{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T14:22:33Z","timestamp":1789827753022,"version":"4.0.1"},"reference-count":28,"publisher":"Wiley","issue":"29","license":[{"start":{"date-parts":[[2008,9,9]],"date-time":"2008-09-09T00:00:00Z","timestamp":1220918400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2008,9,9]],"date-time":"2008-09-09T00:00:00Z","timestamp":1220918400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2008,9,9]],"date-time":"2008-09-09T00:00:00Z","timestamp":1220918400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2008,12,20]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The presence and impact of heterogeneity in the standard one\u2010way random effects model in meta\u2010analysis are often assessed using the <jats:italic>Q<\/jats:italic> statistic due to Cochran. We derive the exact distribution of this statistic under the assumptions of the random effects model, and also suggest two moment\u2010based approximations and a saddlepoint approximation for <jats:italic>Q<\/jats:italic>. The exact and approximate distributions are then applied to obtain the corresponding distributions of the recently proposed heterogeneity measures <jats:italic>I<\/jats:italic><jats:sup>2<\/jats:sup> and <jats:italic>H<\/jats:italic><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:02776715:media:SIM3428:tex2gif-stack-1\"\/>, the power of the standard test for the presence of heterogeneity and confidence intervals for the between\u2010study variance parameter when the DerSimonian\u2013Laird or the Hartung\u2013Makambi estimator is used. The methodology is illustrated by revisiting a recent simulation study concerning the heterogeneity measures and applying all the proposed methods to four published meta\u2010analyses. Published in 2008 by John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.3428","type":"journal-article","created":{"date-parts":[[2008,9,9]],"date-time":"2008-09-09T10:27:21Z","timestamp":1220956041000},"page":"6093-6110","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":102,"title":["The exact distribution of Cochran's heterogeneity statistic in one\u2010way random effects meta\u2010analysis"],"prefix":"10.1002","volume":"27","author":[{"given":"Brad J.","family":"Biggerstaff","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Jackson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2008,9,9]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2897"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/3001666"},{"key":"e_1_2_1_4_2","volume-title":"Methods for Meta\u2010analysis in Medical Research","author":"Sutton AJ","year":"2002"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0197-2456(86)90046-2"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1186"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19980430)17:8<841::AID-SIM781>3.0.CO;2-D"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2692"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19960330)15:6<619::AID-SIM188>3.0.CO;2-A"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/3.4.445"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/87.3.619"},{"key":"e_1_2_1_13_2","volume-title":"Meta\u2010analysis","author":"Hartung J","year":"2003"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2481"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.3.4.486"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.6.3.203"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.9.4.426"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2514"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.2307\/2347721"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v011.i04"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.2307\/3002019"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/86.4.929"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200510175"},{"key":"e_1_2_1_24_2","first-page":"55","article-title":"Positive estimation of the between\u2010group variance component in one\u2010way ANOVA and meta\u2010analysis","volume":"36","author":"Hartung J","year":"2002","journal-title":"South African Statistical Journal"},{"key":"e_1_2_1_25_2","volume-title":"Combining Information: Statistical Issues and Opportunities for Research","author":"Draper D","year":"2002"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.290.6461.17"},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.7326\/0003-4819-117-1-59"},{"key":"e_1_2_1_28_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19991030)18:20<2693::AID-SIM235>3.0.CO;2-V"},{"key":"e_1_2_1_29_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2293"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3428","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.3428","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.3428","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,13]],"date-time":"2023-10-13T04:50:14Z","timestamp":1697172614000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.3428"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,9]]},"references-count":28,"journal-issue":{"issue":"29","published-print":{"date-parts":[[2008,12,20]]}},"alternative-id":["10.1002\/sim.3428"],"URL":"https:\/\/doi.org\/10.1002\/sim.3428","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,9,9]]}}}