Mid-p confidence intervals for the poisson expectation

Conventionally a confidence interval (CI) for the standardized mortality ratio is set using the conservative CI for a Poisson expectation, μ. Employing the mid‐P argument we present alternative CIs that are shorter than the conventional ones. The mid‐P intervals do not guarantee the nominal confidence level, but the true coverage probability is only lower than the nominal level for a few short ranges of μ. The implications for mid‐P confidence intervals of various proposed definitions of two‐sided tests for discrete data are discussed.