Notes on estimation in Poisson frequency data under an incomplete block crossover design

For comparison of two experimental treatments with a placebo under an incomplete block crossover design, we develop the weighted-least-squares estimator (WLSE) and the conditional maximum likelihood estimator (CMLE) of the relative treatment effects in Poisson frequency data. We further develop the interval estimator based on the WLSE, the interval estimator based on the CMLE, the interval estimator based on the conditional-likelihood-ratio test and the interval estimator based on the exact conditional distribution. Using Monte Carlo simulations, we find that all interval estimators developed here can perform well in a variety of situations. The exact interval estimator derived here can be especially of use when both the number of patients and the mean number of event occurrences are small in a trial. We use the data taken as part of a double-blind randomized crossover trial comparing salbutamol and salmeterol with a placebo with respect to the number of exacerbations in asthma patients to illustrate the use of these estimators.