The harmonic mean p-value for combining dependent tests.

Area of Science:

• Genetics
• Statistical analysis
• Bioinformatics

Background:

• Big data analysis often requires comparing millions of hypotheses to find underlying patterns, such as in genome-wide association studies (GWAS).
• Controlling the familywise error rate (FWER) is crucial for minimizing false positives but often reduces statistical power, hindering discovery.
• Existing methods struggle to balance strong error control with sufficient power in large-scale hypothesis testing.

Purpose of the Study:

• To introduce a novel statistical method, the harmonic mean p-value (HMP), for analyzing big data.
• To demonstrate that HMP controls the FWER while significantly increasing statistical power.
• To show HMP's utility in identifying significant signals within groups of hypotheses in complex datasets.

Main Methods:

• Developed the harmonic mean p-value (HMP) by combining dependent hypothesis tests using the generalized central limit theorem.
• Applied HMP to analyze a human GWAS for neuroticism and a joint human-pathogen GWAS for hepatitis C viral load.
• Compared the performance of HMP against the Benjamini-Hochberg procedure for detecting significant hypothesis groups.

Main Results:

• HMP effectively controls the FWER, providing strong protection against false positives.
• HMP significantly improves statistical power, enabling the detection of signals from groups of individually nonsignificant hypotheses.
• HMP demonstrated greater power than the Benjamini-Hochberg procedure in detecting significant hypothesis groups.

Conclusions:

• The harmonic mean p-value (HMP) offers a powerful new approach for analyzing large datasets by enhancing statistical discovery.
• HMP successfully combines information from multiple tests to identify meaningful signals, even when individual tests are not significant.
• This method has broad implications for accelerating scientific discovery across various fields dealing with big data.