Optimal crossover designs for inference on total effects

• Published in: Journal of statistical planning and inference 2021-07, Vol.213, p.253-261
• Main Authors: Aboukhamseen, Suja, Huda, Shahariar, Bose, Mausumi
• Format: Article
• Language: English
• Subjects: Carryover; Direct; Reparametrization; Symmetrization; Universal optimality
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2020.12.002

Crossover designs involve two types of treatment effects, a direct effect and a carryover effect, and several optimality results are available for inferring on these two effects separately. However, an aim of a designed experiment is to recommend a single treatment which will be used over longer time periods. When this treatment is used over many periods, the effect on the subject at any time period will be the total of its direct and carryover effects, and so, at the designed experiment stage it is important to study the sum of the direct and carryover effects of the same treatment, that is, the total effect. Not much is known on the optimality of designs for this total effect. In this article we obtain universally optimal designs for total effects under a non-circular model with two periods and correlated errors. We also report some highly efficient designs in this context. •A designed crossover experiment aims to recommend a single treatment for use.•When this treatment is used over many periods, it will only be followed by itself.•So, the sum of direct and carryover effects of a treatment is important.•Universally optimal designs are obtained for this total effect.