Crossover designs for comparing test treatments to a control treatment when subject effects are random

We study crossover designs for the comparisons of several test treatments versus a control treatment and partially generalize the results of Hedayat and Yang (2005) to the situation in which subject effects are assumed to be random. More specifically, we establish lower bounds for the trace of the inverse of the information matrix for the test treatments versus control comparisons under a random subject effects model and show that most of the small size (3-, 4- and 5-period) designs introduced by Hedayat and Yang (2005) are highly efficient in the class of designs in which the control treatment appears equally often in all periods and no treatment is immediately preceded by itself.