Testing the ratio of two Poisson means based on an inferential model

The ratio of two Poisson means is commonly used in biological, epidemiological, and medical. In this article, we consider the problem of testing the ratio of two Poisson means and propose a valid and efficient test based on the inference model (IM). The simulation studies show that the type I error and power of the IM-based test are competitive or even better than the six recommended tests: The likelihood ratio, mid-p, logarithmic transformation, and three tests based on the method of variance estimates recovery (MOVER). For R1, the Rao-MOVER and fiducial-MOVER tests are slightly conservative. The likelihood ratio and logarithmic transformation tests cannot control the type I error well. Therefore, the IM test could be recommended for practical applications. A real numerical example is presented to illustrate the flexibility of the proposed test.