Fiducial-Based Statistical Intervals for Bounded Bioanalytical Data Using the Kumaraswamy Distribution

Area of Science:

• Statistics
• Biopharmaceutical Analysis
• Data Science

Background:

• Biological measurements (e.g., percent monomer, cell percentages) are continuous and bounded (0-1).
• These data are often skewed, making normal-based statistical intervals inappropriate.
• Existing transformation methods can yield overly wide intervals for skewed data.

Purpose of the Study:

• To develop and evaluate new statistical methods for analyzing bounded, skewed biological data.
• To provide more accurate and practical confidence, prediction, and tolerance intervals for CMC applications.
• To introduce the Kumaraswamy distribution as a viable alternative for modeling bounded data.

Main Methods:

• Development of two new pivotal quantities for the Kumaraswamy shape parameter alpha.
• Integration with an existing pivotal quantity for beta.
• Fiducial-based construction of statistical intervals (confidence, tolerance, prediction).
• Simulation studies to assess finite-sample performance.
• Comparison with existing pivotal methods and data transformations.

Main Results:

• The proposed fiducial-based intervals using the Kumaraswamy distribution demonstrate practical utility.
• The new method provides a flexible and mathematically tractable alternative to existing approaches.
• Simulations indicate favorable performance compared to transformations and other pivotal methods, especially for skewed data.

Conclusions:

• The Kumaraswamy distribution offers a robust model for bounded, skewed biological data in CMC.
• The developed pivotal quantities enable accurate statistical interval construction.
• The methods are recommended for routine use in biopharmaceutical bioanalytical practice for improved data analysis.