Test Equality between Three Treatments under an Incomplete Block Crossover Design

Under a random effects linear additive risk model, we compare two experimental treatments with a placebo in continuous data under an incomplete block crossover trial. We develop three test procedures for simultaneously testing equality between two experimental treatments and a placebo, as well as interval estimators for the mean difference between treatments. We apply Monte Carlo simulations to evaluate the performance of these test procedures and interval estimators in a variety of situations. We note that the bivariate test procedure accounting for the dependence structure based on the F-test is preferable to the other two procedures when there is only one of the two experimental treatments has a non-zero effect vs. the placebo. We note further that when the effects of the two experimental treatments vs. a placebo are in the same relative directions and are approximately of equal magnitude, the summary test procedure based on a simple average of two weighted-least-squares (WLS) estimators can outperform the other two procedures with respect to power. When one of the two experimental treatments has a relatively large effect vs. the placebo, the univariate test procedure with using Bonferroni's equality can be still of use. Finally, we use the data about the forced expiratory volume in 1 s (FEV1) readings taken from a double-blind crossover trial comparing two different doses of formoterol with a placebo to illustrate the use of test procedures and interval estimators proposed here.