Model robust designs for dose-response models.

Area of Science:

• Statistics
• Experimental Design
• Mathematical Modeling

Background:

• Optimal experimental design typically assumes a known model structure.
• Model uncertainty, common in fields like dose-response modeling, can lead to inefficient experimental plans if based on a single assumed model.
• Model robust design aims to mitigate the impact of this uncertainty.

Purpose of the Study:

• To systematically develop approximate optimal model robust experimental designs.
• To address the challenge of selecting experimental designs when the underlying model is uncertain.
• To provide a framework for designing experiments robust to a pool of potential models.

Main Methods:

• Developed three Semidefinite Programming (SDP)-based formulations for model robust designs.
• Leveraged the semidefinite representability of robustness criteria for problem formulation.
• Employed standardized designs to ensure comparability of information measures across different models.
• Focused on locally optimal designs, accommodating nonlinear models within the candidate pool.

Main Results:

• Presented novel SDP formulations for approximate optimal model robust experimental designs.
• Demonstrated the applicability of the approach using a dose-response study with seven candidate models.
• Showcased how standardized designs facilitate cross-model information measure comparison.

Conclusions:

• The proposed SDP-based approach offers a systematic method for constructing model robust experimental designs.
• This methodology enhances the efficiency and adequacy of data collection when model uncertainty exists.
• The framework is particularly useful in applications like dose-response studies with multiple potential models.