Balanced 2(n) factorial designs when observations are spatially correlated

Area of Science:

• Statistics
• Experimental Design
• Pharmaceutical Science

Background:

• Pharmaceutical development requires comparing drug formulations using human trials.
• Subject observations are often correlated due to repeated measures within individuals.
• Existing designs may not optimally handle intra-subject correlation.

Purpose of the Study:

• To develop and characterize balanced factorial and fractional-factorial designs for experiments with correlated observations within blocks.
• To address the specific challenge of comparing controlled-release tablet formulations in human bioavailability studies.
• To provide a method for constructing balanced designs for 2(n) and 2(n-1) factorial experiments.

Main Methods:

• Characterization of balanced designs for 2(n) factorial experiments with spatially correlated observations (AR(1), rho > 0).
• Explicit construction and analytical proof for balanced designs in full and fractional factorial experiments.
• Utilizing optimal/near-optimal designs from Cheng and Steinberg (1991), Martin et al. (1998c), and Elliott et al. (1999) as starting points.
• Illustrative examples using 2(3) full factorial and 2(4) fractional factorial experiments.

Main Results:

• Balanced designs for 2(n) and 2(n-1) factorial experiments with AR(1) positive correlation are explicitly constructed and proven.
• The proposed balanced designs are shown to be efficient, with relative efficiencies compared to existing optimal designs.
• Demonstrated practical application through examples in pharmaceutical formulation development.

Conclusions:

• The developed balanced designs effectively manage correlated observations within subjects in factorial experiments.
• These designs offer improved efficiency for pharmaceutical trials, particularly for controlled-release formulations.
• The explicit constructions and proofs provide a robust framework for applying these designs in practice.