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

Abstract

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 D-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.

Keywords:

• Adaptive subregion algorithm
• Compound criterion
• D-efficiency
• Equivalence theorem
• Fisher information matrix
• P-optimality

Acknowledgments

We are grateful to the editor, associate editor, and two reviewers for their timely review and valuable comments. The contents in this article are solely the responsibility of the authors and do not necessarily represent the official views of the National Institutes of Health.

Disclaimer

The contents in this article are solely the responsibility of the authors and do not necessarily represent the official views of the National Institutes of Health.

Funding

Additional information

Funding

The research of Wong reported in this article was partially supported by a grant award from the National Institute of General Medical Sciences of the National Institutes of Health (NIH funding: R01GM107639). The research of Holling and Masoudi in this article was partially supported by a grant (HO 1286/6 - 4) of the Deutsche Forschungsgemeinschaft (DFG).