In this article we have considered a \(2\times 2\) binary crossover trial. Two main difficulties on designing such trial are: (i) the association of observations measured on the same experimental unit over different time periods; and (ii) the dependency of design selection criterion on the unknown model parameters. Here we present a copula based approach to address (i). Further, a Bayesian approach is adopted to address (ii). Equivalence theorem is provided to verify the optimality of numerically obtained Bayesian design. The proposed methodology is supplemented by thorough numerical studies. Moreover, it is shown that the proposed optimal designs are more efficient than that of based on the generalized estimating equations approach.
