Compound p-values for competition-based testing
Abstract
Standard competition-based multiple testing methods -- such as the knockoff filter and the target-decoy procedure -- are typically formulated as head-to-head competitions between a test unit and its assigned negative control unit. Motivated by real-world applications, which leverage any available negative controls, we study this competition-based framework in more intricate settings where competitions vary in size and structure. We propose new methods based on compound p-values -- p-values that are superuniform only on aggregate -- that enable powerful multiple testing with broader competition structures, via the Bonferroni and Benjamini-Hochberg procedures. The former provides exact familywise error rate control, whereas the latter may incur a false discovery rate inflation factor, for which we derive upper bounds across a range of settings. We showcase the performance of our general competition-based testing methodology through extensive simulations and real-data applications, including analyses of virtual spatial transcriptomics and CRISPR screen datasets that exhibit precisely the complex competition structures that motivate our methods.
Related
- Asymptotic Theory for Combining Dependent p-Values for Global Hypothesis Testing
- Optimal Certified Multiple Testing with E-values
- Federated multiple testing with quantized p-values under family-wise error control
- On the Open Problem in the 2023 Simon Marais Mathematics Competition
- Existence and Asymptotic Stability of Traveling Waves of Two-species Lotka-Volterra Competition-Diffusion Systems via Geometric Singular Perturbations
BibTeX
@misc{lee2026compound,
title = {{Compound p-values for competition-based testing}},
author = {Junu Lee and Rina Foygel Barber and Richard J. Samworth and Zhimei Ren},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20411},
eprint = {2610.20411},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20411},
}
RIS
TY - UNPB
TI - Compound p-values for competition-based testing
AU - Junu Lee
AU - Rina Foygel Barber
AU - Richard J. Samworth
AU - Zhimei Ren
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20411
UR - https://arxiv.org/abs/2610.20411
AB - Standard competition-based multiple testing methods -- such as the knockoff filter and the target-decoy procedure -- are typically formulated as head-to-head competitions between a test unit and its assigned negative control unit. Motivated by real-world applications, which leverage any available negative controls, we study this competition-based framework in more intricate settings where competitions vary in size and structure. We propose new methods based on compound p-values -- p-values that are superuniform only on aggregate -- that enable powerful multiple testing with broader competition structures, via the Bonferroni and Benjamini-Hochberg procedures. The former provides exact familywise error rate control, whereas the latter may incur a false discovery rate inflation factor, for which we derive upper bounds across a range of settings. We showcase the performance of our general competition-based testing methodology through extensive simulations and real-data applications, including analyses of virtual spatial transcriptomics and CRISPR screen datasets that exhibit precisely the complex competition structures that motivate our methods.
ER -