Design and analysis of intra-subject variability in cross-over experiments

Recently, interest has grown in the development of inferential techniques to compare treatment variabilities in the setting of a cross-over experiment. In particular, comparison of treatments with respect to intra-subject variability has greater interest than has inter-subject variability. We begin with a presentation of a general approach for statistical inference within a cross-over design. We discuss three different statistical models where model choice depends on the design and assumptions about carry-over effects. Each model incorporates t-variate random subject effects, where t is the number of treatments. We develop maximum likelihood (ML) and restricted maximum likelihood (REML) approaches to derive parameter estimators and we consider a special case in which closed-form expressions for the variance component estimators are available. Finally, we illustrate the methodologies with the analysis of data from three examples.