Unequal allocation of sample/event sizes with considerations of sampling cost for testing equality, non-inferiority/superiority, and equivalence of two Poisson rates

Abstract For non-inferiority/superiority and equivalence tests of two Poisson rates, the determination of the required number of sample sizes has been studied but the studies for the number of events to be observed are very limited. To fill the gap, the present study first is aimed toward determining the number of events to be observed for testing non-inferiority/superiority and equivalence of two Poisson rates, respectively. Also, considering the cost for each event, the second purpose is to apply an exhaustive search to find the unequal but optimal allocation of events for each group such that the budget is minimal for a user-specified power level, or the statistical power is maximal for a user-specified budget. Four R Shiny apps were developed to obtain the number of events needed for each group. A simulation study showed the proposed approach to be valid in terms of Type I error and statistical power. A comparison of the proposed approach with extant methods from various disciplines was performed, and an illustrative example of comparing the adverse reactions to the COVID-19 vaccines was demonstrated. By applying the proposed approach, researchers also can estimate the most economical number of subjects or time intervals after determining the number of events.