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An Allele-specific Gene Expression Assay to Test the Functional Basis of Genetic Associations
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On Permutation Procedures for Strong Control in Multiple Testing with Gene Expression Data.

Grzegorz A Rempala1, Yuhong Yang2

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Summary
This summary is machine-generated.

This study examines the min P and max T methods for controlling family-wise error rates in multiple testing. A new strong control definition is introduced, ensuring validity even without the subset pivotality property.

Keywords:
multiple testingpermutation teststep down p-value adjustment methodsstrong control of family-wise error ratesubset pivotality property

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Area of Science:

  • Statistics
  • Statistical Methods
  • Multiple Hypothesis Testing

Background:

  • Multiple testing procedures require controlling the family-wise error rate (FWER) to prevent false discoveries.
  • Permutation-based step-down methods like min P and max T are popular for FWER control.
  • The subset pivotality property (SPP) is often assumed for the validity of these methods.

Purpose of the Study:

  • To investigate the validity of min P and max T procedures under the subset pivotality property (SPP).
  • To address subtle issues in ensuring the strong control of the family-wise error rate (FWER) for these methods.
  • To introduce a refined definition of strong control applicable even when SPP does not hold.

Main Methods:

  • Analysis of permutation-based step-down procedures (min P and max T).
  • Examination of the subset pivotality property (SPP) and its implications.
  • Development and introduction of a new, narrower definition for strong control.

Main Results:

  • Identified key issues in validating min P and max T under SPP.
  • Demonstrated that the proposed new strong control definition ensures valid FWER bounds for min P and max T.
  • Showcased the applicability of the new control definition in the absence of SPP.

Conclusions:

  • The validity of min P and max T procedures requires careful consideration, especially regarding SPP.
  • A novel definition of strong control offers a more robust approach to FWER control in multiple testing.
  • The new control definition enhances the reliability of statistical inference when SPP assumptions are not met.