Exact sample size determination for a single Poisson random sample

Classical power analysis for sample size determination is typically performed in clinical trials. A "hybrid" classical Bayesian or a "fully Bayesian" approach can be alternatively used in order to add flexibility to the design assumptions needed at the planning stage of the study and to explicitly incorporate prior information in the procedure. In this paper, we exploit and compare these approaches to obtain the optimal sample size of a single-arm trial based on Poisson data. We adopt exact methods to establish the rejection of the null hypothesis within a frequentist or a Bayesian perspective and suggest the use of a conservative criterion for sample size determination that accounts for the not strictly monotonic behavior of the power function in the presence of discrete data. A Shiny web app in R has been developed to provide a user-friendly interface to easily compute the optimal sample size according to the proposed criteria and to assure the reproducibility of the results.