Subject-treatment interactions in crossover trials: performance evaluation of subgrouping methods

Ghosh and Fairchild (J. Statist. Plann. Inference 88 (2000) 301; In: Sen and Rao (Eds.), Handbook of Statistics 18: Bioenvironmental and Public Health Statistics, North-Holland, Amsterdam, 2000, p. 547.) proposed a model for drawing inference on the subject-treatment interactions in a two-period crossover trial and presented a method of subgrouping subjects in a group. In this paper we present another method of subgrouping for the same purpose of drawing inference on the subject-treatment interactions. This new method is based on a threshold level, a critical adjacent factor (CAF), and a majority rule. We then compare these two methods of subgrouping. Three performance measures are used for our comparison. The first measure is the probability of identifying the correct number of subgroups. The second measure is the probability that a subject is correctly placed in a subgroup under the condition that the number of subgroups has been correctly identified. The third measure is defined for subjects ordered from lowest to highest differences in their responses for two treatments. For the subjects placed into a subgroup by a method, the third measure determines the number of distinct subgroups beyond a single subgroup that these subjects really belong to. Extensive simulations are used for calculating the estimated numerical values of the performance measures and then for comparing the methods of subgrouping.