It was a great Nov. 18, 2020 news from the NYTimes' "New Pfizer Results: Coronavirus Vaccine Is Safe and 95% Effective" (Web Page 2020a).

So, we checked on the offical web page from Pfizer (Web Page 2020b): Data demonstrate vaccine was well tolerated across all populations with over 43,000 (43,661) participants enrolled randomizing into 2 arms: vaccine vs placebo; 170 confirmed cases of COVID-19 were evaluated, with 162 observed in the placebo group versus 8 in the vaccine group.

Let's calculate the VE:

• Vaccine efficacy/effectiveness (VE) is measured by calculating the risk of disease among vaccinated and unvaccinated persons and determining the percentage reduction in risk of disease among vaccinated persons relative to unvaccinated persons. The greater the percentage reduction of illness in the vaccinated group, the greater the vaccine efficacy/effectiveness (Web Page 2012).

$$VE = \frac{\text{Risk among unvaccinated group} - \text{risk among vaccinated group}}{\text{Risk among unvaccinated group}}$$

OR

$$VE = 1 - \text{Risk ratio}$$

Thus,

$$VE = 1 - \frac{8/21830}{162/21830} = 1 - \frac{0.037%}{0.742%} = 1 - 0.037/0.742 = 0.95%$$

If we reproduce the trial 100 times, what would happen? Of course, it would not be conducted in the reality, but let's use the statistics:

a = 8; 
n1 = 43661/2; 

c=162; 
n2=43661/2

rr = (a/n1) / (c/n2)

se = sqrt(1/a + 1/c - 1/n1 - 1/n2)

l95 = exp(log(rr)-1.96*se)
u95 = exp(log(rr)+1.96*se)

cbind(1-rr, 1-u95, 1-l95)

##           [,1]      [,2]      [,3]
## [1,] 0.9506173 0.8995941 0.9757121

m = rnorm(10000, mean=log(rr), sd=se)

hist(1-exp(m), xlab="Vaccine Efficacy", prob=T, col="blue", border="white", xlim=c(0.8, 1.0), ylab="Probability", main="Distribution of Simulated Vaccine Efficacy")

So the lowest probability of VE offered was greater than 90%. Excellent !!!

In conclusion, the greatest of a vaccine development is that it produced a vaccine throughout the shortest timeline in history by using the new technology of messenger RNA (Anderson et al. 2020).