Exact sample size determination for the ratio of two incidence rates under the Poisson distribution

We present sample size determination using exact approaches for testing the ratio of incidence rates from a two-arm non-inferiority trial. The first approach is the exact conditional approach by treating the total number of events from two groups fixed, and the other is the exact unconditional approach based on maximization. Exact approaches guarantee the type I error rate which is often not satisfied in the commonly used asymptotic approaches on the basis of the corresponding limiting distributions of test statistics. We provide tables for sample size determination in commonly used cases in practice, and an example is used to show the application of these exact approaches. Sample size comparison using different exact approaches concludes that the exact unconditional approach based on the Wald-type test statistic has good performance in balanced studies.