Testing Equality of Treatments under an Incomplete Block Crossover Design with Ordinal Responses

The generalized odds ratio (GOR) for paired sample is considered to measure the relative treatment effect on patient responses in ordinal data. Under a three-treatment two-period incomplete block crossover design, both asymptotic and exact procedures are developed for testing equality between treatments with ordinal responses. Monte Carlo simulation is employed to evaluate and compare the finite-sample performance of these test procedures. A discussion on advantages and disadvantages of the proposed test procedures based on the GOR versus those based on Wald's tests under the normal random effects proportional odds model is provided. The data taken as a part of a crossover trial studying the effects of low and high doses of an analgesic versus a placebo for the relief of pain in primary dysmenorrhea over the first two periods are applied to illustrate the use of these test procedures.