Accurate unconditional p-values for a two-arm study with binary endpoints.

Area of Science:

• Biostatistics
• Clinical Trials
• Statistical Methods

Background:

• Unconditional exact tests enhance study power and align data analysis with study design for categorical data.
• Calculating p-values for the exact unconditional Barnard test involves maximizing tail probability over a nuisance parameter (0 to 1).
• Traditional grid search methods for this maximization are imprecise and computationally intensive, especially for complex study designs.

Purpose of the Study:

• To develop a more accurate and computationally efficient method for calculating p-values in unconditional exact tests.
• To address the limitations of the traditional grid search method in maximizing tail probabilities.
• To provide a robust statistical approach for analyzing categorical data in clinical trials.

Main Methods:

• A novel polynomial method is proposed to represent the tail probability as a polynomial function.
• The global maximum of the tail probability is found by solving the derivative of the polynomial.
• The method's accuracy and performance are demonstrated using data from a Phase II cancer clinical trial.

Main Results:

• The polynomial method accurately determines the global maximum of the tail probability, leading to precise p-values.
• Comparison with the traditional grid search method shows superior accuracy and efficiency of the polynomial approach.
• The method is validated in a real-world clinical trial setting.

Conclusions:

• The proposed polynomial method offers an accurate and efficient alternative for computing exact unconditional p-values.
• This method enhances the reliability of statistical analysis for categorical data in research studies.
• Adoption of the polynomial method is recommended for precise p-value computation in practice.