The generalized Fisher's combination and accurate p-value calculation under dependence.

Area of Science:

• Statistics
• Bioinformatics
• Computational Biology

Background:

• Combining dependent significance tests is vital in big data analysis.
• Existing methods like Fisher's combination test struggle with accurate p-value calculation, especially at low significance levels, leading to inflated Type I error rates and false discoveries.
• This issue is particularly problematic in large-scale datasets where even small error rates can yield significant false positives.

Purpose of the Study:

• To develop a generalized Fisher-type statistic (GFisher) encompassing various combination methods.
• To introduce novel p-value calculation techniques for improved accuracy and robustness.
• To address the challenge of inflated Type I error rates in significance testing for big data.

Main Methods:

• Introduced the generalized Fisher (GFisher) statistic, a flexible framework for combining dependent tests.
• Developed new p-value calculation methods using moment-ratio matching and joint-distribution surrogating.
• Validated methods through systematic simulations under various distributions (multivariate Gaussian, generalized linear model, multivariate t-distribution).

Main Results:

• The GFisher framework integrates multiple classic statistics with adaptable weighting schemes.
• New p-value calculation methods demonstrate superior accuracy and robustness compared to existing approximations.
• Simulations confirm improved performance, particularly under non-ideal distributional assumptions.

Conclusions:

• The GFisher statistic and new p-value calculation methods offer a more reliable approach for combining dependent significance tests.
• These advancements can mitigate false discoveries in big data research, enhancing analytical rigor.
• The GFisher R package is available for practical application, including SNP-set association studies.