{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T14:35:43Z","timestamp":1792247743867,"version":"4.4.0"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2134157"],"award-info":[{"award-number":["DMS-2134157"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2045981"],"award-info":[{"award-number":["DMS-2045981"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>A partial conjunction hypothesis test combines information across a set of base hypotheses to determine whether some subset is nonnull. Partial conjunction hypothesis tests arise in a diverse array of fields, but standard partial conjunction hypothesis testing methods can be highly conservative, leading to low power especially in low-signal settings commonly encountered in applications. In this paper, we introduce the conditional partial conjunction hypothesis test, a new method for testing a single partial conjunction hypothesis that directly corrects the conservativeness of standard approaches by conditioning on certain order statistics of the base $ p $-values. Under distributional assumptions commonly encountered in partial conjunction hypothesis testing, the proposed test is valid and produces nearly uniformly distributed $ p $-values under the null, i.e., the $ p $-values are only very slightly conservative. We demonstrate that our proposed test matches or outperforms existing single partial conjunction hypothesis tests with particular power gains in low-signal settings, maintains Type-I error control even under model misspecification and can be used to outperform state-of-the-art multiple partial conjunction hypothesis testing procedures in certain settings, particularly when side information is present. Finally, we illustrate an application of our proposed test through a replicability analysis across DNA microarray studies.<\/jats:p>","DOI":"10.1093\/biomet\/asaf036","type":"journal-article","created":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T08:03:22Z","timestamp":1747296202000},"source":"Crossref","is-referenced-by-count":2,"title":["Powerful partial conjunction hypothesis testing via conditioning"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5461-7829","authenticated-orcid":false,"given":"B","family":"Liang","sequence":"first","affiliation":[{"name":"Department of Statistics, Harvard University , 1 Oxford Street , Cambridge, Massachusetts 02143,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7855-0059","authenticated-orcid":false,"given":"L","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Statistics, Harvard University , 1 Oxford Street , Cambridge, Massachusetts 02143,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L","family":"Janson","sequence":"additional","affiliation":[{"name":"Department of Statistics, Harvard University , 1 Oxford Street , Cambridge, Massachusetts 02143,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,5,21]]},"reference":[{"key":"2026032607101039700_asaf036-B1","first-page":"79","article-title":"Order statistics for nonidentically distributed variables and permanents","volume":"51","author":"Bapat","year":"1989","journal-title":"Sankhya"},{"key":"2026032607101039700_asaf036-B2","doi-asserted-by":"crossref","first-page":"824","DOI":"10.1002\/gepi.22084","article-title":"Testing for the indirect effect under the null for genome-wide mediation analyses","volume":"41","author":"Barfield","year":"2017","journal-title":"Genet. 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