Universal Optimality for Selected Crossover Designs

Abstract

Hedayat and Yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments, n subjects, and p = t periods are universally optimal when n ≤ t ( t - 1)/2. Surprisingly, in the class of crossover designs with t treatments and p = t periods, a balanced uniform design may not be universally optimal if the number of subjects exceeds t ( t - 1)/2. This article, among other results, shows that (a) a balanced uniform design is universally optimal in the entire class of crossover designs with p = t as long as n is not greater than t ( t + 2)/2 and 3 ≤ t ≤ 12; (b) a balanced uniform design with n = 2 t , t ≥ 3, and p = t is universally optimal in the entire class of crossover designs with n = 2 t and p = t ; and (c) for the case where p ≤ t , the design suggested by Stufken is universally optimal, thus completing Kushner's result that a Stufken design is universally optimal if n is divisible by t ( p - 1).