A Metaheuristic Adaptive Cubature Based Algorithm to Find Bayesian Optimal Designs for Nonlinear Models

Finding Bayesian optimal designs for nonlinear models is a difficult task because the optimality criterion typically requires us to evaluate complex integrals before we perform a constrained optimization. We propose a hybridized method where we combine an adaptive multidimensional integration algorithm and a metaheuristic algorithm called imperialist competitive algorithm to find Bayesian optimal designs. We apply our numerical method to a few challenging design problems to demonstrate its efficiency. They include finding <i>D</i>-optimal designs for an item response model commonly used in education, Bayesian optimal designs for survival models, and Bayesian optimal designs for a four-parameter sigmoid Emax dose response model. Supplementary materials for this article are available online and they contain an R package for implementing the proposed algorithm and codes for reproducing all the results in this article.