comparison of statistical tests for crossover designs

In this thesis a comparative study of treatment and carryover effects is performed for five statistical tests as they apply to a three treatment, three period crossover design. These tests are two likelihood based tests, namely, Ordinary Least Squares and Modified F-Test Approximation; two non parametric tests, the one of Bellavance and Tardif (1995) and the other of Ohrvik (1998); and The Generalized Estimating Equations test. This crossover design consists of six possible treatment sequences, (123, 132, 213, 231, 312 and 321) made up of three treatments, say 1, 2 and 3, being assigned to six subjects per group, for n groups. For each sequence, observations are taken for each period following the treatment. The statistical tests were used to determine treatment effects and carryover effects. Data is simulated for group sizes of 4, 8, 12 and 24 subjects per sequence, and different covariance structures. For each simulation, 2000 independent samples were generated and significance tests using the above five methods were carried out. The empirical percentage of Type I error for each test was defined as the proportion of p-values smaller or equal to a specified nominal alpha level. Alpha levels of 0.01%, 0.05% and 0.1% were chosen in this study.