{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T15:20:56Z","timestamp":1787498456730,"version":"build-2736575974"},"reference-count":42,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T00:00:00Z","timestamp":1438041600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p>Network meta-analysis expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, synthesizing both direct and indirect information and thus strengthening inference. Since most of trials only compare two treatments, a typical data set in a network meta-analysis managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with significant missing data. Zhang et\u00a0al. proposed an arm-based method accounting for correlations among different treatments within the same trial and assuming that absent arms are missing at random. However, in randomized controlled trials, nonignorable missingness or missingness not at random may occur due to deliberate choices of treatments at the design stage. In addition, those undertaking a network meta-analysis may selectively choose treatments to include in the analysis, which may also lead to missingness not at random. In this paper, we extend our previous work to incorporate missingness not at random using selection models. The proposed method is then applied to two network meta-analyses and evaluated through extensive simulation studies. We also provide comprehensive comparisons of a commonly used contrast-based method and the arm-based method via simulations in a technical appendix under missing completely at random and missing at random.<\/jats:p>","DOI":"10.1177\/0962280215596185","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T21:39:57Z","timestamp":1438119597000},"page":"2227-2243","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":25,"title":["Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness"],"prefix":"10.1177","volume":"26","author":[{"given":"Jing","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Epidemiology and Biostatistics, University of Maryland, College Park, MD, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haitao","family":"Chu","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, University of Minnesota, Minneapolis, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hwanhee","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Mental Health, Johns Hopkins University, Baltimore, MD, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beth A","family":"Virnig","sequence":"additional","affiliation":[{"name":"Division of Health Policy and Management, University of Minnesota, Minneapolis, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bradley P","family":"Carlin","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, University of Minnesota, Minneapolis, MN, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2015,7,28]]},"reference":[{"key":"bibr1-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1186\/1741-7015-9-79"},{"key":"bibr2-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19961230)15:24<2733::AID-SIM562>3.0.CO;2-0"},{"key":"bibr3-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1016\/j.jval.2011.04.002"},{"key":"bibr4-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(09)60046-5"},{"key":"bibr5-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1875"},{"key":"bibr6-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000001302"},{"key":"bibr7-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2831"},{"key":"bibr8-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxp032"},{"key":"bibr9-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1177\/1740774513498322"},{"key":"bibr10-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1002\/9781119013563"},{"key":"bibr11-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1076\/edre.7.4.353.8937"},{"key":"bibr12-0962280215596185","unstructured":"Hong H, Chu H, Zhang J, et al. A Bayesian missing data framework for generalized multiple outcome mixed treatment comparisons.\n                      Methods Research Reports\n                      . Report no. 13-EHC004-EF. Rockville, USA: Agency for Healthcare Research and Quality."},{"key":"bibr13-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1002\/jrsm.1039"},{"key":"bibr14-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM198312013092204"},{"key":"bibr15-0962280215596185","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.f5195"},{"key":"bibr16-0962280215596185","unstructured":"Coleman CI, Phung OJ, Cappelleri JC, et\u00a0al.\n                      Use of mixed treatment comparisons in systematic reviews\n                      (prepared by the University of Connecticut\/Hartford Hospital Evidence-based Practice Center under Contract No 290-2007-10067-I.) AHRQ Publication No. 12-EHC119-EF. 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