Efficient crossover designs for non-regular settings

Abstract

Crossover designs are called for in situations when several subjects undergo a sequence of treatments. Though, usually, the model contains the direct effects of treatments as well as the carryover effects, the primary interest lies in the estimation of direct effects of the treatment. Most results in the literature on crossover designs are available for the situations where either the number of periods or the number of subjects is a multiple of the number of treatments. In this article, we consider crossover designs for the non-regular settings, that is, the situations when the number of treatments divides neither the number of periods nor the number of subjects. We provide a construction method to obtain highly E-efficient crossover designs for non-regular settings, while also providing a crude lower bound to E-efficiency of the designs constructed through our construction method. In a table, we provide E-efficiencies of a constructed design for the number of treatments up to 10 and the number of subjects up to 50.