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Bonferroni parallel gatekeeping - transparent generalizations, adjusted p -values, and short direct proofs.
1AstraZeneca R&D, S-15185 Södertälje, Sweden. olivier.guilbaud@astrazeneca.com
Biometrical Journal. Biometrische Zeitschrift
|August 30, 2007
Summary
This study generalizes the Bonferroni parallel-gatekeeping multiple-testing procedure (MTP). It allows for flexible MTPs in the second step and introduces a third step for enhanced hypothesis rejection power.
Area of Science:
- Statistics
- Biostatistics
- Statistical Methods
Background:
- The Bonferroni parallel-gatekeeping multiple-testing procedure (MTP) uses a family of hypotheses (F1) to gatekeep another family (F2).
- The standard two-step procedure involves Bonferroni MTP for F1 and Holm's MTP for F2.
Purpose of the Study:
- To generalize the two-step Bonferroni parallel-gatekeeping MTP.
- To introduce a modified parallel gatekeeping procedure with an additional third step.
Main Methods:
- Generalization of the two-step MTP by allowing any MTP with multiplicity-adjusted p-values in the second step.
- Development of a third step for modified Bonferroni parallel gatekeeping, enabling further rejections in F1 if F2 hypotheses are all rejected.
Main Results:
- The generalized procedures maintain multiple-level alpha control.
- Proofs are direct and do not rely on closed-testing arguments.
- Multiplicity-adjusted p-values are readily calculable for the proposed MTPs.
Conclusions:
- The proposed generalized Bonferroni parallel-gatekeeping MTPs offer flexibility and enhanced power.
- These methods are straightforward to extend to multiple successive gatekeeper families.
- The procedures are illustrated with a practical example.
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