The Cauchy Combination Test under Arbitrary Dependence Structures
Bibliographic record
Abstract
Combining individual <i>p</i>-values to perform an overall test is often encountered in statistical applications. The Cauchy combination test (CCT) (<i>Journal of the American Statistical Association</i>, 2020, 115, 393–402) is a powerful and computationally efficient approach to integrate individual <i>p</i>-values under arbitrary dependence structures for sparse signals. We revisit this test to additionally show that (i) the tail probability of the CCT can be approximated just as well when more relaxed assumptions are imposed on individual <i>p</i>-values compared to those of the original test statistics; (ii) such assumptions are satisfied by six popular copula distributions; and (iii) the power of the CCT is no less than that of the minimum <i>p</i>-value test when the number of <i>p</i>-values goes to infinity under some regularity conditions. These findings are confirmed by both simulations and applications in two real datasets, thus, further broadening the theory and applications of the CCT.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.180 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".