In R I am having a problem obtaining exact confidence intervals for the rate ratio as calculated by the poisson.test function. This function uses the method in binom.test to calculate the confidence limits between two rates e.g.
poisson.test(x = c(10000,20000), T = c(15000,15000), r = 1, conf.level = 0.95)
This works fine when x (events) is lower than T (observations). However, at very high x (events) and relatively low T (observations), the variance of the Poisson distribution will approach infinity. This is not accounted for in the poisson.test function, as the binom.test method has no such limits. Consequently, with a progressively higher event rates, the confidence interval of both the individual rates and the ratios of these rates become progressively narrower, while they should asymptotically widen.
Would anybody know an alternative way to test the ratio of two very high rates using the Uniformly Most Powerful method and obtain their correct confidence limits?
