False discovery rate control with compound p-values
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915416694063104 |
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| author | Barber, Rina Foygel Samworth, Richard J |
| author_facet | Barber, Rina Foygel Samworth, Richard J |
| contents | In the setting of multiple testing, compound p-values generalize p-values by asking for superuniformity to hold only \emph{on average} across all true nulls. We study the properties of the Benjamini--Hochberg procedure applied to compound p-values. Under independence, we show that the false discovery rate (FDR) is at most $1.93α$, where $α$ is the nominal level, and exhibit a distribution for which the FDR is $\frac{7}{6}α$. If additionally all nulls are true, then the upper bound can be improved to $α+ 2α^2$, with a corresponding worst-case lower bound of $α+ α^2/4$. Under positive dependence, on the other hand, we demonstrate that FDR can be inflated by a factor of $O(\log m)$, where~$m$ is the number of hypotheses. We provide numerous examples of settings where compound p-values arise in practice, either because we lack sufficient information to compute non-trivial p-values, or to facilitate a more powerful analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_21465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | False discovery rate control with compound p-values Barber, Rina Foygel Samworth, Richard J Statistics Theory Methodology In the setting of multiple testing, compound p-values generalize p-values by asking for superuniformity to hold only \emph{on average} across all true nulls. We study the properties of the Benjamini--Hochberg procedure applied to compound p-values. Under independence, we show that the false discovery rate (FDR) is at most $1.93α$, where $α$ is the nominal level, and exhibit a distribution for which the FDR is $\frac{7}{6}α$. If additionally all nulls are true, then the upper bound can be improved to $α+ 2α^2$, with a corresponding worst-case lower bound of $α+ α^2/4$. Under positive dependence, on the other hand, we demonstrate that FDR can be inflated by a factor of $O(\log m)$, where~$m$ is the number of hypotheses. We provide numerous examples of settings where compound p-values arise in practice, either because we lack sufficient information to compute non-trivial p-values, or to facilitate a more powerful analysis. |
| title | False discovery rate control with compound p-values |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2507.21465 |