Notes on interval estimation of the proportion ratio under a three-treatment three-period crossover trial

When comparing two experimental treatments with a placebo, we focus our attention on interval estimation of the proportion ratio (PR) of patient responses under a three-period crossover design. We propose a random effects exponential multiplicative risk model and derive asymptotic interval estimators in closed form for the PR between treatments and placebo. Using Monte Carlo simulations, we compare the performance of these interval estimators in a variety of situations. We use the data comparing two different doses of an analgesic with placebo for the relief of primary dysmenorrhea to illustrate the use of these interval estimators and the difference in estimates of the PR and odds ratio (OR) when the underlying relief rates are not small.