Analysis of Poisson frequency data under a simple crossover trial.

When the frequency of occurrence for an event of interest follows a Poisson distribution, we develop asymptotic and exact procedures for testing non-equality, non-inferiority and equivalence, as well as asymptotic and exact interval estimators for the ratio of mean frequencies between two treatments under a simple crossover design. Using Monte Carlo simulations, we evaluate the performance of these test procedures and interval estimators in a variety of situations. We note that all asymptotic test procedures developed here can generally perform well with respect to Type I error and can be preferable to the exact test procedure with respect to power if the number of patients per group is moderate or large. We further find that in these cases the asymptotic interval estimator with the logarithmic transformation can be more precise than the exact interval estimator without sacrificing the accuracy with respect to the coverage probability. However, the exact test procedure and exact interval estimator can be of use when the number of patients per group is small. We use a double-blind randomized crossover trial comparing salmeterol with a placebo in exacerbations of asthma to illustrate the practical use of these estimators.