{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:36:40Z","timestamp":1759941400026},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,7,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: In high-dimensional testing problems \u03c00, the proportion of null hypotheses that are true is an important parameter. For discrete test statistics, the P values come from a discrete distribution with finite support and the null distribution may depend on an ancillary statistic such as a table margin that varies among the test statistics. Methods for estimating \u03c00 developed for continuous test statistics, which depend on a uniform or identical null distribution of P values, may not perform well when applied to discrete testing problems.<\/jats:p><jats:p>Results: This article introduces a number of \u03c00 estimators, the regression and \u2018T\u2019 methods that perform well with discrete test statistics and also assesses how well methods developed for or adapted from continuous tests perform with discrete tests. We demonstrate the usefulness of these estimators in the analysis of high-throughput biological RNA-seq and single-nucleotide polymorphism data.<\/jats:p><jats:p>Availability and implementation: implemented in R<\/jats:p><jats:p>Contact: \u00a0nsa1@psu.edu or naomi@psu.edu<\/jats:p><jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btv104","type":"journal-article","created":{"date-parts":[[2015,3,4]],"date-time":"2015-03-04T01:52:31Z","timestamp":1425433951000},"page":"2303-2309","source":"Crossref","is-referenced-by-count":13,"title":["Estimating the proportion of true null hypotheses when the statistics are discrete"],"prefix":"10.1093","volume":"31","author":[{"given":"Isaac","family":"Dialsingh","sequence":"first","affiliation":[{"name":"1 Department of Mathematics and Statistics, The University of the West Indies, St. Augustine Campus, Trinidad and Tobago and"}]},{"given":"Stefanie R.","family":"Austin","sequence":"additional","affiliation":[{"name":"2 Department of Statistics, The Pennsylvania State University, State College, PA 16802-2111, USA"}]},{"given":"Naomi S.","family":"Altman","sequence":"additional","affiliation":[{"name":"2 Department of Statistics, The Pennsylvania State University, State College, PA 16802-2111, USA"}]}],"member":"286","published-online":{"date-parts":[[2015,3,2]]},"reference":[{"key":"2023020202154635400_btv104-B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1541-0420.2012.01825.x","article-title":"Estimation of false discovery rate using sequential permutation p-values","volume":"69","author":"Bancroft","year":"2013","journal-title":"Biometrics"},{"key":"2023020202154635400_btv104-B2","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. 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