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

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
(n. of subjects who received 2nd dose)

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
(pt who received 2nd dose)

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


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