Multiple testing using uniform filtering of ordered p-values
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911771101495296 |
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| author | Jiang, Zhiwen Morgenthaler, Stephan |
| author_facet | Jiang, Zhiwen Morgenthaler, Stephan |
| contents | We investigate the multiplicity model with m values of some test statistic independently drawn from a mixture of no effect (null) and positive effect (alternative), where we seek to identify, the alternative test results with a controlled error rate. We are interested in the case where the alternatives are rare. A number of multiple testing procedures filter the set of ordered p-values in order to eliminate the nulls. Such an approach can only work if the p-values originating from the alternatives form one or several identifiable clusters. The Benjamini and Hochberg (BH) method, for example, assumes that this cluster occurs in a small interval $(0,Δ)$ and filters out all or most of the ordered p-values $p_{(r)}$ above a linear threshold $s \times r$. In repeated applications this filter controls the false discovery rate via the slope s. We propose a new adaptive filter that deletes the p-values from regions of uniform distribution. In cases where a single cluster remains, the p-values in an interval are declared alternatives, with the mid-point and the length of the interval chosen by controlling the data-dependent FDR at a desired level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple testing using uniform filtering of ordered p-values Jiang, Zhiwen Morgenthaler, Stephan Methodology We investigate the multiplicity model with m values of some test statistic independently drawn from a mixture of no effect (null) and positive effect (alternative), where we seek to identify, the alternative test results with a controlled error rate. We are interested in the case where the alternatives are rare. A number of multiple testing procedures filter the set of ordered p-values in order to eliminate the nulls. Such an approach can only work if the p-values originating from the alternatives form one or several identifiable clusters. The Benjamini and Hochberg (BH) method, for example, assumes that this cluster occurs in a small interval $(0,Δ)$ and filters out all or most of the ordered p-values $p_{(r)}$ above a linear threshold $s \times r$. In repeated applications this filter controls the false discovery rate via the slope s. We propose a new adaptive filter that deletes the p-values from regions of uniform distribution. In cases where a single cluster remains, the p-values in an interval are declared alternatives, with the mid-point and the length of the interval chosen by controlling the data-dependent FDR at a desired level. |
| title | Multiple testing using uniform filtering of ordered p-values |
| topic | Methodology |
| url | https://arxiv.org/abs/2402.03192 |