**Abstract**

Crossover designs have received great attention in clinical trials, as they allow subjects to serve as their own controls and gain such advantage as higher efficiency and smaller sample size over parallel designs, because the within-subject variability is in general smaller than between-subject variability. Response-adaptive crossover designs allow clinical trials to adapt and respond to the information acquired during the trials to achieve various objectives. Adaptive designs have been considered to allocate more subjects to superior treatments, improve statistical efficiency, reduce the sample size for cost savings, increase the sample size to maintain prespecified statistical power, or include auxiliary information. We focus on an adaptive allocation scheme to maximize the benefits from superior treatments, while maintaining a sufficiently high level of statistical efficiency, controlled by a suitable weight parameter. We review and discuss the strategy of incorporating multiple objectives, while advocating a regression type estimation approach via the Generalized Estimating Equations method. We show that the multiple objectives can be successfully incorporated to construct a spectrum of designs, ranging over various efficiencies and trial outcomes of success. Moreover, the adaptive allocation scheme successfully constructs designs with a desired efficiency, as illustrated by practical two- and three-period designs.

**Keywords:** crossover design, response adaptive allocation, optimal design, multiple objective function
