Multivariate Analysis of Data From Crossover Clinical Trials

In crossover designs, multiple outcomes are often collected to assess treatment effectiveness in a comprehensive manner. Also, interest has grown in comparing intra-subject variability between treatments in such designs. We present three distinct multivariate linear mixed-effects models, with the choice of the model depending on the design and assumptions regarding carryover effects. We discuss maximum likelihood (ML) and restricted ML (REML) approaches for parameter estimation. For a special case that a crossover design is uniform within sequences, we derive the closed-form expressions for the ML and REML estimators of the variance components. We propose general hypothesis testing methods for the treatment effects and the intra-subject variance matrices. The latter situation has not received much attention in the statistical literature. For the special case, we derive the exact test statistics for treatment means comparisons and for testing the null hypothesis of homogeneous intra-subject variance matrices. Simulation studies are conducted to validate the superior performance of the proposed multivariate approach compared with the usual univariate approach in testing treatment effects. Finally, we apply the methodologies to two data examples.