Optimal Adjustment and Combination of Independent Discrete $p$-Values
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908478086316032 |
|---|---|
| author | Contador, Gonzalo Wu, Zheyang |
| author_facet | Contador, Gonzalo Wu, Zheyang |
| contents | Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete p-values, which constructs a continuous surrogate distribution by minimizing the Wasserstein distance between the transformed discrete null and its continuous analogue. We provide a unified approach for several classical combination methods, including Fisher's, Pearson's, George's, Stouffer's, and Edgington's statistics. Our theoretical analysis and extensive simulations show that accurate Type I error control is achieved when the variance of the adjusted discrete statistic closely matches that of the continuous case. We further demonstrate that, when the likelihood ratio test is a monotonic function of a combination statistic, the proposed approximation achieves power comparable to the uniformly most powerful (UMP) test. The methodology is illustrated with a genetic association study of rare variants using case-control data, and is implemented in the R package DPComb. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Adjustment and Combination of Independent Discrete $p$-Values Contador, Gonzalo Wu, Zheyang Methodology Statistics Theory Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete p-values, which constructs a continuous surrogate distribution by minimizing the Wasserstein distance between the transformed discrete null and its continuous analogue. We provide a unified approach for several classical combination methods, including Fisher's, Pearson's, George's, Stouffer's, and Edgington's statistics. Our theoretical analysis and extensive simulations show that accurate Type I error control is achieved when the variance of the adjusted discrete statistic closely matches that of the continuous case. We further demonstrate that, when the likelihood ratio test is a monotonic function of a combination statistic, the proposed approximation achieves power comparable to the uniformly most powerful (UMP) test. The methodology is illustrated with a genetic association study of rare variants using case-control data, and is implemented in the R package DPComb. |
| title | Optimal Adjustment and Combination of Independent Discrete $p$-Values |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2508.02647 |