Copula-based robust optimal block designs.

Area of Science:

• Experimental Design
• Statistical Modeling
• Biostatistics

Background:

• Blocking is crucial for reducing variability in experiments with homogeneous units.
• Modeling dependencies within blocks is challenging, especially for non-normal responses.
• Computational efficiency is a key concern for optimal experimental design.

Purpose of the Study:

• To develop computationally efficient designs for experiments with blocks of size two using copula models.
• To estimate population-average treatment effects for non-normally distributed responses.
• To provide a robust methodology for design selection in blocked experiments.

Main Methods:

• Utilized copulas and marginal modeling for efficient computation.
• Developed and demonstrated experimental designs with blocks of size two.
• Applied the methodology to a materials testing experiment.

Main Results:

• Copula models offer a computationally efficient approach for blocked experimental designs.
• The proposed designs are effective for non-normally distributed data.
• Demonstrated robustness of the designs to underlying modeling assumptions.

Conclusions:

• Copula-based designs provide an efficient and robust method for blocked experiments, particularly with non-normal data.
• The methodology is applicable to diverse fields including materials science and microarrays.
• This approach enhances the estimation of treatment effects in complex experimental settings.