Power and sample size requirements for tests of differences between two Poisson rates

The statistic (y−x)/(y + x)1/2 is often used as an approximate test for comparing two Poisson observations. When x and y come from different sized sampling frames, a uniformly most powerful unbiased (UMPU) test is obtained using the binomial distribution of the conditional distribution of y given x + y. Shiue and Bain showed that a test based on the normal approximation of the binomial distribution is nearly as powerful as the UMPU test and presented power and sample size formulae. Here we present an alternative test and show that, when the Poisson rate is greater for the larger sampling frame, it has higher power than the Shiue and Bain test. Power and sample size formulae are given.