Sunday, 14 November 2021

Is vaccine efficacy a statistical illusion?

1 Dec 2021 upate: see update to this article showing that the same statistical illusion of efficacy occurs if newly vaccinated deaths are classified as unvaccinated.

To evaluate the risk/benefit of a vaccine for treating a virus, such as covid-19, we can compare the all-cause mortality rate of vaccinated against unvaccinated people on a periodic basis. If the mortality rate for those vaccinated is consistently lower than that for unvaccinated then we might conclude the vaccine must be beneficial.

Placebo Vaccination

Imagine that a placebo rather than a vaccine is quickly rolled out to a population of one million people of similar age and health. Let’s assume the weekly non-virus mortality rate for this population is 15 per 100,000 (100k), so we would expect about 150 out of the million to die in any given week. Because the placebo changes nothing, the mortality rates for both vaccinated and unvaccinated average the same 15 per 100k, each week every week. Hence, on average, what we should observe – as the ‘vaccination’ programme rolls out to most of the population - is shown in Table 1. Notice that the placebo vaccine roll-out programme is enacted at pace and the cumulative percentage of the population vaccinated rises to 98% within 12 weeks.

Table 1 Roll out of placebo ‘vaccine’. No observed differences in mortality rates (no population growth and each week total population reduced by previous week’s deaths)

 

Vaccinated

Unvaccinated

Week

Population

Cumulative Percentage vaccinated

Deaths

Population

Mortality rate

Deaths

Population

Mortality rate

1

1,000,000

0.5

1

5,000

15

149

995,000

15

2

999,850

1

1

9,999

15

148

989,852

15

3

999,700

2

3

19,994

15

147

979,706

15

4

999,550

4

6

39,982

15

144

959,568

15

5

999,400

7

10

69,958

15

139

929,442

15

6

999,250

14

21

139,895

15

129

859,355

15

7

999,100

28

42

279,748

15

108

719,352

15

8

998,950

45

67

449,528

15

82

549,423

15

9

998,801

65

97

649,220

15

52

349,580

15

10

998,651

80

120

798,921

15

30

199,730

15

11

998,501

93

139

928,606

15

10

69,895

15

12

998,351

98

147

978,384

15

3

19,967

15

13

998,201

98.5

147

983,228

15

2

14,973

15

14

998,052

98.6

148

984,079

15

2

13,973

15

15

997,902

98.7

148

984,929

15

2

12,973

15

16

997,752

98.9

148

986,777

15

2

10,975

15

17

997,603

99

148

987,627

15

1

9,976

15

18

997,453

99.1

148

988,476

15

1

8,977

15

19

997,303

99.2

148

989,325

15

1

7,978

15

20

997,154

99.3

149

990,174

15

1

6,980

15

 

Now suppose there is a one-week delay in the reporting of deaths. Such delays are routine in statistical reporting of mortality and vaccine data. Then the data reported by the authorities is different from reality, here shown in Table 2, which is the same as Table 1 but where the death totals are simply ‘shifted’ down one week.

Table 2 Death reporting delayed by one week

 

Vaccinated

Unvaccinated

Week

Population

Cumulative Percentage vaccinated

Deaths

Population

Mortality rate

Deaths

Population

Mortality rate

1

1,000,000

0.5

-

5,000

-

-

995,000

-

2

999,850

1

1

9,999

7.50

149

989,852

15.08

3

999,700

2

1

19,994

7.50

148

979,706

15.16

4

999,550

4

3

39,982

7.50

147

959,568

15.31

5

999,400

7

6

69,958

8.57

144

929,442

15.49

6

999,250

14

10

139,895

7.50

139

859,355

16.22

7

999,100

28

21

279,748

7.50

129

719,352

17.92

8

998,950

45

42

449,528

9.33

108

549,423

19.64

9

998,801

65

67

649,220

10.39

82

349,580

23.57

10

998,651

80

97

798,921

12.19

52

199,730

26.25

11

998,501

93

120

928,606

12.91

30

69,895

42.86

12

998,351

98

139

978,384

14.24

10

19,967

52.51

13

998,201

98.5

147

983,228

14.93

3

14,973

20.00

14

998,052

98.6

147

984,079

14.99

2

13,973

16.07

15

997,902

98.7

148

984,929

14.99

2

12,973

16.16

16

997,752

98.9

148

986,777

14.97

2

10,975

17.73

17

997,603

99

148

987,627

14.99

2

9,976

16.50

18

997,453

99.1

148

988,476

14.99

1

8,977

16.67

19

997,303

99.2

148

989,325

14.99

1

7,978

16.88

20

997,154

99.3

148

990,174

14.99

1

6,980

17.15

 (Update) Here's a 60-second video showing how to this is done in Excel and proving there are no tricks involved other than simply shifting the deaths down by one week:


Suppose we want to examine and compare the mortality rates of the unvaccinated and vaccinated cohorts based on the data in Table 2. Figure 1 shows this comparison, and we can see that the mortality rate is consistently lower for the vaccinated than that for the unvaccinated throughout the roll out of the vaccination programme and it reduces as soon as vaccination nears population saturation at close to 100%.

 

Figure 1 Reported weekly mortality rates vaccinated against unvaccinated

We might conclude that those who remain unvaccinated look to be suffering much higher levels of mortality than the vaccinated. The reporting delay therefore creates a completely artificial impression that the vaccine must be highly effective.  In fact, it looks like a magic ‘cure all’ wonder drug!

The fact that the mortality rate of the unvaccinated peaks when the percentage of those vaccinated peaks should ring some alarm bells that something strange is going on (unless there is independent evidence that the virus was peaking at the same time).

 

ONS data on Covid-19 Vaccination

While the placebo vaccine example was purely hypothetical, Figure 2 shows the vaccinated against unvaccinated mortality using the data in the latest ONS report mortality in England by Covid-19 vaccination status (weeks 1 to 38)[1], complemented by NIMS vaccination survey data (up to week 27 only). Here we show other-than covid mortality to remove the virus signal.

 

Figure 2 Reported weekly other-than covid mortality rates for vaccinated versus unvaccinated for 60-69 age group for weeks 1-38 2021

Note that we see the same features as the shifted graph in Figure 1. In other words, a perfectly reasonable explanation for what is observed here could be that there is no difference in mortality rates between vaccinated and unvaccinated and the mortality differences are simply a result of a delay in death reporting. Moreover, given we have removed covid deaths (which were only a small percentage of all-cause deaths in the reported data) we get a near identical result for non-covid mortality to that which would result if the vaccine were a placebo! Thus, we appear to have created a statistical illusion of vaccine efficacy.

It is important to note that we are not claiming the death reporting is delayed in the ONS data. In fact our work on this is ongoing and we believe that the most plausible explanation is misclassification and underestimation of proportion of unvaccinated. 

If this is not a statistical illusion how is it possible that the unvaccinated are dying from non-covid causes at a higher rate than vaccinated? Also how is it possible that, at the time vaccination rates are ramped up to nearly 100% of the population, the nonvaccinated are dying from non-covid deaths at almost twice the rate of those who are vaccinated?

These same patterns are also observable in the 70-79 and 80+ age groups (with the mortality peaks for the unvaccinated appearing at different weeks because these age groups received vaccinations earlier). This strongly suggests that what we are observing is a genuine statistical illusion unexplainable by any real impact of the vaccine on mortality rates. 

 

Consider a deadly placebo

It is also important to note that even if the actual mortality rate for the vaccinated was higher than that of the unvaccinated, where the vaccine was causing death, as a side effect, we would still likely observe the same illusion.

To see this effect let’s revisit our placebo vaccine example and make a small change to Table 1 where instead of a mortality rate of 15 per 100k for the vaccinated, suppose it is 17 per 100k (a rise in mortality of approximately 13%). So, the placebo vaccine is killing two more people per 100k and gives no mortality benefit otherwise. In this scenario the reported mortality rate for the ‘deadly placebo’ is compared to the first ‘placebo’ scenario, in Figure 3. Even here we see the illusion that the mortality rate for the vaccinated is lower than unvaccinated. Both scenarios are the opposite of reality, and both look interchangeable. This means the chance of picking up a vaccine side effect signal is close to impossible and instead the illusion is created of vaccine efficacy.





Figure 3 Reported weekly mortality rates vaccinated against unvaccinated for ‘placebo’ scenario and ‘deadly placebo’ scenarios

 

The illusion of declining vaccine efficacy

Finally, it is important to note that the same statistical illusion applies to all measures of vaccine efficacy whether they be cases, hospitalizations, or deaths. In fact, replacing the number of deaths in Table 1 with number of cases, with a one week reporting delay, would result in vaccine efficacy rates as shown in Figure 4.


Figure 4 Reported vaccine efficacy rates equivalent for placebo vaccine

This occurs when the actual placebo vaccine efficacy for cases is zero.

This reporting bias is one type of bias that might be called ‘reporting lag censoring’, a phenomenon whereby structural or process factors systematically interfere with when data is handled and reported with the consequential effect that it is then misinterpreted, leading to false conclusions.

 

UPDATE: Here is a 25 minute lecture explain the background and ongoing work:

 


[1] https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/bulletins/deathsinvolvingcovid19byvaccinationstatusengland/deathsoccurringbetween2januaryand24september2021

151 comments:

  1. Can you reverse this effect in the ONS data somehow, knowing how you modelled it?

    ReplyDelete
    Replies
    1. That would be easy to do if this simple mistake had in fact been made. The authors provide no evidence for this. They seem to be just speculating that, if all statisticians making such reports were idiots, this might happen.

      Delete
    2. Our institute reporting deaths(Netherlands) IS lagging behind. All the time. Where as a change of vaccination status is made right after every jab.

      Delete
    3. This comment has been removed by the author.

      Delete
    4. The authors DID provide evidence for this illusion being employed by the UK's ONS dataset. See the excel spreadsheets for yourselves. The ONS calculated age-specific all-cause mortality rate per 100K people, using precisely this methods of (deaths in a certain week) divided by (population with that vaccination status). Even though they say date-of-death is used (so assuming delayed death registration is not involved here), the same illusion is completely inherent in this way of calculation because deaths caused by the vaccination don't usually happen on the day of vaccination.
      https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

      Delete

    5. The assumption is that the only way to deal with Covid, is after it arrives as Covid in your body, after the initial cold infection, in your head, some 20 days earlier
      .Why is that?
      Kill the Flu or Coronavirus in the head, soon after getting the virus in the nasal passages inside the head, the brain bulb and brain stem, etc, with my free salt water cure, which flushes out the nasal passages (so no Long Covid) and kills off the Coronavirus infection, immediately, or during the 10 to 14 days of self isolation.
      No infection in the head, no Covid – it is as simple as that.
      Then the purpose and functions of the vaccines, ceases to be a problem and you simply can’t get sick and won’t ever get Covid.
      Mix one heaped teaspoon of “iodine” table or sea salt in a mug of clean warm or cold “clean” water, cup a hand and pour some of the solution in, then sniff or snort that mugful up into your nose, spitting out everything which comes down into your mouth, from the back of your throat, by so doing, you flush out your nasal cavity, where Coronavirus lives.
      If you get a burning sensation (which lasts for 2-3 minutes) then you have a Coronavirus infection.
      When the soreness goes away, blow out your head with toilet paper and flush away, washing your hands afterwards and continue doing my salt clean water nasal cavity flush cure, morning, noon and night, or more often, if you want, until, when you do my free salt water cure, you don’t experience any soreness at all in your nasal cavity inside your head.
      While you are at it, swallow a couple of mouthfuls and if you get a burning sensation in your chest, then you are killing the Covid/Pneumonia there too, so keep it up, each time you do a salt water sniffle, until the soreness in your head and lungs goes away – job done.
      When you flush your head with the salt water remedy, it should feel like you are flushing your head with water – no reaction felt at all.
      I have been doing this for 27 years and I am never ill from viruses and there is no reason for anyone else to be either and of course, I never have vaccines - what is the point?
      You don’t need to be tested to see if you have a head infection, you will know instantly if you have or not, with my free salt water cure
      We will need a cure for Coronavirus or the Flu, which everyone will get sooner or later and this is it – my Covid Crusher.
      Pass it around to everyone and take credit for it yourself, if you want.
      Richard.

      Delete
    6. Mix one heaped teaspoon of “iodine” table or sea salt in a mug of warm or cold “clean” water, cup a hand and pour some of the solution in, then sniff or snort that mugful up into your nose, spitting out everything which comes down into your mouth, from the back of your throat, by so doing, you flush out your nasal cavity, where Coronavirus lives.

      If you get a burning sensation (which lasts for 2-3 minutes) then you have a Coronavirus infection.

      When the soreness goes away, blow out your head with toilet paper and flush away, washing your hands afterwards and continue doing my salt clean water nasal cavity flush cure, morning, noon and night, or more often, if you want, until, when you do my free salt water cure, you don’t experience any soreness at all in your nasal cavity inside your head.

      While you are at it, swallow a couple of mouthfuls and if you get a burning sensation in your chest, then you are killing the Covid/Pneumonia there too, so keep it up, each time you do a salt water sniffle, until the soreness in your head and lungs goes away – job done.

      When you flush your head with the salt water remedy, it should feel like you are flushing your head with water – no reaction felt at all.

      I have been doing this for 27 years and I am never ill from viruses and there is no reason for anyone else to be either and of course, I never have vaccines - what is the point?

      You don’t need to be tested to see if you have a head infection, you will know instantly if you have or not, with my free salt water cure

      We will need a cure for Coronavirus or the Flu, which everyone will get sooner or later and this is it – my Covid Crusher.

      Pass it around to everyone and take credit for it yourself, if you want.

      Richard.

      Delete
  2. How the hell do you even notice something like this?

    ReplyDelete
    Replies
    1. Seriously: by being a statistician. To an expert, the possibility of the mistake explained here is a triviality. For the same reason, it is a priori implausible that the mistake was made. It would be upon the bloggers to provide some evidence of this, which they do not.

      Delete
    2. Seriously,

      from Wiki: The criminal (UK) standard was formerly described as "beyond reasonable doubt". That standard remains, and the words
      ... commonly used. The civil standard is 'the balance of probabilities', often referred to in judgments as
      "more likely than not".

      So, you could stick your “a priori” where the sun does shine; that would be in all other jurisdictions other than the UK’s and/or other than - this blog@GOOG, given the Warp-speed of the stage i-iv “trials” (on iii+6)... That do show, lately, that :

      … all cause mortality is higher in the vaxxed than the unvaxxed cohorts. OAS & Statistical significance - completely aside.

      Event tho, the words “vax” and “fully vaxxed“ changed from “stage ii” from the

      “commonly used”.

      And the latter again for the “stage second year”, after 7bn inoculations. Again. In UK, mind u !


      This are the Interwebs. Post factum.

      Welcome!

      Please, do not perform "ignoratio elenchi" here.

      Delete
    3. Anonymous - the paper IS the evidence, right? If, as you insist, it is impossible for people to make a mistake, ergo it was not a mistake.

      Delete
  3. Great piece by the way and (as a teacher myself), I love the combination of the original model being simple enough that a high school student could build it with spreadsheet software, yet the final conclusion being rather profound. Look how easily you could be fooled.

    ReplyDelete
    Replies
    1. ..look how easily we are fooled.

      Delete
    2. "Lies, damn lies, and statistics" is a phrase prominent in my mind lately.

      Delete
    3. I have to disagree a bit. You are right that a high schooler can understand the argument; but by the same token, the conclusion is (to a professional statistician) trivial and describes a silly mistake that was presumably avoided. If the authors want to claim that it was not avoided, they should provide some evidence.

      Delete
    4. Anonymous, you seem to be a bit hell bent on discrediting what is a simple hypothesis compared with reality hinting at a connection. Did you even read the article, particularly the bit where it says:

      "It is important to note that we are not claiming the death reporting is delayed in the ONS data. In fact our work on this is ongoing and we believe that the most plausible explanation is misclassification and underestimation of proportion of unvaccinated."

      Cause going by how insistent you are about "evidence", I don't think you did.

      Delete
    5. Anonymous, the "evidence" is in the GOVERNMENT CALCULATED mortality rate that Figure 2 in this blog simply plotted out for us to see. Lying government statisticians count on us to think that "silly mistakes" like this are "presumably avoided".

      Delete
  4. Same question as Duncan Cragg: if your explanation is correct then you should be able to cancel the illusion by shifting mortality data backwards in time... did you try it?

    ReplyDelete
    Replies
    1. As well would love to hear an answer to this...otherwise I'll try to do it on my own with the data available in Germany

      Delete
    2. Any results as of yet?

      Delete
    3. This comment has been removed by the author.

      Delete
    4. To cancel the illusion requires shifting the deaths correctly to the date of vaccination of the dead, or else there's still the delay of when infection or death occurs relative to the expanding vaccinated population size subject to the infection or death.

      Delete
    5. This comment has been removed by the author.

      Delete
  5. Can you show what the curves would look like for an effective vaccine with reporting delay, for comparison?

    ReplyDelete
    Replies
    1. I tried this on spreadsheets I created. It is possible that I did something incorrect but my first model matched the one presented here so I think I am doing it right. Then I did one with a 13 per 100K mortality rate for vaccinated and retained the posited 15 per 100K death rate for unvaccinated - presuming that to be a baseline. I found essentially the exact same shapes and magnitudes of the curves in the graphs and with only some very slight shifting. Intriguing.

      Delete
  6. Isn't the use of 'Efficacy' for description of outcomes within lab conditions and the use of the word 'Effectiveness' for discussion of reaults in the real world?

    ReplyDelete
  7. Even worse if you consider that many vaccine deaths appear to have been recorded as "unvaccinated."

    ReplyDelete
    Replies
    1. Exactly right. Often vaccine related deaths happen within the first two weeks after vaccination, and to hide this everyone is labelled unvaccinated for the first two weeks after any shot. It's a shell game.

      Delete
  8. Yes and it would be good to label correctly the people who are in their first 14 or 21 days post-vac (i.e. in the vac group, just not seeing any benefit yet).

    By the way, if we're all worried about Big Brother, could this blog transfer from G***** to another platform? Censorship is rife after all and led by G*****.

    ReplyDelete
  9. How is unvaccinated being defined? Is it people who have had no shots, or does it include those who have had one shot or are less than 21 days after their second shot?

    ReplyDelete
    Replies
    1. in this simulation im pretty sure unvaccinated were completely unvaccinated and vaccinated had 1+

      Delete
  10. Thank you for your analysis.

    Just to make sure we pin all the tails on the right donkeys:
    Where you discuss the deadly placebo and the inability to pick up a 13% excess mortality, the delay effect clearly makes this difficult while the vax/unvax ratio is changing, but I'd expect it to become obvious once things had asymptotically settled. It appears not to in your examples, but I thnk this is an effect of rounding errors not the delay. If figures were given per million, you would see it clearly by week 12?

    ReplyDelete
    Replies
    1. That's exactly what was seen in the >21 after 1st dose group by ONS data, which a previous blog (Sep 21) discussed. And the rush to roll out boosters is precisely to cover up the slowly revealing truth, to keep the illusion going.

      The newly released dataset needs the same analysis as that Sep blog! I could already see that the same higher mortality in the >21 after 1st dose group continued just like in the earlier dataset. This new dataset additionally provided the age-stratified mortality, so it's much better.

      Delete
  11. Just saying that more people are vaccinated, than actually are vaccinated hides a multitude of vaccine sins.
    Listing deaths as "unvaccinated" by default, unless full evidence of full vaccination is in-hand, as is the case at most hospitals, makes vaccineslook good, even if there is ADE at work after 6 months, and they are predisposing to infection and death.
    This exercise is most instructive.
    Thank You! John Day MD, COVID-19 treating physician, until fired for mandatory vaccination refusal
    www.johndayblog.com

    ReplyDelete
  12. This is encouraging if it is noticed, correctable, and corrected. It is discouraging if it is not corrected, whether because it isn't noticed, deliberately ignored, or not correctable because the reporting issues make it impossible to correct correctly.

    I suspect we live in the latter world and thus have no idea what's really going on.

    ReplyDelete
    Replies
    1. There's nothing to correct because the trivial mistake belabored in the blog was not made. Or at least, the bloggers provide no evidence that it was made.

      Delete
    2. real world evidence:

      US:
      https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/

      UK:
      https://twitter.com/theotherphilipp/status/1460662778201612293?s=20

      Germany:
      https://twitter.com/ReginaLouf/status/1461325574073372680?s=20

      Delete
  13. It seems to be the case here: https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/index.html

    ReplyDelete
  14. I checked the dataset from the latest ONS release (Nov 1), which said they were using date of death, not date of registration of death, so perhaps their trick was not achieved by a delay in death reporting, but by the other equivalent option, i.e., inflating reported vaccine rollout speed, since the vaccinated population estimates at any timepoint was based on the weekly announced vaccinations - see Table 7, Notes 3,4 in link below - which many had suspected were inflated.)
    https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

    Bill Gates told us in the summer of 2020, that he enjoys reading a book titled "HOW TO LIE WITH STATISTICS". Like with everything they do to us, it's all in plain sight if we pay attention. Starts at 0:45 mark.
    https://www.facebook.com/catcrosby.idealist.dreamer/videos/993764841059908/

    ReplyDelete
    Replies
    1. Actually, Gates made the book recommendation in 2015, in multiple video/photo shoots. Here’s a 3 minute video on his YouTube channel: https://www.youtube.com/watch?v=mtXuNUEM3vg

      To get a flavor of what the book actually talks about: https://www.bitchute.com/video/dvXxMpLs5n2b/

      Delete
    2. You cannot use date of death for this estimation, you need to use date of infection!

      This is the big issue. Date of infection is not known and in case of death may be weeks earlier.

      Delete
    3. And if one wants to consider possible adverse impact of the vaccines, it should be the date of vaccination.

      Delete
  15. Dr. Fenton & Dr. Neil, it would be really nice if you could repeat the modeling of placebo, poison vaccine, and perhaps also a truly efficacious vaccine, but in each case, separate the 3 categories of the vaccinated (<21 days 1 dose, 21 days or more 1 dose, 2 doses), to see how the dynamic would look like for each category compared to the unvaccinated. Thank you for your excellent work!

    ReplyDelete
  16. fascinating analysis

    I think the problem is calculating mortality by dividing the number of deaths 'today' by the number of vaccinated 'today' when the number vaccinated is increasing. even if you got rid of the death reporting delay, the mortality rate should be the death 'today' divided by the vaccinated 'on the day that the deceased contracted covid'. This could be a 2-4 week delay


    ReplyDelete
    Replies
    1. Great point! I realized that months ago. Two to four weeks is too low. After someone is fully vaxxed, they need to walk around a while first to get Covid. They don’t get it the first day they are fully vaxxed. Then it takes at least two to four weeks before they succumb. Probably more!

      Delete
    2. Yes, great point! But date of contracting COVID isn't relevant to all-cause mortality anyway. I can think of two strategies to compare the vaxxed vs. unvaxxed all-cause mortality, the first is an end-point comparison, the second is dynamic comparison:

      Strategy 1: Take an endpoint date that is sufficiently late in the rollout process, e.g., Sep 24, 2021 as in the latest available dataset by ONS (ref 1 above).

      For each age group, calculate the number of person-days that were spent as an unvaccinated person during the study period, and the number of person-days spent as a vaccinated person in each of the 3 categories of vaccinated status. This gives us 4 denominators, 3 of which can be summed up to arrive at the total person-days spent as a vaccinated person.

      For each age group, find the number of total deaths of the unvaccinated and the vaccinated who died in each of the 3 categories, by the endpoint date, then divide by their respective denominators.

      This gives the all-cause mortality rate per person-day lived, in each group. The total number of deaths of the 3 categories of the vaccinated can be summed up to the total vaccinated death count, which can be used to calculate the total death rate of the vaccinated group, per person-day lived as a vaccinated person.

      Strategy 2: On the latest available endpoint date sufficiently distant from the last calculated week (as to allows for delay in death registration and for the vaccine to manifest its effects), calculate eventual death rate for each prior week during the rollout, as follows:

      The (live/death) outcome of each person up to the latest end-point date, is compared by their vaccination status for the week in question. So anyone vaccinated during or prior to that week, who died from the beginning of the study period up to the latest end-point date, counts towards total vaccinated deaths in their age group, for that week in question.

      For the unvaccinated deaths, count all the people who ever died while unvaccinated during the entire period from the beginning of study till end-point date.

      To calculate all-cause mortality rate for each group, the denominator for the vaccinated is the total number of people who had been vaccinated during or prior to that week in question. The denominator for the unvaccinated is the sum of all the people who remain unvaccinated on the end-point date, plus all the people who died as an unvaccinated person.

      The death rates thus calculated reflects the cumulative eventual outcome (by the latest available endpoint date) for the vaccinated vs. unvaccinated up to any particular week during the rollout process, rather than the immediate deaths that occurred during that week. And obviously, the more distant the endpoint date is from the week in question, the more accurate the result.

      Delete
    3. I'd love to see the two good professors (or anyone else) make a comparison with these strategies (if they make sense). We need solid evidence to defeat the vaccine propaganda.

      Delete
    4. Your strategy 1 is exactly what is done in a phase 3 study: calculate the exact number of days at risk.
      If you do this in table 1 you will get after 20 week a mortality of 14.98 against 15.22 (calculated with integer not floating point). Even when you do not fix the known time lag.

      But it's stupid not to fix the time lag when you know about it.

      https://pbs.twimg.com/media/FEWDr82X0AI7nRz?format=png&name=large

      Delete
    5. Thank you Eagle, yes your spreadsheet illustrates this nicely.

      My second strategy is flawed, I realized the unvaxxed denominator is the problem, it's hard to define properly, since the unvaxxed population continues to whittle down, while all the unvaxxed deaths remains in the unvaxxed category! So scrap strategy 2!

      Delete
  17. Is this a form of Simpson's Paradox? Trying to understand where this effect comes from. Thanks

    ReplyDelete
    Replies
    1. No. It comes from evaluating numerator and denominator at different dates. However, this is a completely trivial mistake that professionals would be unlikely to make, and the bloggers provide no evidence that it was in fact made. The blog post is mere speculation on what could have happened in a parallel universe where all reports were provided by idiots.

      Delete
    2. The bloggers DID provide evidence for this illusion being employed by the UK's ONS dataset. The bloggers simply plotted out in Figure 2 what the government calculated for mortality rates. See the excel spreadsheets for yourselves. The ONS calculated age-specific all-cause mortality rate per 100K people, using precisely this methods of (deaths in a certain week) divided by (population with that vaccination status in that week). Even though they say date-of-death is used (so assuming delayed death registration is not involved here), the same illusion is completely inherent in this way of calculation because deaths caused by the vaccination don't usually happen on the day of vaccination.
      https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

      Delete
  18. This is fantastic, thanks. Any chance you could make the spreadsheet available for download somewhere?

    ReplyDelete
  19. I've worked in data modelling, not extensively mind, and have been trying to explain this phenomenon for nearly a year and half now, getting mostly blank looks from people. Thank you for a cogent and easily digested breakdown, I will share this widely.

    ReplyDelete
  20. How to manipulate data and stupid people, edition 18443859345

    Vaccines work. Deal with it people.

    ReplyDelete
    Replies
    1. Why don't you deal with it by exposing the flaws. Or are you paid by the post so need to keep them short?

      Delete
  21. Fortunately you can pretty easily correct for this by calculating the sum of the mortality rate rather than using the weekly statistics. So instead of calculating the mortality rate just for that week, as you do in your spreadsheet, calculate it as the sum of the total deaths up to that week divided by the sum of the population up to that week. There is still a statistical illusion in early weeks, but as time goes on both unvaccinated and vaccinated converge to the true mortality rate, which is 15% in your example, regardless of how much time shifting has happened.

    Can you do this to the ONS data? That would give a better picture of what's going on.

    ReplyDelete
    Replies
    1. What you suggested doesn't correct for the delay of death registration, nor the delay between injection and dying. But see my response to another commenter above for 2 strategies I suggested. None will actually correct for inflated vaccination uptake though, if that's present.

      Delete
    2. Delay between date of injection and death isn't relevant, unless you are making an additional claim that the vaccine is actually harmful, or unless this period is brief. The only issue, which is well-known, is that an individual should be in neither the "unvaccinated" nor "fully vaccinated" bucket until two weeks after the final dose, and the UK does not show this consistently. (Some other jurisdictions, e.g. Israel, Canada, and the USA state of Virginia, do.)

      Anonymous is of course correct that using cumulative statistics for the mortality rate, reduces the effect of the error, or anomaly, introduced by the delay in reporting deaths. The error is basically divided by the number of weeks so far. Of course, no such reduction will happen when accumulating the real-world data, because it is the real world data, and in the real world the vaccines work. And the vaccines’ effect if we looked just at covid deaths would be quite remarkable.

      Delete
  22. Certainly vaccines work HarroH. But this is not a vaccine "within the meaning of the act", any more than this is a pandemic "within the meaning of the act" - until of course the WHO and CDC changed the definition.

    ReplyDelete
  23. Would this analysis provide an explanation as to why Pfizer eliminated the control group by giving them all the vaccine??

    ReplyDelete
  24. Is it on factor that could muddy all of this the question of how accurately "Covid deaths" and "Covid cases" are tested and defined?

    ReplyDelete
    Replies
    1. Correction, that should start "Isn't one factor..."

      Delete
  25. I worked out something strange using a table the government published. If you take the % if non vaccinated each month then divided by an average it gives the unvaccinated 51% average. However the unvaccinated all cause deaths only make up 34% which suggests people are dying from the vaccines at a disproportionate rate?

    ReplyDelete
  26. Absolutely clear mechanism. If the vaccinated cohort steadily grows, the delayed reporting of deaths will always undercount the actual mortality. The opposite for the unvaccinated. But who now pays attention to the government statistics anyway?

    ReplyDelete
  27. Efficacy trials compared the vaxxed to the totally unimmune.

    Comparing the vaxxed to the unvaxxed, when the process of vaxxination whittles the unvaxxed down to mostly those that know they've had it.

    Is the biggest fraud of this last 2 months.

    Read this...
    https://medium.com/pragmapolitic/tobys-vax-efficacy-fraud-fd6f73718f1a

    As to your silly spreadsheet, it doesn't explain why the mortality rate initially for those vaxxed was at about 1/40th of the unvaxxed.

    ReplyDelete
    Replies
    1. If "the mortality rate initially for those vaxxed was at about 1/40th of the unvaxxed", that can be easily achieved by a high speed of initial rollout.

      Delete
    2. ... but we know the speed of the rollout, we have exact data for that, and it wasn't even as fast as they present in their mock up in the table above.

      So you're just speculating with theory, that doesn't match reality.

      Crucailly, if it was a placebo, with mobility/contact-rates now almost normal, at 2x the rate they were this time last year, we'd be having cases and deaths far higher than in previous waves, yet the mortality rate is about 5-10x lower than either peak.

      The real world data does not match their mathematical wet dream.

      Delete
    3. Simon Nicholls, there're some fatal flaws in your arguments, so pls stop being so insulting to the authors of this article:

      1. I realized you're talking about "COVID-19" mortality, a very unreliable yardstick with also questionable classification (few really die of covid if they were otherwise healthy enough). It doesn't capture mortality caused by or facilitated by the vaccines. What truly matters is the all-cause mortality, a point these authors emphasized in their previous article. https://probabilityandlaw.blogspot.com/2021/09/all-cause-mortality-rates-in-england.html

      2. Now having looked at your blog article (which doesn't allow comments, why afraid of having your errors pointed out there?), it's clear your "1/40th" mortality of the vaxxed vs. unvaxxed at initial rollout stage, refers to the 2 dose vaxxed, and refers to the "COVID mortality". But vast majority of the deaths reported to VAERS occurred within a week of any dose. As the above linked article showed, the age-standardized all-cause mortality rate of the >21 days 1 dose group has been several times that of the unvaxxed since late spring. This means many people got bad reactions from first dose, refused the second dose, kept on dying at higher rate, but the 2 dose group are now purged of the people who're most susceptible to the vaccines' adverse effects, and therefore you see a lower all-cause mortality in that group, which is an artifact of the selection of the fittest, on top of the statistical illusion from the rollout process that's discussed in this article.

      3. Previous waves of deaths were caused by:
      A) midazolam + morphine, Do Not Resuscitate orders, ventilators, denial of nourishment & water, etc. in many care homes and hospitals, by NHS guidelines, similar to some NY City hospitals and nursing homes (they used remdesivir for their poison). Countries all had a synchronous mortality peak immediately following the WHO pandemic announcement. https://www.researchgate.net/publication/341832637_All-cause_mortality_during_COVID-19_No_plague_and_a_likely_signature_of_mass_homicide_by_government_response

      B) the lockdown and other measures that caused immense economic, social and emotional trauma in the most vulnerable. In most US states, there was NO FIRST WAVE, No excess mortality until the fall of 2020, despite huge events in spring 2020 like BLM protests, riots, etc. There was no pandemic, only govt measures causing death waves. https://www.researchgate.net/publication/355574895_Nature_of_the_COVID-era_public_health_disaster_in_the_USA_from_all-cause_mortality_and_socio-geo-economic_and_climatic_data

      Delete
    4. It's really not so difficult to understand if you put aside the snark. Because the vaccinated population is growing, delaying the report date and plotting it against current vaccinated figures artificially inflates the denominator, and effect that gradually diminishes over the period to produce a sigmoid curve.

      Conversely, the unvaccinated deaths are always plotted against a denominator that is too small, an effect that peaks when the vaccination rate peaks.

      Plot it shifted and unshifted for yourself and you'll see it quite clearly.

      Delete
  28. Yes, it's true that when you compare proportional rates but shift them back in time, it makes an expanding group skew lower, and a shrinking group skew higher. And as the shrinking group approaches zero it skews very high. So you have correctly shown something interesting, that the vaccine provides a "placebo" reduction in deaths from "non-covid causes". But that's correct, since the vaccine is a placebo against things other than covid! The line here "Here we show other-than covid mortality to remove the virus signal." is doing all the work for you. Analysis of the vaccine's effectiveness to prevent death from a disease is not possible if you ignore the data of people dying from the disease..... Very weak...

    ReplyDelete
    Replies
    1. Callum Moffat, what you said is correct. But I have now used the same latest dataset from England (ref 1 above), and charted for each age group separately, the ALL-CAUSE mortality rate per 100K people for different vaccination status. If the jabs are to help saving lives, the vaxxed SHOULD have done better than in the placebo model shown here. Yet, for every age group, the vaxxed generally did worse, despite this skewing due to the rollout dynamic helping to make the vaxxed groups look better. I will write it up soon and post a link here.

      Delete
  29. Does it matter for this analysis that the vaxxed are more prone to dying from Covid than the avrage person because the most fragile are vaxxed first?

    ReplyDelete
    Replies
    1. That is a concern in reality but is separate from the example. The primary issue with the example in this blog post is that it belabors a trivial mistake that government statisticians could hypothetically have made on a very bad day, without providing any evidence that they in fact did.

      Delete
    2. The authors DID provide evidence for this illusion being employed by the UK's ONS dataset. See the excel spreadsheets for yourselves. The ONS calculated age-specific all-cause mortality rate per 100K people, using precisely this methods of (deaths in a certain week) divided by (population with that vaccination status in that week). Even though they say date-of-death is used (so assuming delayed death registration is not involved here), the same illusion is completely inherent in this way of calculation because deaths caused by the vaccination don't usually happen on the day of vaccination.
      https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

      Delete
  30. Thanks for demonstrating what can go wrong when someone is bad in statistics.

    Let me ask some questions.

    When you know there is a time lag between population count and death reporting of one week, why don't you simply divided the death of the current week by the population the week before. You would get the correct mortality from the first table.

    This is common practice when estimating the CFR. Because people die in the mean 14 days after infection you get a better guess, when you divide the current deaths sum by the sum of cases 14 days before.

    AFAIK, these corrections are common practice in Germany.

    Why do you calculate only the mortality of one week? If you calculate the time over risk from the beginning, you would get much better and stable results at any point of time.

    Even with an unknown time lag the results would be near to the mortality of 15 / 1000000. You would see after a few weeks that the placebo does not work.

    AFAIK, this is the common approach in Phase 3 vaccine studies.

    Best regards and thanks for your answer in advance.

    ReplyDelete
    Replies
    1. The corrections you mention are common practice everywhere. That renders this blog post slightly mysterious.

      Delete
    2. Please show an example where the current COVID vaccine efficacy is demonstrated after having employed this "common practice" correction. Also, is there any study that found efficacy with all-cause mortality, not just "covid mortality"? The clinical trials data only examined COVID illness & mortality, ignoring the rest.

      Delete
    3. Sorry, that 's not how it works. If the bloggers want to claim that this beginner's mistake was made, it's on them to provide some evidence. Happy to respond again if they do.

      Delete
    4. real world evidence:

      US:
      https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/

      UK:
      https://twitter.com/theotherphilipp/status/1460662778201612293?s=20

      Germany:
      https://twitter.com/ReginaLouf/status/1461325574073372680?s=20

      Delete
    5. The bloggers DID show that it's the UK government that made this "beginner's mistake" in their release, which the bloggers simply plotted out in Figure 2 - the bloggers didn't calculate the mortality rate, they used the mortality rate the government provided, which according to the government's own explanation, is calculated exactly this way, making the "beginner's mistake".

      And this is why Bill Gates told us in a 2015 publicity video, to read the book "How to Lie with Statistics". They think they've disclosed it, it's your own fault if you don't catch on.

      Delete
  31. How do you actually define/calculate mortality rates? Let's look at table 2, week 2: 1 death, 9999 population, that would be 1/9999 *100.000= 10 ,yet you report 7,5. Week 3: 1 death, 19999 population, that would be 1/19999 * 100.000=5, yet you report 7,5 in your table. Something is wrong here.

    ReplyDelete
    Replies
    1. Grandcru

      To get the right death figures at 15/100K its done by excel formula. He formatted the death cells to show no decimal places. The actual figure in week 2: 1 death is actually 0.75 behind the scenes and that is the value that Excel is using to get to 7.5

      Delete
  32. Most interesting post.

    To the authors; you ask : »If this is not a statistical illusion how is it possible that the unvaccinated are dying from non-covid causes at a higher rate than vaccinated? In a recent study, CDC managed to find: that the vaxxed are 34% less likely to die of non-Covid cause vs. the unvaxxed (same cause). If your pivot sentence, that drives this post and thus, the efficacy of its results in the midst of anti v. provax (cult) World War: »Here we show other-than Covid mortality to remove the virus signal«, could have been understood as:_ »vax a placebo« - as to the non-Covid deaths » ...well, here's roughly 50% of yor answer.

    The vaxx'd start roughly 1/3 higher from the get-go. Hence, the VE starts @66%; fully, mind you, detached from any Covid & its Covid-related efficay. Purely from the non-Covid related variables (that do confound) in both cohorts (as does age). And also comorbidty. Therein lies the other »special«-one, and it is ranging from 10-14-21 (who knows , plus individuals are well, »individual«) days post mrna jab, no. 1 (TLRs?). Here, any data generating model should take into its architectural account, the new epidemic-spreading vector, that these people t represent. To cases, hospitals, ICUs & deaths, later on. Inoculating all the 1st mrna jabs (even as if: the boosters) in the midst of the high Covid prevalance period – highly enahances this »brand new« spready vector (from 1,4-2x; sc Danish study) of the »epidemics«. So, here's another part; a major one !

    ReplyDelete
  33. @Zhou: its not the »delay between injection and dying« or »jab & the registration of death« so much; In fact its the introduction of these brand »new spreading vectors» (and consequently cases, and hospitalizations, ICUS and then: deaths, not necessarly : its own ones :) that doest that. & its higher xactly when the prevelance of Covid is high (...Germany next) . Thus: amplifying the ...»demics«. & consequently: deaths. That one, I suggest, is far greather. & that in turn allows for even« moar efficient« introduction of the heavier segregation »tools« on the unvaxxed population; Sold-on to the masses as »the true fight for the EU democracy«.

    Also don't confuse the trial with the real life, as the eagle says. Or the ONS ;) Wait, what? mr. Eagle; was that in fact: done in these trials? Or just the non-Warp ones ?

    ReplyDelete
  34. mr Nicholls : when you say that: »the biggest fraud of this last 2 months is comparing the vaxxed to the unvaxxed, when the process of vaxxination whittles the unvaxxed down to mostly those that know they've had it ....« you either do not pay attention @all or @least, must have forgotten adding this essential waiver .....«and are batshit stupid/crazy!«. Namely, the last few months were mostly about »translating« those »who had it«, as you put it, into the ...vaccinated cohort.
    @ VE = 19* that is; *from the preprint of the Pfizer-BT »Six Month Safety and Efficacy of the BNT162b2 mRNA COVID-19 Vaccine«. (e.g.: less than 50, forgotten by the FDA and now forced by theCDC on those unvaxxed who »had it« nontheless ;).

    Also, from the same source, coupled with the page 23 of the FDAs latest » Summary basis for regulatory action« it follows: that the »all cause mortality« is 21 vaxxed v. 16 unvaxxed, 6 months after ...

    ALL'cause appears to be the same. Give or take.

    ReplyDelete
  35. Dieter«: Almost all of your arguments can be explained by the Delta's lower mortality rate. In other words, while »effectiveness to prevent death from a disease is not possible if you ignore the data of people dying from the disease« holds watter - the reverse is true too. Namely, »the effectiveness« to cause death (or injury) from the vaxx is not possible (to assess) if you ignore that the dead were in fact vaxxed and/or caused the unvaxxed and the other vaxxed to die. Later on.

    On a conditionally -approved FDA license.

    ...Since Dose 2 (3 now) + another 14 days to flatten, aren't fully out yet.

    ReplyDelete
  36. @UK: where have all your N-ab's gone ??? Asking for a friend. He is under the impression, that that problem is a separate one (from this »illusion«).

    ReplyDelete
    Replies
    1. Seems like N-ab's are attenuated by the vax due to immune response reprogramming to S-ab's.
      Seems like it won't come back even after infection.

      Page 26 and 29:
      https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1034383/Vaccine-surveillance-report-week-46.pdf


      Seems like infected without vax build 80% N-ab's:

      Vaccinated participants with a breakthrough had detectable anti-S antibodies, as expected post vaccination.

      Notably, only 6/23 (26%, 95%CI: 11–49) had detectable anti-N antibodies in response to their infection, compared to 663/812 (82%, 95%CI: 79–84) of Unvaccinated infections

      https://www.journalofinfection.com/article/S0163-4453(21)00394-7/fulltext

      Delete
  37. Vaxx ARR is less than 0,5%. & NNV moar than 216. The wtg , no ?
    Hope that helps.

    ps
    to the person who wrote: »What would be the numbers if unvaccinated would take real placebo instead of nothing. Then we would see the truth«...

    Many many thanxx !!!
    LMAO & ROTFLd too.

    ReplyDelete
  38. So I asked other statisticians on Twitter about this (as I myself have no clue about these things) and they convincingly explained to me that what is explained here is full on basic knowledge and that this effect is most certainly considered in practice. So it seems to be a theoretical problem which has no practical relevance. It is the responsibility of the authors to prove this mistake is indeed maliciously done by statisticians all around the world. A good indicator of why this effect is actually not taken place is that in Germany in summer where vaccination rate was very steep, the artefact should have presented itself the clearest, but it didnt at all.

    ReplyDelete
    Replies
    1. How about this case: https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/index.html

      Delete
    2. When the vacation rate is steep, the prevalence is low. R0 less than 0. No Amp. If one tries to climb the S (rollout) with Mrna no 1 (panic, case-rise, boosting after AZ, JJ) under high prevalence, the deaths rise. Amp.

      The vacation rate however, is low.

      I do refrain from any comment on the ”burden of proof” the same way your German-twitter friends should refrain from skiing the slopes (this coming winter).

      Delete
    3. What Egal says. The bloggers wildly conjecture that a beginner's mistake was made but do nor provide a shred of evidence. Why they willfully damage their reputations will probably remain their secret. The CNN piece linked by another anonymous commenter above is unrelated.

      Delete
    4. Egal, those statisticians either are lying, or they haven't bothered to check the government released official statistics, where this exact trick is used to create the illusion. See the UK's ONS dataset (excel spreadsheets) for yourselves. The ONS calculated age-specific all-cause mortality rate per 100K people, using precisely this methods of (deaths in a certain week) divided by (population with that vaccination status). Even though they say date-of-death is used (so assuming delayed death registration is not involved here), the same illusion is completely inherent in this way of calculation because deaths caused by the vaccination don't usually happen on the day of vaccination.
      https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

      Delete
    5. lol. the effect is observed in germany:
      https://twitter.com/ReginaLouf/status/1461325574073372680?s=20

      Delete
    6. The fact that the signal is present in the data falsifies the excuse. We know that the quality of data-science and modelling has been absolutely abysmal from the start, why give the benefit of the doubt now? Regulatory officials have been doing nothing *other* than making obvious mistakes and failing to rectify them.

      Delete
  39. Last, not least: as for »we'd be having cases and deaths far higher than in previous waves” I presume that means “from-Covid” and disregards the rising hospital occupancy, ICUs and deaths from all the non-Covid causes (including deaths from the brand new CDC disease that is “Covid-like but PCR negative”, enhanced CVDs & neurologic disorders + deaths from some of those diseases when the body’s natural defense system can’t tell the difference between your own cells and foreign cells, causing the body to mistakenly attack its own normal cells, that shall not be named). Also, early treatment & variants.

    Given the weights in both from-Covid and non-Covid contributions to the all cause mortality, one could easily not see all the cases and all the deaths from the one and the only public health intervention - whose relative efficacy might vane to less than advertised, be illusionary high from the start, is in fact operating at the end of the long tail @ its mighty 0,8% ARR - into the latter bracket.

    Also, I presume (from contract tracing), that the author is not Austrian or German. To the former I offer sincere congrats for their lockdown of the unvaxxed, under the extending 2g system for the new, breakthrough record. Really. I guess the from-Covid ICUs are still down (yoy), tho the occupancy of all the non-Covid (same) ICUs beds must be fairly high. Full lockdown next (boost the non-Covid deaths).
    … Rinse, repeat.

    ReplyDelete
  40. … enhance (the virus, through S-spike mutation). Judging from the Gompertz-German (under 2g) curve, the next fully vax-evading, fittest variant could easily come from continental EU. In that case, VE flips sub-zero. That-then turns all the QR-holders into brand new tinder wood. A huge pile.

    Now that would fit “concern”.

    ReplyDelete
  41. This is german data. How does this look to you?
    https://i.postimg.cc/bvLKy2Mc/how-to-lie-with-statistics.png

    ReplyDelete
    Replies
    1. Source? And did the German media or the authorities present the hospitalization rates as used in this graph? If so, would be very useful to use as evidence that they're actively using this trick too, same as in the England mortality dataset the ONS released (where they're the ones that calculated mortality rates per 100K that utilized this illusion). https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsbyvaccinationstatusengland

      Delete
    2. Yes, this is the official data from the government (RKI)
      Sources:

      Hosp. (Page 26)
      https://rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Situationsberichte/Wochenbericht/Wochenbericht_2021-10-28.pdf%3F__blob%3DpublicationFile&ved=2ahUKEwjnw6jrh6L0AhWGqaQKHe28BfsQFnoECAMQAQ&usg=AOvVaw2NIHq7QOJAiPpC1mjyK61H

      Share population vaccinated
      (Metric: people fully vaccinated, Germany)
      https://ourworldindata.org/covid-vaccinations

      Delete
    3. all german data show the peak around week 34/35 and they changed the method of calculation from week 38 onwards (refers to not counting unvaccinated in the same group as people with unknown status but stays vague)

      Delete
    4. Anonymous: thanks. The percentage by age of FULLY vaxxed in Germany is also in the German link you posted, on page 20. But the more interesting is the percent remaining UNVAXXED (which I don't see in either link you posted), which is probably very low for most age groups except the young (in the UK, only 3-5% of over 60 y.o. remained unvaxxed by Sep 24), and we know that people who are seriously ill are contraindicated for vaccination, so the small residue unvaxxed group is enriched of these sick people, explaining some of the apparent higher mortality rate of the unvaxxed.

      Delete
  42. Sorry, may be wrong, i tried to rebuild the excel sheet. But how did you calc the mortality rate cols?
    for example Table 1 : (vaccinated) 1 death per 5000 vacc. result to mortality rate 15, but (1/5000)*100000 = 20 .
    Sekond line 1 death per 9999 vacc shows mortality 15, but(1/9999)*100000 =10 ?

    ReplyDelete
    Replies
    1. The total mortality always sums to 150 and the "vaccine" is a placebo, so the total deaths is just the proportion of the population in each pool times the 150. The rate is then the number of deaths in each pool divided by the population (times 100k).

      Delete
  43. This comment has been removed by the author.

    ReplyDelete
  44. The simulated scenario in the contribution “Is vaccine efficacy a statistical illusion ?” is interesting and noteworthy, but it does not give a valid account of the empirical data on vaccine efficacy in the context of Covid-19. Several points of criticism on the authors’ methodology and assumptions have already been pointed out in the previous discussion, and here I want to summarize and explain some key issues and misconceptions:

    (a) First, it is true that changing proportions of groups over time (in the scenario: increasing rate of the vaccinated group and decreasing rate of the unvaccinated group) lead to statistical artifacts in the case of delayed effects (in the scenario: delayed death) if the corresponding bias is not controlled for. The authors have nicely demonstrated this source of potential artifacts in their simulation, and it is important to consider such sources of bias in the analysis of epidemiological and pharmacological data.

    (b) However, the simulated scenario does not match the structure of empirical data on mortality rates in the context of the Covid-19 pandemic and the roll-out of vaccines. In the simulation, the potential artifact (i.e., biased estimate of vaccine efficacy) is largely exaggerated by the arbitrary choice of parameters that do not reflect the real situation. The authors vastly overstated the speed of vaccination per time unit (called “week” in the simulated scenario) in combination with an extremely high mortality rate. As a consequence of the unrealistic parameter settings, the simulated overestimation of vaccine efficacy appears very large, but it does not account for the real situation:
    In most industrialized countries, the vaccination rates have reached a rather static state, so that groups of vaccinated and unvaccinated individuals can be compared that have built up over the previous months and that currently show little change. As a result, the potential source of bias (i.e., overestimation of vaccination efficacy due to changing proportions in the face of delayed mortality) persists and needs to be considered, but it is very small and does not outweigh the observed differences in the mortality rates between vaccinated and unvaccinated individuals.

    (c) To illustrate, consider the situation in Germany in the time period from week 40 to week 43 this year (i.e., 4th October-31st October). In this time period, the proportion of vaccinated individuals in the population increased by 1.9%. If we follow the authors’ rationale of a placebo vaccine and assume identical infection and relative mortality rates for vaccinated and unvaccinated individuals in the given period, we find a rate of mortality that is spuriously larger for unvaccinated individuals by a factor of 1.0896. Put differently, under the hypothesis that there is no true vaccine effect and if we do not control for the small change in group sizes, unvaccinated individuals appear to be 1.09 times as likely to die of a Covid-19 infection as vaccinated people (i.e., an illusory increase by 9%). Empirically, in the same time period the mortality rate was more than 10 times as large for unvaccinated adults than for vaccinated adults of age 18-59 (i.e., real increase by more than 900%) and about 4 times as large for unvaccinated adults than vaccinated adults older than 59 (i.e., real increase by ca. 300%). Hence, when we take into account the real but small effect of changing group proportions, a large difference in mortality risk persists.

    To conclude, the authors’ simulation demonstrates an existing source of potential bias in estimating vaccine efficacy, but this bias can easily be controlled for and does NOT explain the empirical effect of vaccine efficacy. The interpretation suggested by the authors and some of the discussants, that empirical findings on vaccine efficacy in the context of Covid-19 can be attributed to the simulated statistical illusion, is therefore wrong and severely misleading.

    ReplyDelete
    Replies
    1. (b) real world data:

      US:
      https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/

      UK:
      https://twitter.com/theotherphilipp/status/1460662778201612293?s=20

      Germany:
      https://twitter.com/ReginaLouf/status/1461325574073372680?s=20


      (c) Germany

      every rate in favour of the vaccinated peaks around week 34-35 right when the vaccination uptake begins to plateau. after this point, the risk for the unvaccinated vanishes and the risk for the vaccinated increases, it seems.


      RKI changed the way they count all cases in week 38 and this messed up the table as all rates keep rising after that.
      (there is still a huge part of people that is counted as "no status available" which is not documented well)

      Delete
    2. Dear Anonymous, as elaborated in my post above, a huge difference in mortality rates between vaccinated and unvaccinated individuals persists after week 34-35 in Germany, that is, after the relative plateau was reached. My computation refers to weeks 40-43 and shows a much larger mortality rate for unvaccinated individuals even when the "statistical illusion" is considered.

      Delete
    3. Hi, MT; one question: how many vaccinated and how many unvaccinated Germans (absolute numbers) have died (all cause) in the same period ?

      Thank you in advance.

      Delete
    4. MT, the mortality rate and every other rate indicating vax efficacy is decreasing after week 34-35, when uptake slows down

      There was very little uptake in weeks 40-43, speed didn't change, and rates kept decreasing just like in the blog examples.

      You have to look at the points where there is continuously high uptake or a change in speed of uptake.

      All german rates look exactly like in the blog example

      Delete
    5. MT: 1. you need to provide a link when you claim actual empirical data, so it can be verified. Unreasonable to expect everyone to try to hunt it down for themselves or to take your word for it.

      2. You made a mistake so your conclusion is incorrect. If indeed "In this time period, the proportion of vaccinated individuals in the population increased by 1.9%", then all this means is that the mortality rate calculated for the VACCINATED is 1.9% lower than it should be, if no correction is done. But how big the distortion of the mortality rate of the UNvaccinated is compared to its true value, needs to be determined by the percentage of change relative to the UNvaccinated population size. And since this is late in the rollout, as the two professors here illustrated nicely, the smaller the remaining UNvaccinated population is, the bigger the artificial inflation of their calculated mortality rate. If the vaccinated population is already the majority, then 1.9% of that population translates to a much higher percentage of decrease of the UNvaccinated population. Therefore, the UNvaccinated mortality rate is inflated much more than 1.9% relative to its true value. Now, the artificial difference expected between the two groups will be 1.9% PLUS whatever larger percentage change is for the UNvaccinated. This could easily be 10 times difference.

      Delete
  45. In addition to this form of confounding, the big reason observational vaccine studies can never work for all-cause mortality is confounding by contraindication. Sicker people avoid vaccines the most. I've modeled this in vaccine-autism studies. The effect is huge. All the relative risks are off by like a factor of 1.5 at least. This is partly why flu vaccine studies have historically shown 50% drops in mortality. Turns out that vaccine avoidance in the elderly is a predictor of death. The CDC lately put out a study saying vaccinated have lower non-covid mortality, with the "effect" being greater for 2 doses than 1 dose. Not only do sick people shy away more from vaccines, but people who are prone to adverse reactions also are pretty good at screening themselves. And those who react badly to the first vaccine will avoid the second. Just go look at WebMD reviews of covid vaccines. Plenty of people there learned their lesson well enough after the first dose.

    Folks, be aware of this study which strangely reports negative vaccine efficacy after 210 days:
    https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3949410
    They fail to report efficacy against death after 210 days though. That does not appear to wane (yet). Whether it (death efficacy) wanes in the future and uncovers a grimmer reality is the real question I think.

    ReplyDelete
    Replies
    1. One thing I can't reconcile is that even though efficacy against infection "wanes" in this study, efficacy against death remains steady. Can something like this be reconciled with this blog posts implied hypothesis?

      Delete
    2. Hi David, such confounds are typical of merely observational studies, in which you cannot rule out ddfferential self selection. This is why serious clinical studies use randomized designs that rule out self-selection. This means that confounds in observational studies do not contradict the better interpretable effects that are found in studies with randomized groups.

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    3. Reply to MT: are you not aware that none of the countries set up prospective randomized cohorts for such strictly needed comparisons, even though doing so immediately after the outbreak of an epidemic is an absolute necessity for epidemiological studies according to medical school textbooks?

      Delete
    4. David, did you notice that even though Figure 2 (vaccine effectiveness against symptomatic infection) goes till about 280 days, and the effectiveness is negative from close to 240 days onwards, yet Figure S1 (for severe COVID & deaths) stops at around 250 days? Why are we not shown the last 30 days?

      There's also a comment by the same lady, ReginaLouf (that posted the German graph on the twitter thread someone else posted above), who asked why the data in Supplemental Table 5 was changed (that's the severe illness & deaths table). Interesting.

      Delete
    5. Maggie: Yes, I noticed that same thing. I posted on that thread that I don't see a COI statement on that paper, which I wouldn't ask if they hadn't bizarrely omitted that data. Six months from now the 2-dosers might have some bad news. Thanks.

      Delete
    6. MT: We have zero randomized data other than what Pfizer tells us for 6 months. And now the control groups have been unblinded. And the FDA is fighting FOIA requests and won't release trial data in a timely fashion. Trial isn't trustworthy or particularly useful. Observational studies are no better. Maybe you know that, but the system will believe whatever observational study it wants to and declare all randomized designs unethical for all time.

      Delete
    7. "And the FDA is fighting FOIA requests and won't release trial data in a timely fashion." Make that 55 year, i.e. 2076 before full release complete. https://aaronsiri.substack.com/p/fda-asks-federal-judge-to-grant-it

      Delete
  46. (b) real world data:

    US:
    https://edition.cnn.com/2021/10/22/health/covid-vaccines-death-rates/

    UK:
    https://twitter.com/theotherphilipp/status/1460662778201612293?s=20

    Germany:
    https://twitter.com/ReginaLouf/status/1461325574073372680?s=20


    (c) Germany

    every rate in favour of the vaccinated peaks around week 34-35 right when the vaccination uptake begins to plateau. after this point, the risk for the unvaccinated vanishes and the risk for the vaccinated increases, it seems.


    RKI changed the way they count all cases in week 38 and this messed up the table as all rates keep rising after that.
    (there is still a huge part of people that is counted as "no status available" which is not documented well)

    ReplyDelete
    Replies
    1. Dear Anonymous, as elaborated in my post above, a huge difference in mortality rates between vaccinated and unvaccinated individuals persists after week 34-35 in Germany, that is, after the relative plateau was reached. My computation refers to weeks 40-43 and shows a much larger mortality rate for unvaccinated individuals even when the "statistical illusion" is considered.

      Delete
    2. MT, the mortality rate and every other rate indicating vax efficacy is decreasing after week 34-35, when uptake slows down

      There was very little uptake in weeks 40-43, speed didn't change, and rates kept decreasing just like in the blog examples.

      You have to look at the points where there is continuously high uptake or a change in speed of uptake.

      All german rates look exactly like in the blog example

      You have to look at the points where injections start, keep growing and slow down and not at the points where there is no uptake anymore

      Delete
    3. Hi Anonymous. The "points where there is continuously high uptake or a change in speed of uptake" can illustrate the potential spurious effect. But time periods in which the rates of vaccinated and unvaccinated individuals reach an approximate steady state allow us to estimate vaccination efficacy where the potential spurious effect is very small, and close to negligible. And, most importantly, randomized clinical studies in which groups of vaccinated and unvaccinated participants are created a priori and compared over a pre-defined time interval are free from the spurious effect of changing base-rates.

      Therefore, periods with fast changes in vaccination rates are good to demonstrate the potential spurious effect, as reflected in the authors' simulation. But periods with rather constant rates give an unbiased view on vaccination efficacy. For a period with a rather steady state (e.g., week 40-43 in Germany) the difference in Covid-19 mortality between unvaccinated and vaccinated individuals is much larger than one would expect on the basis of the potential spurious effect alone. Hence, the simulated statistical artifact does not explain the empirical vaccination effect.

      Thank you for taking the time to consider my previous analysis. Best wishes, MT

      Delete
    4. MT: Pfizer explicitly admitted that their pre-rollout clinical trial size was too small, there were too few deaths in both vaxxed & unvaxxed, so no statistically significant difference in COVID deaths or hospitalizations (i.e., those were NOT trial endpoints, only "COVID symptoms" were the stated endpoints of study). In fact, if one looks at the ALL-CAUSE mortality, then the vaxxed group had even slightly higher mortality rate than the unvaxxed.

      As to the point in your second paragraph, I already showed how you've made a big mistake, see my comment above in the other sub-thread: https://probabilityandlaw.blogspot.com/2021/11/is-vaccine-efficacy-statistical-illusion.html?showComment=1637380751616#c2255859063814956741

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  48. Sadly few want to be informed just how they have been conned. Mark Twain was right and it is easier to fool the gullible than to persuade them that they've been fooled. One of the old time showmen said that no-one ever lost money by underestimating the intelligence of the public, but the disappointing thing is that this scam has exposed the total veniality - or more bluntly corruption - of MPS, MSM, NHS, teachers and so on , many of whom must know quite well that things are not as they are presented.

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  49. Anyone knows where to find the previous 5-year average all-cause mortality by week for each age group for England or UK?

    I think one can model a placebo vaccine using the real world COVID vaccine rollout, and show what a placebo cause the mortality curves of each vaccination status to look like due to the rollout speed alone.

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  50. the most beautiful article of the whole pandemic! Translated into Italian. Very good.

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  51. Three questions:
    Question 1:
    Why do the mock curves come back down in 1 to 2 weeks, whereas the real-world curves take many weeks? Perhaps it would be useful to graph some example combinations of the lag bias plus a real VE occurring simultaneously. If we can’t produce bias-containing graphs that look just like some examples of real-world data, then the hypothesis may not stand. For example, VE against infection “wanes” considerably faster than does VE against death (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3949410). If both efficacies were solely due to bias, one would expect the curves to be more identical than they are. That they are not suggests a combination of both real efficacy and bias is present, in at least one of the two types of efficacies.

    Question 2:
    What are some examples of observational vaccine studies that would and would not be affected significantly by such bias?

    Question 3:
    What other vaccines besides covid might such a bias have been overlooked? I would guess for example this doesn’t really affect something like observational flu vaccine studies which typically just have a single far-off endpoint, by which time the bias has washed out. Yes?

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    Replies
    1. Note that the mock curves are graphed on a much shorter time scale; graphed on the same scale they would look even less similar.

      Delete
  52. Prof Fenton: Regarding the trouble you have getting your research published, Peter Doshi at BMJ may be partial to something you produce.

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  53. Probably this is not what is going on. For this to happen day (in this example week ) of death should be assumed as day of report. To say the truth no one do that. There are two distinct columns “day of report” and “day of death”.

    People update the number of death for the past weeks as the new data come.

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  54. Your effect is largely an artifact of a 19-week x-axis for the hypothetical placebo vs a 38-week x-axis for the real world data. Graphed on the same time scale, the orange "unvaccinated" death curves look nothing alike. They would look even less alike if you added back in the deaths attributed to covid. Not surprising, because _prospective_ randomized clinical trials as well as data from many countries show far more than 0% efficacy for the covid vaccines.

    Your mathematical pedigree and acumen is better than mine, and mine isn't shabby (Ph.D., occasional statistical analysis for a leading law firm). Why are you doing this? Is this a subtle way of letting bad actors know that your private risk management firm will prepare all sorts of deceptive charts for a suitable fee?

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    1. Andrew, FYI: "It is important to note that we are not claiming the death reporting is delayed in the ONS data. In fact our work on this is ongoing and we believe that the most plausible explanation is misclassification and underestimation of proportion of unvaccinated."

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  55. yet the peak is there even if larger... and as a physics student I do know a peak is the derivative of a sigmoid shape... so either there is the said error in the reporting... or some other real effects... so unvaccinated would show a larger death counts which correlates with rate of vaccinations... ? in any case these vaccination/vaccination rates are correlated with higher death counts either among vaccinated or unvaccinated...

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  56. Can someone please make a plot of the real-world unvaxxed and vaxxed covid (not non-covid) mortality rates? It is important to see how identical those really are to the non-covid mortality curves. I'll post more thoughts later. There is definitely a lag reporting (or analogous) bias here, despite the long tail.

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  57. dear Dr. Fenton and Neil, thank you for your nice toy model able to explain the reporting lag censorship effect! very fundamental and interesting. So if I understand some of the comments, would something similar happen also in case of no reporting lag, but because of the blank time window (14 days?) during which a fatality is considered unvaccinated anyway?

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  59. https://www.cdc.gov/mmwr/volumes/70/wr/mm7043e2.htm?s_cid=mm7043e2_w
    CDC found similarly. Two-dosers have lower non-covid mortality than than one-dosers.

    "The overall aRR among Pfizer-BioNTech vaccine recipients compared with the unvaccinated comparison group was 0.41 (95% CI = 0.38–0.44) after dose 1 and 0.34 (95% CI = 0.33–0.36) after dose 2 (Table 3)."

    Pretty uniform across age groups. However, the difference doesn't look as pronounced as in ONS data. Not sure why.

    Also note they address "immortal time bias", which seems like a possible cousin to lag reporting censoring.

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  60. https://www.nejm.org/doi/full/10.1056/NEJMoa2114255
    Third booster allegedly increases VE much more sharply than the placebo VE chart Dr. Fenton made. Not sure what to make of that.

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  61. I am no statistician so evidently I am missing something, but wouldn't 1 death per 5000 be 20 deaths/100,000, not 15?

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  62. Thank you for this piece showing
    1. It is easy to create something from nothing
    2. It is not so easy to comprehend this although no higher mathematics at all
    3. It is much more difficult to prove vaccine risk and benefit from real world data than I thought. Thank you for opening my eyes.
    4. We need a process to collect and evaluate mortality data in a way that we gat reasonable results. Do you have one?

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  63. In table 1 & 2 how is column "Cumulative Percentage vaccinated" calculated? I.e. what is the vaccination rate? Why does the population of vaccinated do a little jump from week 15 to 16? 14->15: 984929-984079=850 but 15->16: 986777-984929=1848

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  64. What is the difference between "misclassification" and "underestimation of the proportion vaccinated"? These, along with delayed reporting, are the three possible explanations Dr. Fenton concludes his YouTube video with.

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    Replies
    1. Apologies, his comment on this YouTube video clarifies: "NOTE error at end of conclusions: should say "proportion of unvaccinated underestimated" - not vaccinated". In any case, I still have the same question.

      Delete
    2. The way I understand it: With misclassification he means issues "what is a case" (point 1 on the conclusions slide). The issue with "underestimation of the proportion unvaccinated" is that these numbers are calculated/modeled. If these calcs lead to numbers lower than what is actually the case (underestimation) this would explain some of the artifacts.

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    3. Thanks, that must be what he means. "Misclassification of vaccination status" would have been a redundant point. And "misclassification of alive/dead status" would be a feat. So he must be referring to cases.

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  65. Hi all, is it possible to know if and when the paper will be published on a journal? tx

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  66. MODELLING, the poorest form of science and not even science by any real definition is the curse of our modern age.

    ReplyDelete