Estimation of the proportion ratio under a simple crossover trial

The proportion ratio (PR) of patient response is one of the most commonly used indices for measuring the relative treatment effect in a randomized clinical trial (RCT). Assuming a random effect multiplicative risk model, we develop two point estimators and three interval estimators in closed forms for the PR under a simple crossover RCT. On the basis of Monte Carlo simulation, we evaluate the performance of these estimators in a variety of situations. We note that the point estimator using a ratio of two arithmetic means of patient response probabilities over the two groups (distinguished by the order of treatment-received sequences) is generally preferable to the corresponding one using a ratio of two geometric means of patient response probabilities. We note that the three interval estimators developed in this paper can actually perform well with respect to the coverage probability when the number of patients per group is moderate or large. We further note that the interval estimator based on the ratio of two arithmetic means of patient response probabilities with the logarithmic transformation is probably the best among the three interval estimators discussed here. We use a simple crossover trial studying the suitability of two new inhalation devices for patients who were using a standard inhaler device delivering Salbutamol published elsewhere to illustrate the use of these estimators.