# BioNTech-Pfizer COVID-19 Vaccine Candidate Efficacy - Part 4

## Nov 18, 2020 · 250 words · 2 minutes read bayesian statistics • biontech • covid-19 • pfizer

Today Pfizer and BioNTech released findings from their latest analysis of their COVID-19 vaccine candidate. The press release is based on more recently available data. There have been 41,135 participants who have received both doses and 170 confirmed cases of COVID-19; 162 cases occurred in the placebo group while 8 cases occurred in the treatment group.

Based on this information, I re-ran the model from my earlier post. The plots below show the posterior distribution for vaccine candidate efficacy and the group probabilities of COVID-19.

## Inference for Stan model: 88c4792d2ae31f0d91937cb65a7a3c38.
## 4 chains, each with iter=6000; warmup=3000; thin=1;
## post-warmup draws per chain=3000, total post-warmup draws=12000.
##
##               mean se_mean    sd      2.5%       50%     97.5% n_eff Rhat
## theta1       0.000   0.000 0.000     0.000     0.000     0.001  9629    1
## theta2       0.008   0.000 0.001     0.007     0.008     0.009  9243    1
## efficacy     0.946   0.000 0.019     0.904     0.949     0.976  9604    1
## lp__     -1026.762   0.014 1.005 -1029.459 -1026.456 -1025.770  5207    1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 18 20:14:19 2020.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).

The vaccine candidate efficacy has a 95% credible interval from 90.4% to 97.6%, which looks quite good. The chance of a confirmed COVID-19 case within the treatment group has 95% credible interval from 0.02% to 0.07%, compared to 0.67% to 0.91% for the control group. Thus the results are looking excellent.