Yes, I wondered if anyone else enjoyed that as much as I did.

> On Sep 17, 2021, at 1:15 AM, Roger Critchlow <[email protected]> wrote:
> 
> sum(reasons_for_death) != number_of_deaths, and Death itself is listed as a 
> reported cause of death.
> 
> -- rec --
> 
> On Thu, Sep 16, 2021 at 12:01 PM Pieter Steenekamp 
> <[email protected] <mailto:[email protected]>> wrote:
> For what it's worth, from table S4 in the supplementary data 
> https://www.medrxiv.org/content/medrxiv/early/2021/07/28/2021.07.28.21261159/DC1/embed/media-1.pdf
>  
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.medrxiv.org%2fcontent%2fmedrxiv%2fearly%2f2021%2f07%2f28%2f2021.07.28.21261159%2fDC1%2fembed%2fmedia-1.pdf&c=E,1,6VfStpuSzrEd0AAiOsShT0R5D3p6OBIjgLpPVffJphF-rw0GBDmGlU5GWImascp4KtBdoqX7fEevwAFa0itV31yZ6ORM__prytVuyeBn&typo=1>
> 
> Reported Cause of Death       BNT162b2 (N=21,926)         Placebo (N=21,921)  
> Deaths                                                15                      
>                        14 
> Acute respiratory failure                      0                              
>                  1 
> Aortic rupture                                      0                         
>                        1 
> Arteriosclerosis                                   2                          
>                       0 
> Biliary cancer metastatic                    0                                
>                 1 
> COVID-19                                          0                           
>                      2 
> COVID-19 pneumonia                       1                                    
>             0 
> Cardiac arrest                                    4                           
>                      1 
> Cardiac failure congestive                 1                                  
>               0 
> Cardiorespiratory arrest                     1                                
>                 1 
> Chronic obstructive pulmonary 
> disease                                              1                        
>                         0 
> Death                                                 0                       
>                          1 
> Dementia                                           0                          
>                       1 
> Emphysematous cholecystitis           1                                       
>           0 
> Hemorrhagic stroke                           0                                
>                  1 
> Hypertensive heart disease              1                                     
>              0 
> Lung cancer metastatic                    1                                   
>                 0 
> Metastases to liver                           0                               
>                     1 
> Missing                                             0                         
>                           1 
> Multiple organ dysfunction 
> syndrome                                         0                            
>                         2 
> Myocardial infarction                        0                                
>                     2 
> Overdose                                         0                            
>                         1 
> Pneumonia                                       0                             
>                        2 
> Sepsis                                              1                         
>                            0 
> Septic shock                                     1                            
>                        0 
> Shigella sepsis                                 1                             
>                       0 
> Unevaluable event                           1                                 
>                   0
> 
> On Thu, 16 Sept 2021 at 17:37, Frank Wimberly <[email protected] 
> <mailto:[email protected]>> wrote:
> Pittsburgh irony:  Ooh.  Yinz are rill tough.  I'm skeered.  Cf. Kasich, who 
> is from McKees Rocks which is across the river from "dahntahn" Pittsburgh.
> 
> Yinz = "you ones" similar to "y'all" in the South.
> 
> ---
> Frank C. Wimberly
> 140 Calle Ojo Feliz, 
> Santa Fe, NM 87505
> 
> 505 670-9918
> Santa Fe, NM
> 
> On Thu, Sep 16, 2021, 8:41 AM <[email protected] 
> <mailto:[email protected]>> wrote:
> 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.
> 
> Oh I am so glad.  So reassuring*. 
> 
>  
> 
> You guys are scaring the total crap out of us citizens. 
> 
>  
> 
> N
> 
>  
> 
> PS to Frank.  There’s lot’s of irony in Pittsburgh.  I count on you to 
> recognize it. 
> 
> Nick Thompson
> 
> [email protected] <mailto:[email protected]>
> https://wordpress.clarku.edu/nthompson/ 
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson%2f&c=E,1,TyDEVSRIE0SeXH4oUb2NLH72-_MtKz_3q8bY-68jXaX-I6J08KlUumptKiq48nFPVHkWzQKv06aXGvUNpUaCCWg1kX7WnPxaJ7cRF9sE74wro1UffhXjfHYd&typo=1>
>  
> 
> From: Friam <[email protected] <mailto:[email protected]>> On 
> Behalf Of Pieter Steenekamp
> Sent: Thursday, September 16, 2021 7:34 AM
> To: The Friday Morning Applied Complexity Coffee Group <[email protected] 
> <mailto:[email protected]>>
> Subject: Re: [FRIAM] Could this possibly be true?
> 
>  
> 
> 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 <[email protected] 
> <mailto:[email protected]>> 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 
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.nejm.org%2fdoi%2ffull%2f10.1056%2fnejmoa2034577&c=E,1,3vBgbhTMbNvgPkNNCkoG1Di9PyMZ4wdlO_pfzcTwmmrCnsjA4GOZCpQ3jcAwkdDg3MuW6p4TH9Am9S_vCjZ3nwn7L7B-NwD9c48FznmRRZhUg49OGdEewGI,&typo=1>,
>  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 
> <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 <[email protected] 
> <mailto:[email protected]>> 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 
> <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwww.medrxiv.org%2fcontent%2f10.1101%2f2021.07.28.21261159v1.full.pdf&c=E,1,rlz_7kNdzmE-APflnOi4QbkbTnzEjDoF0f6_1hvABs56UG4pARFKFhjcckwqhM3SXoup6y2AdMAq5784aRgbG7Plt64B5sKV2h1El8T4&typo=1>)
>  , 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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