{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T04:02:53Z","timestamp":1790395373474,"version":"4.1.0"},"reference-count":18,"publisher":"Wiley","issue":"28","license":[{"start":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T00:00:00Z","timestamp":1597795200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["YZ"],"award-info":[{"award-number":["YZ"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2020,12,10]]},"abstract":"<jats:p>In the literature of statistical analysis with missing data there is a significant gap in statistical inference for missing data mechanisms especially for nonmonotone missing data, which has essentially restricted the use of the estimation methods which require estimating the missing data mechanisms. For example, the inverse probability weighting methods (Horvitz &amp; Thompson, 1952; Little &amp; Rubin, 2002), including the popular augmented inverse probability weighting (Robins et al, 1994), depend on sufficient models for the missing data mechanisms to reduce estimation bias while improving estimation efficiency. This research proposes a semiparametric likelihood method for estimating missing data mechanisms where an EM algorithm with closed form expressions for both E\u2010step and M\u2010step is used in evaluating the estimate (Zhao et al, 2009; Zhao, 2020). The asymptotic variance of the proposed estimator is estimated from the profile score function. The methods are general and robust. Simulation studies in various missing data settings are performed to examine the finite sample performance of the proposed method. Finally, we analysis the missing data mechanism of Duke cardiac catheterization coronary artery disease diagnostic data to illustrate the method.<\/jats:p>","DOI":"10.1002\/sim.8727","type":"journal-article","created":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T19:53:57Z","timestamp":1598558037000},"page":"4325-4333","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Statistical inference for missing data mechanisms"],"prefix":"10.1002","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9768-7683","authenticated-orcid":false,"given":"Yang","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics University of Regina  Regina Saskatchewan Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2020,8,19]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780110608"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119482260"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/63.3.581"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476818"},{"key":"e_1_2_9_6_1","volume-title":"Semiparametric Theory and Missing Data","author":"Tsiatis A","year":"2006"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2016.1256814"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19970115)16:1<39::AID-SIM535>3.0.CO;2-D"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000001844"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200810487"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10260-020-00530-w"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920802618392"},{"key":"e_1_2_9_13_1","first-page":"5","article-title":"An overview of composite likelihood methods","volume":"21","author":"Varin C","year":"2011","journal-title":"Stat Sin"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474938"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/83.4.916"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10474219"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7833"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177705693"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1952.10483446"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8727","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.8727","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8727","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T21:52:40Z","timestamp":1693864360000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.8727"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,19]]},"references-count":18,"journal-issue":{"issue":"28","published-print":{"date-parts":[[2020,12,10]]}},"alternative-id":["10.1002\/sim.8727"],"URL":"https:\/\/doi.org\/10.1002\/sim.8727","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,19]]},"assertion":[{"value":"2019-08-30","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-07-23","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-08-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}