Universal Optimality for Selected Crossover Designs

• Published in: Journal of the American Statistical Association Vol. 99; no. 466; pp. 461 - 466
• Main Authors: Hedayat, A. S, Yang, Min
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2004; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Balanced design; Carryover effect; Clinical trials; Crossover design; Crossovers; Data analysis; Data collection; Design efficiency; Exact sciences and technology; Experimental design; General topics; Inference; Integers; Linear models; Mathematical methods; Mathematical models; Mathematics; Minimum value; Optimization; Pharmacology; Probability and statistics; Repeated measurements; Research methods; Sciences and techniques of general use; Statistical methods; Statistical variance; Statistics; Theory and Methods; Statistical method; Experimental design; Balanced design; Uniform design; Optimal design(statistics); Application; Universal optimality
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000000331

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 withp = t as long as n is not greater than t(t + 2)/2 and 3 ≤ t ≤ 12; (b) a balanced uniform design with n = 2t, t ≥ 3, and p =t is universally optimal in the entire class of crossover designs with n = 2t 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).