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The Generalized Harmonic Mean for p $$ p $$ -Values: Combining Dependent and Independent Tests.

Zhengbang Li1, Xinjie Zhou1

  • 1School of Mathematics and Statistics, Key Laboratory of NAA-MOE, Central China Normal University, Wuhan, China.

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Summary

This study introduces a new generalized harmonic mean for p-values (GHMP(ξ)) method to combine results from multiple medical studies. GHMP(ξ) offers robust statistical power and computational efficiency for genomics and meta-analysis.

Keywords:
combining p‐valuesgeneralized harmonic meannonasymptotic approximationstable distributiontail approximation

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Area of Science:

  • Biostatistics
  • Genomics
  • Medical Research

Background:

  • Combining p-values from multiple hypothesis tests is a statistical challenge in medical research.
  • Fields like genomics, multi-center trials, and meta-analysis require effective p-value combination methods.

Purpose of the Study:

  • To propose a generalized harmonic mean for p-values (GHMP(ξ)) combination method.
  • To develop two novel combination tests to enhance statistical power in comprehensive analyses.

Main Methods:

  • Developed GHMP(ξ) framework with two types of combination tests.
  • First test: suitable for small significance levels and complex correlations.
  • Second test: utilizes high-order tail approximation for large significance levels under weak correlations.

Main Results:

  • Both GHMP(ξ) tests demonstrated robust performance across various configurations.
  • Statistical power was comparable or superior to Cauchy combination test (CCT) and minimum p-value (MinP) methods.
  • GHMP(ξ) showed superior detection capabilities in specific scenarios and high computational efficiency.

Conclusions:

  • GHMP(ξ) is a reliable and practical tool for high-dimensional medical research.
  • Validated in genetic data, suitable for genome-wide association studies (GWAS) and large-scale meta-analysis.