### A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions $\left(\lambda S\right)$x1d4ab;(λS) and $\left(\mu T\right)$x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. In this paper we...