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Inferring vaccine efficacies and their uncertainties.
A simple model implemented in JAGS/rjags

Giulio D'Agostini and Alfredo Esposito

For details: https://www.roma1.infn.it/~dagos/prob+stat.html#vaccini

Abstract:

Taking the cue from the incredibly precise value of the efficacy of Moderna's COVID-19 vaccine candidate broadcasted by the media these days (94.5%, without any uncertainty attached to it, as instead it should always be the case for a scientific result) we try to get the probability distribution of such efficacy with the limited information available. The work has been done with the help of a simple Bayesian Network, processed by a Markov Chain Monte Carlo. The inferred efficacy results $(93.3\pm 2.9)\%$ (mean $\pm$ standard uncertainty) and a 95% credible interval of $[86.6\%,97.6\%]$. We have also processed through the same model the new Pfizer results, claiming a 95% efficacy, getting $(94.4\pm 1.9)\%$ with a 95% credible interval of $[90.0\%,97.5\%]$. The efficacies reported by the two companies correspond indeed to the modal values of the distributions.

“It is scientific only to say what is more likely

and what is less likely”

(R. Feynman)