Testing treatment by covariate interactions when treatment varies within subjects

In contrast to the situation when an independent or treatment variable varies between subjects, procedures for testing treatment by covariate interactions rue not commonly understood when the treatment varies within subjects. The purpose of this article is to identify analytic approaches that test such interactions. Two design scenarios are discussed, one in which the covariate is measured only a single time for each subject and hence varies only between subjects, and the other in which the covariate is measured at each level of the treatment variable and hence varies both within and between subjects. In each case, alternative analyses are identified and their assumptions and relative efficiencies compared.