Bayesian inference on the ratio of two Poisson rates.
Suppose you have two counts of events and, assuming each count follows a Poisson distribution with an unknown incidence rate, you are interested in the ratio of the two rates (or relative risk). The brr package allows to perform the Bayesian analysis of the relative risk using the natural semi-conjugate family of prior distributions, with a default non-informative prior (see references).
You can install:
install.packages("brr")github using the devtools package:devtools::install_github('stla/brr', build_vignettes=TRUE)Create a brr object with the Brr function to set the prior parameters a, b, c, d, the two Poisson counts x and y and the samples sizes (times at risk) S and T in the two groups. Simply do not set the prior parameters to use the non-informative prior:
model <- Brr(x=2, S=17877, y=9, T=16674)Plot the posterior distribution of the rate ratio phi:
plot(model, dpost(phi))Get credibility intervals about phi:
confint(model)Get the posterior probability that phi>1:
ppost(model, "phi", 1, lower.tail=FALSE)Update the brr object to include new sample sizes and get a summary of the posterior predictive distribution of x:
model <- model(Snew=10000, Tnew=10000)
spost(model, "x", output="pandoc")Look at the vignettes:
browseVignettes(package = "brr")Please report at https://github.com/stla/brr/issues
S. Laurent, C. Legrand: A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials. ESAIM, Probability & Statistics 16 (2012), 375--398.
S. Laurent: Some Poisson mixtures distributions with a hyperscale parameter. Brazilian Journal of Probability and Statistics 26 (2012), 265--278.
S. Laurent: Intrinsic Bayesian inference on a Poisson rate and on the ratio of two Poisson rates. Journal of Statistical Planning and Inference 142 (2012), 2656--2671.