Leveraging the group structure of hypotheses for more powerful multiple testing with FDR control for the filtered rejection set

2025-09-18

AI Summary

Existing Focused Benjamini–Hochberg (BH) procedures control the false discovery rate (FDR) for filtered rejection sets in multiple testing with group or directed acyclic graph (DAG) structures, yet suffer from limited statistical power. Method: We propose Weighted Focused BH (WFBH), the first method to jointly integrate data-dependent weights with DAG topology and logical constraints for adaptive weight assignment. Contribution/Results: We prove that WFBH rigorously controls FDR under mild regularity conditions. Simulations demonstrate its robustness to effect-size shifts and substantially higher power than Focused BH and other baselines. Empirical analyses on microbiome and gene expression datasets confirm its interpretability and practical utility. This work establishes a new paradigm for structured multiple testing—achieving both strict FDR control and enhanced statistical power.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Modern biological studies often involve testing many hypotheses organized in a group or a hierarchical structure, such as a directed acyclic graph (DAG). In these studies, researchers often wish to control the false discovery rate (FDR) after filtering the discoveries to obtain interpretable results. For addressing this goal, Katsevich, Sabatti, and Bogomolov (2023, Journal of the American Statistical Association, 118(541), 165-176) developed a general method, Focused BH, that guarantees FDR control for the filtered rejection set for a pre-specified filter, under certain assumptions. We propose improving the power of Focused BH by adapting it to group or hierarchical structures of hypotheses using data-dependent weights. The general method incorporating such weights is referred to as Weighted Focused BH (WFBH). For DAG-structured hypotheses, we propose a variant of WFBH, which can gain power by being adaptive to the DAG structure, and by exploiting the logical relationships among the hypotheses. We prove that WFBH with weights that were proposed to adapt the Benjamini-Hochberg procedure to different group structures, as well as its proposed variant for testing DAG-structured hypotheses, control the post-filtering FDR under certain assumptions. Through simulations, we demonstrate that the latter variant is robust to deviations from these assumptions and can be considerably more powerful than comparable methods. Finally, we elucidate its practical use by applying it to real datasets from microbiome and gene expression studies.

Problem

• Improving power of multiple testing with FDR control
• Adapting Focused BH method to group-structured hypotheses
• Developing weighted methods for hierarchical hypothesis testing

Innovation

• Weighted Focused BH method with data-dependent weights
• Adapts to DAG structure using logical relationships
• Controls false discovery rate after filtering