Smoothed Nested Testing on Directed Acyclic Graphs

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Multiple hypothesis testing is crucial in analyzing complex datasets.
• Logical nested structures in hypotheses present unique challenges for traditional methods.
• Existing methods may lack power when dealing with hierarchical data relationships.

Purpose of the Study:

• To develop a general framework for hypothesis testing with logical nested structures.
• To propose and evaluate a smoothing procedure to increase statistical power.
• To ensure control of key error rates under various dependency conditions.

Main Methods:

• Modeling hypothesis structures as directed acyclic graphs.
• Adjusting node-level test statistics based on logical constraints.
• Implementing a smoothing procedure combining nodes with descendants.
• Proving error rate control for independent and dependent test statistics.

Main Results:

• A broad class of smoothing strategies effectively controls familywise error rate, false discovery exceedance rate, and false discovery rate.
• Arithmetic averaging demonstrates error rate control even with positively-correlated normal observations.
• Simulations and a biological dataset application show substantial power gains through smoothing.

Conclusions:

• The proposed smoothing framework offers a powerful approach for nested multiple hypothesis testing.
• The method provides robust error rate control across different statistical assumptions.
• This technique has practical implications for biological data analysis and other fields with hierarchical hypotheses.