#Statistics rant follows - feel free to tune out.
The Vaccine Efficacy scale is one of the silliest scales in the whole #epidemiology. Formally it is just 1 - RR (relative risk), and while the RR is a personal fav of mine when comparing event rates, the 1 - RR is an idiotic Frankestein for the following reasons ....
1. If one uses a model (such as a Poisson or Neg Binom #GLM) to compute it, then one is fitting a non-canonical scale to often small datasets; under these circumstances all the standard central limit theorems lose their typically fast convergence rates and you run the risk of your inference being a hot pile of numerical garbage unless ofc you have an unrealistically huge sample.
Those who have delved in the original GLM lit will continue to shiver, knowing the numerical mathematics of finite differencing when computing the Hessians which give you the standard errors (and the confidence intervals) for the estimates.
2. If you forego a model and use something like a bootstrap , please hit the mathematical lit to see why you end up fitting the same model as 1 with perhaps some (small) protection of the original numerical sin of not fitting the model in the canonical scale
3. If somehow you are able to survive the wrath of the malformed geometry of non canonical GLM links, you have to consider the #psychology of reporting a negative value for a number that a non-technical audience expects to be positive. A technical person will object that the RR will be over unity in this case, so subtracting the RR from one provides the same information , but this misses the psychological aspects of interpretation of numerical quantities.
