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A general consonance principle for closure tests based on p-values
Sonja Zehetmayer1, Franz Koenig1, Martin Posch1
1Center for Medical Data Science, Medical University of Vienna, Austria.
Statistical Methods in Medical Research
|October 23, 2024
Summary
This study enhances closed testing procedures for multiple hypotheses by improving consonant tests. Simulations show these modified tests significantly increase statistical power for familywise error rate control.
Area of Science:
- Statistical methodology
- Hypothesis testing
- Biostatistics
Background:
- The closure principle offers efficient methods for controlling familywise error rate (FWER) in strong sense.
- Closed tests utilize p-value combination tests for intersection hypotheses, but some lack consonance.
Purpose of the Study:
- To develop a general principle for uniformly improving closed tests based on p-value combination tests.
- To ensure consonant procedures where global null rejection implies elementary null rejection.
Main Methods:
- Investigated closed tests using various p-value combination tests (Fisher, Stouffer, Omnibus, etc.).
- Developed a principle to modify rejection regions for improved consonance.
- Conducted simulations to compare power of new and existing methods.
Main Results:
- Identified non-consonant combination tests (Fisher, Stouffer, Omnibus).
- Demonstrated that modified closed tests become consonant.
- Simulations revealed substantial power increases for Fisher and Stouffer combination tests.
Conclusions:
- The proposed principle effectively enhances closed testing procedures.
- Modified closed tests offer improved statistical power while maintaining FWER control.
- This advancement is particularly beneficial for statistical analyses with multiple hypotheses.
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