A semi-parametric approach to the frequency of occurrence under a simple crossover trial

To analyze the frequency of occurrence for an event of interest in a crossover design, we propose a semi-parametric approach. We develop two point estimators and four interval estimators in closed forms for the treatment effect under a random effects multiplicative risk model. Using Monte Carlo simulations, we evaluate these estimators and compare the four interval estimators with the classical interval estimator suggested elsewhere in a variety of situations. We note that the point estimator using the ratio of two arithmetic averages of mean frequencies under a multiplicative risk model can be comparable to the point estimator using the ratio of two geometric averages of mean frequencies. We note that as long as the number of patients per group is large, all the four interval estimators developed here can perform well. We also note that the classical interval estimator derived under the commonly assumed Poisson distribution for the frequency data can be conservative and lose precision if the Poisson distribution assumption is violated. 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.