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Simultaneous confidence regions corresponding to Holm's step-down procedure and other closed-testing procedures.
1AstraZeneca R&D, S-15185 Södertälje, Sweden. olivier.guilbaud@astrazeneca.com
Biometrical Journal. Biometrische Zeitschrift
|October 22, 2008
Summary
This study introduces simultaneous confidence regions for multiple testing procedures (MTPs), including Holm's method. These regions offer additional information beyond hypothesis rejection, aiding in statistical analysis and clinical study interpretation.
Area of Science:
- Statistics
- Statistical Inference
- Hypothesis Testing
Background:
- Holm's step-down multiple-testing procedure (MTP) offers flexibility but lacks simultaneous confidence regions.
- Deriving confidence regions for MTPs has been a long-standing challenge in statistical methodology.
Purpose of the Study:
- To derive simultaneous confidence regions for a class of MTPs, including Holm's procedure.
- To provide a method for obtaining additional statistical information beyond simple hypothesis rejection.
Main Methods:
- Development of simultaneous confidence regions for MTPs within the framework of short-cut consonant closed-testing procedures.
- Utilizing marginal p-values and weighted Bonferroni tests for intersection hypotheses.
- Ensuring validity based on the validity of underlying marginal p-values and confidence regions.
Main Results:
- Simultaneous confidence regions are provided for Holm's MTP, fixed-sequence MTP, gatekeeping MTPs, and the fallback MTP.
- The proposed regions offer extra information for non-rejected null hypotheses when not all hypotheses are rejected.
- In cases where all hypotheses are rejected, extra information is provided for some or all null hypotheses.
Conclusions:
- The derived simultaneous confidence regions enhance the interpretability of MTPs by providing additional statistical insights.
- These regions are generally valid and applicable to various MTPs, offering a valuable tool for statistical analysis.
- Illustrative examples from clinical studies demonstrate the practical utility of the proposed confidence regions.
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