Testing composite null hypotheses with high-dimensional dependent data: a computationally scalable FDR-controlling procedure

2024-04-08

AI Summary

In high-dimensional dependent data, conventional multiple testing procedures for composite null hypotheses often fail to control the false discovery rate (FDR) due to neglect of underlying dependence structures. Method: This paper proposes a novel framework for reproducibility analysis across multiple studies. It introduces a four-state hidden Markov model to jointly capture dependency and heterogeneity in p-value sequences from two primary studies, and develops an e-value-based scalable synthesis framework that reduces the computational complexity of joint inference across *n* studies from exponential to *O(n²)*, while guaranteeing asymptotic FDR control. Contribution/Results: Extensive simulations and real-world genome-wide association study (GWAS) analyses demonstrate that, at the same nominal FDR level, the proposed method achieves substantially higher statistical power and successfully identifies biologically meaningful mechanisms missed by standard approaches.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Humans and AI: Other Foundations of Human Computation & AI
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Testing composite null hypotheses arises in various applications, such as mediation and replicability analyses. The problem becomes more challenging in high-throughput experiments where tens of thousands of features are examined simultaneously. Existing large-scale inference methods for composite null hypothesis testing often fail to explicitly incorporate the dependence structure, producing overly conservative or overly liberal results. In this work, we first develop a four-state hidden Markov model (HMM) to model a bivariate $p$-value sequence from replicability analysis with two studies, accounting for local feature dependence and study heterogeneity. Building on the HMM, we propose a multiple testing procedure that controls the false discovery rate (FDR). Extending the HMM to model the $p$-values from $n$ studies requires a computational cost of exponential order of $n$. To address this challenge, we introduce a novel e-value framework that reduces the computational cost to quadratic growth in the number of studies while maintaining FDR control. We show that the proposed method asymptotically controls the FDR and exhibits higher power numerically than competing methods at the same FDR level. In a real data application to genome-wide association studies (GWAS), our method reveals new biological insights that are overlooked by existing methods.

Problem

• Testing composite null hypotheses with high-dimensional dependent data
• Incorporating dependence structure in large-scale inference methods
• Reducing computational cost while maintaining FDR control

Innovation

• Uses four-state HMM for bivariate p-value modeling
• Introduces e-value framework for computational efficiency
• Ensures FDR control in high-dimensional data