Contributi,  COVID-19,  Senza categoria,  Statistica

Efficacy = Excess Risk/Risk ratio


10th Dec 2020, New England Journal of Medicine:


“Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine”



Non-cases (randomized)

Covid positive
Vaccinated (dose 2 of BNT162b2)18.5568
Unvaccinated (dose 2 of Placebo)18.530162

“BNT162b2 mRNA Covid-19 Vaccine conferred 95% protection against Covid-19 in persons 16 years of age or older.”



FDA Advisory Committee Meeting on
Pfizer-BioNTech COVID-19 Vaccine

December 10, 2020

Briefing Document (at pag 42)

3410 total cases of suspected but unconfermed Covid-19″

Should ever be mentioned these 3,410 cases in the paper?

“As specified in the protocol, suspected cases of symptomatic COVID-19 that were not PCR-confirmed were not recorded as adverse events unless… seriousness”

Should these suspected cases ever undergo for PCR follow up considering their potentialities of switching to Covid-19 positivity?

“…these data do not raise a concern that protocol-specified reporting of suspected but unconfirmed COVID-19 cases could have masked clinically significant adverse events that would not have otherwise been detected…”

Whereas all the suspected cases had been re-tested for Covid-19, would that have concerned safety or, rather, results?



CDC (Centers for Disease Control and Prevention)

Modified from https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section6.html

E = Efficacy


In the Worst Theoretical Scenario…

Where Risk Ratios would include 3,410 suspected but unconfirmed Covid cases (100% false negative hypothesis)



Covid positive confirmed + suspected unconfirmed
Non-cases
(n. of subjects who received 2nd dose)
Total
Vaccinated8+1,594=1.60218,55620,158
Unvaccinated162+1,816=1.86818,53020,508
Total3,58037,08640,666

Risk of Covid among vaccinated group = 1,602/20,158 = 0.0794 = 7.9% (a)
Risk of Covid among unvaccinated group = 1,868/20,508 = 0.0910 = 9.1% (b)


Risk Ratio* = a/b = 0.0794/0.0919 = 0.86 (86%) indicating that subjects in the vaccinated group would approximately be 4/5 as likely to develop Covid as would subjects in the unvaccinated group.

*If all the suspected unconfirmed cases were included into the 2nd dose group, this would not affect the result, as shown below:
a = 1,602/18,556 = 0,086 and b = 1,868/18,530 = 0,1 a/b = 0,86 = 86%

Vaccine Efficacy (VE)


…the vaccinated group would experience 13% fewer Covid cases than it would have if this group had not been vaccinated.



However, here reviewed the NEJM perspective



Covid pos tested
Non-cases
(pt who received 2nd dose)
Total
Vaccinated818,55618,564
Unvaccinated16218,53018,692
Total17037,08637,256

Risk of Covid among vaccinated group = 8/18,564 = 0.00043 = 0.043%
Risk of Covid among unvaccinated people = 162/18,692 = 0.0086 = 0.86%

Risk Ratio = 0.00043/0.0086 = 0.05 (5%) indicating that subjects in the vaccinated group are approximately 1/20 as likely to develop Covid as are subjects in the unvaccinated group.

Vaccine Efficacy = 0.86-0.043/0.86 = 0.95 (95%)

Confirming a 95% efficacy: therefore consistent with a very high protection.
As expected in this case.



Pfizer reported 170 PCR confirmed covid-19 cases, split 8 to 162 between vaccine and placebo groups. But these numbers were dwarfed by a category of disease called “suspected Covid-19″… We need the raw data…

Peter Doshi, BMJ, January 4, 2021


Further Bibliographic Resources

  1. https://blogs.bmj.com/bmj/2021/01/04/peter-doshi-pfizer-and-modernas-95-effective-vaccines-we-need-more-details-and-the-raw-data/
  2. https://wayback.archive-it.org/7993/20201217213133/https://www.fda.gov/advisory-committees/advisory-committee-calendar/vaccines-and-related-biological-products-advisory-committee-december-10-2020-meeting-announcement
  3. https://www.cdc.gov
  4. https://restoringtrials.org/2020/09/18/covid19trialprotocolandstudydocs/

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