Hypotheses on a tree: new error rates and testing strategies.

Area of Science:

• Statistical methodology
• Genomics
• Microbiome research

Background:

• Multiple testing procedures are crucial for controlling false discoveries in high-dimensional data.
• Existing methods may lack power or flexibility when dealing with structured hypotheses.
• Hierarchical organization of hypotheses is common in biological research.

Purpose of the Study:

• To introduce a novel multiple testing procedure that controls global error rates at multiple resolution levels.
• To frame hypothesis testing within a hierarchical tree structure for enhanced interpretability.
• To develop a computationally efficient algorithm for this procedure.

Main Methods:

• A novel multiple testing procedure based on hierarchical hypothesis organization.
• Development and analysis of a fast algorithm for the proposed procedure.
• Simulations under various dependency structures of p-values to assess performance.

Main Results:

• The procedure controls relevant error rates under specified dependency assumptions.
• Simulations confirm desired guarantees across diverse dependency structures.
• The method demonstrates potential for increased statistical power compared to alternatives.

Conclusions:

• The proposed hierarchical multiple testing procedure offers robust error control and potential power gains.
• The method is applicable to complex biological datasets, such as gene expression and microbiome studies.
• This approach provides a valuable tool for analyzing structured hypothesis testing scenarios.