{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T19:03:37Z","timestamp":1780427017205,"version":"3.54.1"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2018,12,8]],"date-time":"2018-12-08T00:00:00Z","timestamp":1544227200000},"content-version":"vor","delay-in-days":365,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1418362"],"award-info":[{"award-number":["DMS-1418362"]}],"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-1407813"],"award-info":[{"award-number":["DMS-1407813"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000011","name":"Howard Hughes Medical Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000011","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Researchers in data-rich disciplines\u2014think of computational genomics and observational cosmology\u2014often wish to mine large bodies of $P$-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp, a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the $P$-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous \u2018standard\u2019 methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com\/dobriban\/pvalue_weighting_matlab (accessed 11 October 2017).<\/jats:p>","DOI":"10.1093\/imaiai\/iax013","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T11:09:42Z","timestamp":1507806582000},"page":"251-275","source":"Crossref","is-referenced-by-count":2,"title":["Weighted mining of massive collections of P-values by convex optimization"],"prefix":"10.1093","volume":"7","author":[{"given":"Edgar","family":"Dobriban","sequence":"first","affiliation":[{"name":"Department of Statistics, The Wharton School, University of Pennsylania, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,12,8]]},"reference":[{"key":"2020030521242446300_B1","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1038\/ng.171","article-title":"Systematic meta-analyses and field synopsis of genetic association studies in schizophrenia: the szgene database.","volume":"40","author":"Allen,","year":"2008","journal-title":"Nat. Genet."},{"key":"2020030521242446300_B2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ajhg.2013.01.001","article-title":"Improved detection of common variants associated with schizophrenia by leveraging pleiotropy with cardiovascular-disease risk factors.","volume":"92","author":"Andreassen,","year":"2013","journal-title":"Am. J. Hum. Genet."},{"key":"2020030521242446300_B3","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","article-title":"Controlling the false discovery rate: a practical and powerful approach to multiple testing.","volume":"57","author":"Benjamini,","year":"1995","journal-title":"J. Roy. Stat. Soc. B Stat. Meth."},{"key":"2020030521242446300_B4","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1111\/1467-9469.00072","article-title":"Multiple hypotheses testing with weights.","volume":"24","author":"Benjamini,","year":"1997","journal-title":"Scand. J. Stat."},{"key":"2020030521242446300_B5","doi-asserted-by":"crossref","first-page":"9546","DOI":"10.1073\/pnas.0914005107","article-title":"Independent filtering increases detection power for high-throughput experiments.","volume":"107","author":"Bourgon,","year":"2010","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2020030521242446300_B6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"Boyd,","year":"2004"},{"key":"2020030521242446300_B7","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1002\/sim.3495","article-title":"A graphical approach to sequentially rejective multiple test procedures.","volume":"28","author":"Bretz,","year":"2009","journal-title":"Stat. Med."},{"key":"2020030521242446300_B8","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1038\/nature05911","article-title":"Genome-wide association study of 14,000 cases of seven common iseases and 3,000 shared controls.","volume":"447","author":"Burton,","year":"2007","journal-title":"Nature"},{"key":"2020030521242446300_B9","first-page":"339","article-title":"A genome-wide association study in Europeans and South Asians identifies five new loci for coronary artery disease.","volume-title":"Nat. Genet.","author":"Coronary Artery Disease Genetics Consortium","year":"2011"},{"key":"2020030521242446300_B10","doi-asserted-by":"crossref","first-page":"i147","DOI":"10.1093\/bioinformatics\/bts235","article-title":"Incorporating prior information into association studies.","volume":"28","author":"Darnell,","year":"2012","journal-title":"Bioinformatics"},{"key":"2020030521242446300_B11","doi-asserted-by":"crossref","first-page":"4420","DOI":"10.1093\/hmg\/ddu139","article-title":"Genome-wide association meta-analysis of human longevity identifies a novel locus conferring survival beyond 90 years of age.","volume":"23","author":"Deelen,","year":"2014","journal-title":"Hum. Mol. Genet."},{"key":"2020030521242446300_B12","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1093\/biomet\/asv050","article-title":"Optimal multiple testing under a Gaussian prior on the effect sizes.","volume":"102","author":"Dobriban,","year":"2015","journal-title":"Biometrika"},{"key":"2020030521242446300_B13","volume-title":"Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction","author":"Efron,","year":"2012"},{"key":"2020030521242446300_B14","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1101\/gr.072785.107","article-title":"Increasing power in association studies by using linkage disequilibrium structure and molecular function as prior information.","volume":"18","author":"Eskin,","year":"2008","journal-title":"Genome Res."},{"key":"2020030521242446300_B15","doi-asserted-by":"crossref","first-page":"e1005728","DOI":"10.1371\/journal.pgen.1005728","article-title":"Genome-wide scan informed by age-related disease identifies loci for exceptional human longevity.","volume":"11","author":"Fortney,","year":"2015","journal-title":"PLoS Genet."},{"key":"2020030521242446300_B16","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1093\/biomet\/93.3.509","article-title":"False discovery control with p-value weighting.","volume":"93","author":"Genovese,","year":"2006","journal-title":"Biometrika"},{"key":"2020030521242446300_B17","doi-asserted-by":"crossref","DOI":"10.1186\/1756-0381-5-4","article-title":"Weighted multiple testing procedures for genomic studies.","volume":"5","author":"Gui,","year":"2012","journal-title":"BioData Mining"},{"key":"2020030521242446300_B18","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure.","volume":"6","author":"Holm,","year":"1979","journal-title":"Scand. J. Stat."},{"key":"2020030521242446300_B19","doi-asserted-by":"publisher","DOI":"10.1101\/034330","article-title":"Data-driven hypothesis weighting increases detection power in big data analytics.","author":"Ignatiadis,","year":"2015","journal-title":"bioRxiv"},{"key":"2020030521242446300_B20","article-title":"An estimate of the science-wise false discovery rate and application to the top medical literature.","author":"Jager,","year":"2013","journal-title":"Biostatistics"},{"key":"2020030521242446300_B21","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1086\/377220","article-title":"First-year Wilkinson microwave anisotropy probe (wmap)* observations: Tests of Gaussianity.","volume":"148","author":"Komatsu,","year":"2003","journal-title":"Astrophys. J. Suppl. Series"},{"key":"2020030521242446300_B22","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1038\/ng.568","article-title":"New loci associated with kidney function and chronic kidney disease.","volume":"42","author":"K\u00f6ttgen,","year":"2010","journal-title":"Nat. Genet."},{"key":"2020030521242446300_B23","volume-title":"Testing Statistical Hypotheses","author":"Lehmann,","year":"2005"},{"key":"2020030521242446300_B24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3389\/fgene.2013.00103","article-title":"Using eQTL weights to improve power for genome-wide association studies: a genetic study of childhood asthma.","volume":"4","author":"Li,","year":"2013","journal-title":"Front. Genet."},{"key":"2020030521242446300_B25","volume-title":"Numerical Optimization","author":"Nocedal,","year":"2006"},{"key":"2020030521242446300_B26","doi-asserted-by":"crossref","first-page":"D1036","DOI":"10.1093\/nar\/gkr899","article-title":"DistiLD Database: diseases and traits in linkage disequilibrium blocks.","volume":"40","author":"Palleja,","year":"2012","journal-title":"Nucleic Acids Res."},{"key":"2020030521242446300_B27","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1214\/10-AOS844","article-title":"Power-enhanced multiple decision functions controlling family-wise error and false discovery rates.","volume":"39","author":"Pe\u00f1a,","year":"2011","journal-title":"Ann. Stat."},{"key":"2020030521242446300_B28","doi-asserted-by":"crossref","first-page":"13790","DOI":"10.1073\/pnas.1404623111","article-title":"Common genetic variants associated with cognitive performance identified using the proxy-phenotype method.","volume":"111","author":"Rietveld,","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2020030521242446300_B29","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1086\/500026","article-title":"Using linkage genome scans to improve power of association in genome scans.","volume":"78","author":"Roeder,","year":"2006","journal-title":"Am. J. Hum. Genet."},{"key":"2020030521242446300_B30","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1214\/09-STS289","article-title":"Genome-wide significance levels and weighted hypothesis testing.","volume":"24","author":"Roeder,","year":"2009","journal-title":"Stat. Sci."},{"key":"2020030521242446300_B31","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1214\/09-EJS430","article-title":"Optimal weighting for false discovery rate control.","volume":"3","author":"Roquain,","year":"2009","journal-title":"Electron. J. Stat."},{"key":"2020030521242446300_B32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2202\/1544-6115.1148","article-title":"A method to increase the power of multiple testing procedures through sample splitting.","volume":"5","author":"Rubin,","year":"2006","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"2020030521242446300_B33","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1093\/hmg\/ddl438","article-title":"Cholinergic nicotinic receptor genes implicated in a nicotine dependence association study targeting 348 candidate genes with 3713 SNPs.","volume":"16","author":"Saccone,","year":"2007","journal-title":"Hum. Mol. Genet."},{"key":"2020030521242446300_B34","first-page":"969","article-title":"Genome-wide association study identifies five new schizophrenia loci.","volume-title":"Nat. Genet.","author":"Schizophrenia Psychiatric Genome-Wide Association Study Consortium","year":"2011"},{"key":"2020030521242446300_B35","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1038\/ng.784","article-title":"Large-scale association analysis identifies 13 new susceptibility loci for coronary artery disease.","volume":"43","author":"Schunkert,","year":"2011","journal-title":"Nat. Genet."},{"key":"2020030521242446300_B36","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1097\/00041552-200403000-00004","article-title":"The association between congestive heart failure and chronic renal disease.","volume":"13","author":"Silverberg,","year":"2004","journal-title":"Curr. Opin. Nephrol. Hypertens."},{"key":"2020030521242446300_B37","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1214\/aoms\/1177692621","article-title":"On the optimality of some multiple comparison procedures.","volume":"43","author":"Spj\u00f8tvoll,","year":"1972","journal-title":"Ann. Math. Stat."},{"key":"2020030521242446300_B38","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1111\/j.1467-9868.2007.005592.x","article-title":"The optimal discovery procedure: a new approach to simultaneous significance testing.","volume":"69","author":"Storey,","year":"2007","journal-title":"J. Roy. Stat. Soc. B"},{"key":"2020030521242446300_B39","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1002\/gepi.20164","article-title":"Stratified false discovery control for large-scale hypothesis testing with application to genome-wide association studies.","volume":"30","author":"Sun,","year":"2006","journal-title":"Genet. Epidemiol."},{"key":"2020030521242446300_B40","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1198\/016214507000000545","article-title":"Oracle and adaptive compound decision rules for false discovery rate control.","volume":"102","author":"Sun,","year":"2007","journal-title":"J. Am. Stat. Assoc."},{"key":"2020030521242446300_B41","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1038\/ng.3507","article-title":"Weighting sequence variants based on their annotation increases power of whole-genome association studies.","volume":"48","author":"Sveinbjornsson,","year":"2016","journal-title":"Nat. Genet."},{"key":"2020030521242446300_B42","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1038\/nature09270","article-title":"Biological, clinical and population relevance of 95 loci for blood lipids.","volume":"466","author":"Teslovich,","year":"2010","journal-title":"Nature"},{"key":"2020030521242446300_B43","doi-asserted-by":"crossref","first-page":"5116","DOI":"10.1073\/pnas.091062498","article-title":"Significance analysis of microarrays applied to the ionizing radiation response.","volume":"98","author":"Tusher,","year":"2001","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"2020030521242446300_B44","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0378-3758(01)00077-5","article-title":"Optimally weighted, fixed sequence and gatekeeper multiple testing procedures.","volume":"99","author":"Westfall,","year":"2001","journal-title":"J. Stat. Plann. Infer."},{"key":"2020030521242446300_B45","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1002\/(SICI)1097-0258(19980930)17:18<2107::AID-SIM910>3.0.CO;2-W","article-title":"Using prior information to allocate significance levels for multiple endpoints.","volume":"17","author":"Westfall,","year":"1998","journal-title":"Stat. Med."},{"key":"2020030521242446300_B46","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1214\/lnms\/1196285632","article-title":"Weighted FWE-controlling methods in high-dimensional situations.","volume-title":"Recent Developments in Multiple Comparison Procedures","author":"Westfall,","year":"2004"}],"container-title":["Information and Inference: A Journal of the IMA"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imaiai\/article-pdf\/7\/2\/251\/32468803\/iax013.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/imaiai\/article-pdf\/7\/2\/251\/32468803\/iax013.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T18:13:08Z","timestamp":1719511988000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imaiai\/article\/7\/2\/251\/4711136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,8]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,12,8]]},"published-print":{"date-parts":[[2018,6,7]]}},"URL":"https:\/\/doi.org\/10.1093\/imaiai\/iax013","relation":{},"ISSN":["2049-8764","2049-8772"],"issn-type":[{"value":"2049-8764","type":"print"},{"value":"2049-8772","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,6]]},"published":{"date-parts":[[2017,12,8]]}}}