On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm

Abstract

Finding optimal designs for nonlinear models is challenging in general. Although some recent results allow us to focus on a simple subclass of designs for most problems, deriving a specific optimal design still mainly depends on numerical approaches. There is need for a general and efficient algorithm that is more broadly applicable than the current state-of-the-art methods. We present a new algorithm that can be used to find optimal designs with respect to a broad class of optimality criteria, when the model parameters or functions thereof are of interest, and for both locally optimal and multistage design strategies. We prove convergence to the optimal design, and show in various examples that the new algorithm outperforms the current state-of-the-art algorithms.

Keywords:

• Convergence
• Locally optimal design
• Multistage design
• Φ _p -optimality

Acknowledgments

The authors are thankful for detailed comments and suggestions by the editor, the associate editor, and three referees on an earlier version of the article. Yang's research was supported by NSF grants DMS-0707013, DMS-1322797, and FDA MCM Challenge Grant. Tang's research was partially supported by the Donald W. Reynolds Journalism Institute. The contents are solely the responsibility of the authors and do not necessarily represent the official views of FDA.