[FRIAM] Could this possibly be true?

Thu Sep 16 07:34:17 EDT 2021

Thank you Roger,

Using the numbers from Phizer's report, I did a sort of quick and dirty
manual iteration process to get to the following Monte Carlo testing
conclusion

If:
a) the total death rate of the unvaccinated is 14/22000 (all causes) and
b) a total of 15 out of 22000  (again all causes)  of the vaccinated group
died
Then we can say with a 99% probability that the vaccination does not
increase the total  (again all causes) death rate with more than a factor
of 1.6.

My Python program to do this is as follows:
import random
total_of_tentousand_samples_less_than_16=0
r=1.6 # manually iterate this number until the answer is less than 100,
with 1000 test runs for a probability of 99%
numberList = [0, 1] # 0 = live, 1=dead
for i in range(1000):
  x=(random.choices(numberList, weights=((1-r*14/22000), r*14/22000),
k=22000))
  if( sum(x)<16):

total_of_tentousand_samples_less_than_16=total_of_tentousand_samples_less_than_16+1

print(total_of_tentousand_samples_less_than_16)

# iteration tally:
# with r=1.5 then total_of_tentousand_samples_less_than_16=105
# with r=1.6 then total_of_tentousand_samples_less_than_16=69

Pieter

On Wed, 15 Sept 2021 at 22:26, Roger Critchlow <rec at elf.org> wrote:

> Pieter -
>
> The initial safety and efficacy report was published in the New England
> Journal of Medicine at the end of 2020,
> https://www.nejm.org/doi/full/10.1056/nejmoa2034577, it has smoother
> language and inline graphics.  It also has fewer deaths in the treatment
> group than in the control group, but it is only reporting the first two
> months of the study.
>
> The numbers of deaths reported in the "Adverse Reactions" section of these
> reports will eventually track the expected death rate of the population in
> the trial, and apparently they do, since there is no comment to indicate
> otherwise.   Every clinical trial that tests the safety of a treatment is
> expected to agree with the baseline mortality statistics for the population
> in the trial.
>
> If you see 14 and 15 deaths out of 22000 participants and your immediate
> response is that 15 is bigger than 14, then you should probably stop
> torturing yourself with statistical data.  You're making and agonizing over
> distinctions that the data can never support.  The number of deaths in a
> population over a period of time has an average value and a variance which
> are found by looking at large populations over long periods of time.  In
> any particular population and period of time there are a lot trajectories
> that the death count can take that will be consistent with the long term
> average even as they wander above and below the average.
>
> I append a simple simulation in julia that you can think about.
>
> -- rec --
>
> # from https://www.cdc.gov/nchs/fastats/deaths.htm
> death_rate = 869.7              # raw deaths per 100000 per year
>
> # simulate the action of a 'death rate' on a population of 'sample'
> individuals for 'days' of time.
> # convert the raw death rate to the death_rate_per_individual_per_day, ie
> death_rate/100000/365.25,
> # allocate an array of size sample*days, size coerced to an integer value,
> # fill the array with uniform random numbers.
> # if an array value is less than the death rate per person per day, score
> 1 death.
> # this overcounts because individuals can be scored as dying more than
> once, YODO!
>
> simulate(death_rate, sample, days) =
>     sum(rand(Int(sample*days)) .< death_rate/100000/365.25)
>
> # accumulate an ensemble of death rate simulation results.
> # run 'trials' simulations of 'death_rate' for 'sample' individuals for
> 'days' time.
> # accumulate an array with the number of deaths in each simulation
> accumulate(death_rate, sample, days, trials) =
>     [simulate(death_rate, sample, days) for i in 1:trials]
>
> # check the model: run the simulation with death_rate for 100000
> individuals and 365.25 days,
> # the result averaged over multiple simulations should tend to the
> original death_rate.
> # we report the mean and standard error of the accumulated death counts
> julia> mean_and_std(accumulate(death_rate, 100000, 365.25, 50))
> (868.34, 31.64188002361066)
>
> # That's in the ball park
> # Now what are the expected deaths per 22000 over 180 days
> julia> mean_and_std(accumulate(death_rate, 22000, 180, 50))
> (94.3, 10.272312697891614)
>
> # that's nowhere close to the 14 and 15 found in the report.
> # Probably the trial population was chosen to be young and healthy,
> # so they have a lower death rate than the general population.
> # let's use 14.5 deaths per 22000 per 180 days as an estimated trial
> population death rate
> # but convert the value to per_100000_per_year.
> julia> est_death_rate = 14.5/22000*100000/180*365.25
> 133.74053030303028
>
> # check the model:
> julia> mean_and_std(accumulate(est_death_rate, 22000, 180, 50))
> (14.96, 3.6419326558007294)
>
> # in the ball park again.
>
> # So the point of this simulation isn't the exact result, it's the pairs
> of results that this process can generate
> # let's stack up two sets of simulations, call the top one 'treatment' and
> the bottom one 'control'
> # treatment and control are being generated by the exact same model,
> # but their mutual relation is bouncing all over the place.
> # That treatment>control or vice versa is just luck of the draw
>
> julia> [accumulate(est_death_rate, 22000, 180, 20),
> accumulate(est_death_rate, 22000, 180, 20) ]
> 2-element Vector{Vector{Int64}}:
>  [12, 12, 13, 11, 22, 13, 14, 16, 13, 14, 21, 17, 13, 14, 19, 11, 20, 11,
> 9, 19]
>  [11, 14, 15, 17, 11, 19, 17, 12, 16, 14, 18, 16, 11, 16, 12, 16, 10, 14,
> 17, 13]
>
>
> On Wed, Sep 15, 2021 at 2:25 AM Pieter Steenekamp <
> pieters at randcontrols.co.za> wrote:
>
>> In the Phizer report "Six Month Safety and Efficacy of the BNT162b2 mRNA
>> COVID-19 Vaccine" (
>> https://www.medrxiv.org/content/10.1101/2021.07.28.21261159v1.full.pdf)
>> , I picked up the following:
>>
>> "During the blinded, controlled period, 15 BNT162b2 and 14 placebo
>> recipients died"
>>
>> Does this mean the Phizer vaccine did not result in fewer total deaths in
>> the vaccinated group compared to the placebo unvaccinated group?
>>
>> I sort of can't believe this, I obviously miss something.
>>
>> But of course, there are clear benefits in that the reported vaccine
>> efficacy was 91.3%
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