Combining independent, weighted P-values: achieving computational stability by a systematic expansion with...

Area of Science:

• Cross-disciplinary scientific research
• Statistical analysis
• Data integration

Background:

• Increasing availability of scientific data necessitates robust methods for combining assessments.
• P-values serve as a method-independent standard for evaluating information reliability.
• Existing methods like Good's formula and Fisher's method have limitations with unequal or degenerate weights.

Purpose of the Study:

• To develop a numerically stable method for combining P-values from multiple groups with varying weights.
• To address the issue of computational instability when weights are nearly degenerate.
• To provide a general framework for P-value combination that encompasses existing methods.

Main Methods:

• Derivation of a controlled expansion for combined P-value computation.
• Analysis of the probability distribution function for the general case of P-value combination.
• Development of a C++ program for stable computation of combined P-values.

Main Results:

• A novel, systematic approach for combining P-values that ensures numerical stability.
• The derived formula accurately computes combined P-values, even with degenerate weights.
• The general formula reduces to Good's and Fisher's methods as special cases.

Conclusions:

• The proposed method offers a reliable and stable solution for combining P-values across diverse scientific fields.
• This approach enhances the accuracy of statistical analysis when integrating heterogeneous data.
• A downloadable C++ program is available to facilitate the application of this method.