classified as unvaccinated.

Moreover, as we will explain in the full analysis that we are currenly preparing, the ONS data provides other clues that suggest different types of errors in reporting. For example, even at the end of the reporting period (when errors such as death misclassification should be minimal and indeed the plots converge) the non-covid mortality rate for the vaccinated is still consistently lower than that of the unvaccinated. This suggests that the proportion of unvaccinated must be systematically underestimated.

Proof that, for a population with constant weekly mortality rate, a one-week delay in reporting deaths is equivalent to misclassifying newly vaccinated deaths.

We are assuming that every person who dies in the same week that hey are vaccinated is classified as unvaccinated. Before providing the formal proof, Table 2 provides an informal explanation

Table 2: Informal explanation showing why one week delay in death reporting is equivalent to misclassifying newly vaccinated deaths

 week Total vaccinated (P) Newly vaccinated (N) Weekly vaccinated deaths  (A) Newly vaccinated deaths  (B) Reported vacc deaths 1-week delay Reported vacc deaths with misclassification (A-B) 1 10,000 10,000 5 5 0 2 100,000 90,000 50 45 5 5 3 200,000 100,000 100 50 50 50 4 400,000 200,000 200 100 100 100 5 800,000 400,000 400 200 200 200 6 820,000 20,000 410 10 400 400 7 830,000 10,000 415 5 410 410

Formal Proof

1.       Let m be weekly mortality rate

2.       Let Pt be total vaccinated at week t

3.       Let Nt be number newly vaccinated in week t. Then Nt=PtPt-1

4.       Let At be total number of deaths of vaccinated in week t. So,  At=m*Pt

5.       Let Bt the number of deaths of newly vaccinated in week t.  So Bt=m*Nt = m*( Pt Pt-1) by (3)

6.       The number of reported deaths in week t is At Bt = m*Pt m*( PtPt-1) = m*Pt-1  by (5) which is the number of actual deaths in week (t-1)

1. i think the plots should be on the same timescale

2. The vaccinated counting as unvaccinated for a week after vaccination sounds a more plausible explanation of the hump in non covid deaths in the unvaccinated after the vaccinations are in full swing as opposed to a delay in reporting deaths.

It's clear from the ONS 1st November dataset that the total deaths showing for the week ending say 26th March 2021 (7,489 deaths) are actually the deaths for the week ending 2nd April 2021. You can work that out by looking at when the under 10 population stops adding into the ONS dataset. After 27th March 2021 (10 years after the 2011 census date) nobody who subsequently has a 10th birthday will have been on the 2011 census so won't add to the ONS dataset. So after 27th March 2021 it is a closed dataset with only deaths reducing the total population, but before that it's a static dataset except for the reduction through deaths and the addition of those reaching their 10th birthday.

But you can imagine ONS saying lets look up those 7,489 deaths and check what their vaccination status was during the week ending 26th March 2021 (because that's the week they have them wrongly recorded against in their data). What they actually should be looking up is their vaccination status during the week ending 2nd April 2021 by which time those who die within a week of vaccination are vaccinated.

I still think there is a selection effect going on also in relation to those people right at the end of life who can't get vaccinated. This should be separated from the vaccination of the most vulnerable (which I would interpret as those most vulnerable apart from those at the very very end of life). That would explain the 3 humps, the increase in non vaccinated mortality after vaccination starts, the increase in within 21 days mortality as some of those most sick are then just about well enough to be vaccinated for the first time, and the third hump as those too ill to get the second jab are left behind in a rapidly reducing single jab group.

3. I have a question that is related to your previous blog post "Is vaccine efficacy a statistical illusion?" With regards to the the efficacy of a Covid-19 vaccine against infection, what, if any, is the impact of the "delay" between infection and detection of this infection with a PCR-test? Potentially, an infection could be detected for some period of time after the infection started. For example see this paper "Persistence of SARS-CoV-2 nasopharyngeal swab PCR positivity in COVID-19 convalescent plasma donors": https://pubmed.ncbi.nlm.nih.gov/32840002/

4. Incredible work! Thank you Prof. Fenton.

I think this is a MAJOR discovery.

I believe there is something even more tricky than this phenomenon. As you know, most data sets (and figures/plots) related to COVID distinguish between "vaccinated" and "unvaccinated" individuals (as you did in your simulation). However, such a label is very misleading because it actually means "have a complete vaccination program" or "do not have a complete vaccination program."

This information is critical and relevant to your analyses because having a full vaccination schedule requires taking your dose 14 days after the second injection (except for J&J). In other words, if you receive your second injection and suffer any adverse event within 13 days of that second injection, you will be labeled as "not on a full vaccination schedule," or more simply as "unvaccinated."

So there is an obvious (and, in my opinion, deliberately crafted) delay mechanism in the way we consider people as vaccinated (and report adverse events).

This is not trivial, as most adverse events would begin to appear within the first week after injection, i.e., during the period when you are still officially "unvaccinated." It is also reasonable to consider that some of these adverse events would be officially labeled as "COVID-19" and not as "adverse events" (because vaccines officially have no side effects), which would amplify the statistical bias you describe.

Therefore, by design, there is not a one-week, but a two-week lag in how we consider people as "vaccinated" or not. So the statistical phenomenon you describe might be even stronger if you considered a 2-week lag (and I am only considering the second dose here for simplicity, but arguably the lag between taking the first dose and the official vaccination status is at least 5 weeks for RNA-based vaccines and 3 weeks for J&J).

Thank you again for your work,
MG

1. EDIT: "This information is critical and relevant to your analyses because having a full vaccination schedule requires taking your dose 14 days after the second injection (except for J&J)." should read:

"This information is critical and relevant to your analyses because having a full vaccination schedule requires being 14 days after the second injection (except for J&J)."
MG

5. I had thought this myself. I felt sick when it occurred to me. The notion of fully vaccinated is a Rubicon that means saline would look like a wonder drug. The sick part for a drug with deadly side effects would look even better. I actually wanted to be sick when this thought hit me.

6. I think there is a time effect too as in the preceding article because the NOS says:
"Age and vaccination status are defined on the date of death where a death has occurred, and on the last day of the week if not."

So it means that when binification is done during one week, the number of dead people, for each population, is recorded along that week, and that at the end of the week, the number of people in each population is determined.
So the bias occurs naturally, when descretizing the rates on a 1 week period.

7. Does your unvax total combine Unvaccinated, Within 21 days of first dose and 21 days or more after first dose?

8. I am not a statistician. I have drawn up a set of all the graphs for all the age groups in the ONS data. I had wondered about those peaks and now this makes sense. Both you and Mathew Crawford however seem to look at the fully vaccinated - i.e. 2 dose. If I put in the single dose data as a combination of both the before and after 21 days, I get a peak for every age group over 59 (that one is different and more complex - perhaps due to a difference between the two vaccines?). If I overlay the single dose graphs on top of each other, the order the peaks occur is by age group - oldest first. Is this a statistical error or is this real?

9. I used the per 100,000 data.

10. In US yes. between doses and two after second.

11. fascinating result/observation! An interesting feature even of such a simple model is that to observe the descending part of the mortality peak, we will need at least 98% vaccination rate (which, probably, is not practically attainable.)

12. this is incredible. I know you said they’re the same shape but can you send me the links to the non-Covid death graphs because I just want to see it with my own eyes. thanks!

1. I found a non-covid death graph you posted here for 60-69 year olds https://probabilityandlaw.blogspot.com/2021/11/is-vaccine-efficacy-statistical-illusion.html but It appears to be literally identical to the all mortality 60-69 graph in this article but that doesn't make sense. Am I missing something?

13. In NSW, Australia (my state), statistics are collected 4-fold.

(1) 1 Effective Dose
(2) 2 Effective Doses
(3) No Effective Doses
(4) Undetermined

In Australia, COVID vaccines are not considered "effective" until 2 weeks post 1st or 2nd dose. So a person that gets 1 dose and dies on the third day afterwards is counted as a (3) in NSW, rather than as a (1). A person who has had their second dose and dies on day 13 afterwards is also counted as a (3) rather than a (2).

How would this kind of counting affect the statistics distribution in the way you have calculated above in these articles?

Thanks for your work. I hope to use it at court when I take on my employer over their flawed risk analysis when it comes time to enforce a vax mandate.

1. Hallo Australian "fighter", I am also collecting as much data as possible in order to take the German government to court, if they rwally start their vax mandate.
Here is my thoughts about the risk-benefit evaluation, using official data from German institutions/government/WHO:
1.800 admitted deaths from vaccines, times a 15% statistic infection rate, leaving 270 people which would've ended up getting Covid infection. Then I look at the mortality rate of the people infected, which is 2,1%, that leaves 6 deaths by Covid compared to 1.800 deaths caused by the vaccines.
Maybe you agree with my way of looking at vaccine safety and figure out how the relation would be in Australia.
Greetings from Germany!

14. What’s the graphs look like for younger people? Could it be possible that for older age groups the spike in unvaccinated mortality is because old people on their death beds weren’t given the vaccine? If we saw mortality rate spikes in younger people labeled unvaccinated as well then I think you’d be onto something.

15. I live in Germany and when Covid started over here I was just as scared as everybody else. When they started vaccinating the elderly (80+) end of December 2020 a lot of deaths occured, matter of fact the highest deaths rate Germany experienced in the whole pandemic. Back then I was very sad, thinking if they would've approved the vaccine two weeks earlier, those poor people might have been saved. And of course we had no problem waiting our turn in order to protect the most vulnerable first.
Months later there was a doctor in Berlin saying that they used the old folks as lab-rats, and that they didn't want to risk the working class dying off. That's when I started research, and I came across a report about Dengvaxia used on 800.000 children on the Philippines. That's the first time I ever heard about ADE, Antibody-Dependent Enhancement, and I also found an article that the risk of ADE in the Covid vaccines was considered during their development. Now, why in the world, would the government publish an article like this, when the average person has never even heard about it?
I believe a lot of the deaths in December last year have to do with ADE.
The government, as well as the RKI and the PEI, still state that the benefits of these vaccines outweigh the risk, always using the 100+ million doses admitted for their mathmatic risk calculations.
But when I look at 1.800 deaths (this is the number they admit to!) caused by getting the jab, and assume that only about 15% of them statistically would've been infected (WHO lists the infection rate in the population of almost every country there is), that leaves 270 persons. Looking at the mortality rate among the infected people which is 2,1% for Germany (again WHO) I come up with 6 people that would have died from Covid, compared to 1.800 dead from the vaccines.
Do I look at this wrong, or is the the risk higher than the benefit?

1. ADE takes months or years to develop. No evidence of that as of yet. I would not argue that route. There might however be a short term derangement of the immune system that makes you more likely to get covid in the first 2 weeks following a shot. Some have argued that with some plots of covid cases spiking after vaccine rollouts. The mechanism of this would not however be called "ADE". As for the deaths from vaccines, deaths associated with vaccines are not necessarily caused by vaccines. So if you present that 1800 number as a fact in court, it won't serve your cause. I would stick to exactly what Dr. Fenton is presenting about all-cause mortality curves. Also do some research into vaccines apparently not preventing transmission. Several studies have suggested this recently.

2. Also, preventing covid and delaying covid are not the same thing. Even if it were assumed vaccine mandates reduced spread, the working class will be alive 20 years from now. So mostly covid can at best be delayed to later in life, not prevented. Where is your employer's evidence that this will decrease *lifetime* risk of dying from covid? Mandates are to protect the already vaccinated (not the unvaccinated). If you are vaccinated, would you rather get covid today or in 20 years? In 20 years there will be better treatments and plenty of ICU beds. But you will also have 10 or 100 times the risk of dying of covid since you are older. So much for the sense in "preventing" covid.

16. Good work, but don't get lost in the weeds. Look at the aggregates. Per table 10a (see link below), there are ~ 25 Covid deaths/day in the unvaccinated vs ~ 89/day in the vaccinated. And this is during a somewhat expected winter surge. That's ~ 10k deaths/year at current rates (many are old and co-morbid). Accounting for a lower summer mortality rate we'll likely see 5k unvaccinated Covid deaths/year ~ 1% of expected mortality. Puny numbers in the aggregate!

Sensible policy must recognize that this is much ado about nothing. Wreck your economy and destroy personal liberties for some statistically meaningless "gains"? Insanity!

As we say in the U.S., KISS! (Keep it simple, stupid).

p.s. I would argue that (based on Pfizer phase 3 trial) 14 days post first mRNA jab, a person is considered vaccinated. But even that doesn't change the aggregates to a large degree.

17. Does this pattern hold up if the vaxxed are counted as unvaxxed for two weeks after the second dose?

18. dear prof. Norman and Martin, thank you for the great work.
I am wondering if you were planning to or already submitted or published it on any preprint and journal? please do keep us updated, best LC

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