Testing equality and interval estimation of the generalized odds ratio in ordinal data under a three-period crossover design

The crossover design can be of use to save the number of patients or improve power of a parallel groups design in studying treatments to noncurable chronic diseases. We propose using the generalized odds ratio for paired sample data to measure the relative effects in ordinal data between treatments and between periods. We show that one can apply the commonly used asymptotic and exact test procedures for stratified analysis in epidemiology to test non-equality of treatments in ordinal data, as well as obtain asymptotic and exact interval estimators for the generalized odds ratio under a three-period crossover design. We further show that one can apply procedures for testing the homogeneity of the odds ratio under stratified sampling to examine whether there are treatment-by-period interactions. We use the data taken from a three-period crossover trial studying the effects of low and high doses of an analgesic versus a placebo for the relief of pain in primary dysmenorrhea to illustrate the use of these test procedures and estimators proposed here.