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Robust tests for combining p-values under arbitrary dependency structures.

Zhongxue Chen1

  • 1Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th Street, Bloomington, IN, 47405, USA. zc3@indiana.edu.

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The Cauchy distribution combination test (CCT) has limitations in statistical power and can be less effective than the MinP test in certain scenarios. New robust tests, MCM and CMC, offer improved performance for combining dependent p-values.

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Area of Science:

  • Statistics
  • Statistical Methods
  • Hypothesis Testing

Background:

  • The Cauchy distribution combination test (CCT) was proposed for combining dependent p-values.
  • CCT controls Type I error rates at small significance levels and approximates p-values using the Cauchy distribution.
  • A key feature of CCT is its applicability to dependent p-values.

Purpose of the Study:

  • To evaluate the performance of CCT compared to the commonly used MinP test.
  • To address limitations of CCT, including situations where it is less powerful or even powerless.
  • To propose and evaluate new robust p-value combination tests.

Main Methods:

  • Comparative analysis of CCT and MinP tests.
  • Development of new combination tests: MinP-CCT-MinP (MCM) and CCT-MinP-CCT (CMC).
  • Comprehensive simulation studies to assess the performance of CCT, MinP, MCM, and CMC.

Main Results:

  • The MinP test demonstrates significantly higher power than CCT under certain conditions.
  • CCT can be powerless in specific situations, necessitating cautious application.
  • The proposed MCM and CMC tests exhibit robustness and power across various conditions.

Conclusions:

  • CCT should be used with caution due to potential limitations in power.
  • The novel MCM and CMC tests provide robust and powerful alternatives for combining dependent p-values.
  • MCM and CMC offer viable options compared to CCT and MinP in statistical analysis.