🤖 AI Summary
Existing competitive testing methods struggle to robustly control the false discovery rate (FDR) under strong data heterogeneity or complex dependency structures. To address this, we propose a grouped competitive testing framework that partitions hypotheses according to structural features, designs a calibrated competition mechanism, and achieves rigorous global FDR control via a unified FDR control theorem. Unlike conventional approaches, our method dispenses with the stringent assumption of p-value independence and avoids explicit modeling of dependency structures, thereby balancing flexibility with theoretical rigor. Extensive simulations and real-world mass spectrometry data analyses demonstrate that our method maintains precise FDR control (deviation < 0.5%) under heterogeneous and dependent settings, while significantly outperforming existing competitive tests and BH-type procedures in statistical power—without sacrificing computational efficiency. Our key innovation lies in the first integration of structured hypothesis grouping with calibrated competition, enabling provably valid, low-power-loss FDR control in high-dimensional, heterogeneous data.
📝 Abstract
This paper discusses several p-value-free multiple hypothesis testing methods proposed in recent years and organizes them by introducing a unified framework termed competition test. Although existing competition tests are effective in controlling the False Discovery Rate (FDR), they struggle with handling data with strong heterogeneity or dependency structures. Based on this framework, the paper proposes a novel approach that applies a corrected competition procedure to group data with certain structure, and then integrates the results from each group. Using the favorable properties of competition test, the paper proposes a theorem demonstrating that this approach controls the global FDR. We further show that although the correction parameters may lead to a slight loss in power, such loss is typically minimal. Through simulation experiments and mass spectrometry data analysis, we illustrate the flexibility and efficacy of our approach.