{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T14:53:32Z","timestamp":1786978412020,"version":"build-2736575974"},"reference-count":35,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T00:00:00Z","timestamp":1581638400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2020,5,20]]},"abstract":"<jats:p>Nonignorable missing data poses key challenges for estimating treatment effects because the substantive model may not be identifiable without imposing further assumptions. For example, the Heckman selection model has been widely used for handling nonignorable missing data but requires the study to make correct assumptions, both about the joint distribution of the missingness and outcome and that there is a valid exclusion restriction. Recent studies have revisited how alternative selection model approaches, for example estimated by multiple imputation (MI) and maximum likelihood, relate to Heckman\u2010type approaches in addressing the first hurdle. However, the extent to which these different selection models rely on the exclusion restriction assumption with nonignorable missing data is unclear. Motivated by an interventional study (REFLUX) with nonignorable missing outcome data in half of the sample, this article critically examines the role of the exclusion restriction in Heckman, MI, and full\u2010likelihood selection models when addressing nonignorability. We explore the implications of the different methodological choices concerning the exclusion restriction for relative bias and root\u2010mean\u2010squared error in estimating treatment effects. We find that the relative performance of the methods differs in practically important ways according to the relevance and strength of the exclusion restriction. The full\u2010likelihood approach is less sensitive to alternative assumptions about the exclusion restriction than Heckman\u2010type models and appears an appropriate method for handling nonignorable missing data. We illustrate the implications of method choice for inference in the REFLUX study, which evaluates the effect of laparoscopic surgery on long\u2010term quality of life for patients with gastro\u2010oseophageal reflux disease.<\/jats:p>","DOI":"10.1002\/sim.8504","type":"journal-article","created":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T12:49:52Z","timestamp":1581684592000},"page":"1658-1674","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Estimating treatment effects under untestable assumptions with nonignorable missing data"],"prefix":"10.1002","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1428-1232","authenticated-orcid":false,"given":"Manuel","family":"Gomes","sequence":"first","affiliation":[{"name":"Department of Applied Health Research University College London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael G.","family":"Kenward","sequence":"additional","affiliation":[{"name":"Department of Medical Statistics LSHTM  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Grieve","sequence":"additional","affiliation":[{"name":"Department of Health Services Research and Policy LSHTM  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Carpenter","sequence":"additional","affiliation":[{"name":"Department of Medical Statistics LSHTM  London UK"},{"name":"MRC Clinical Trials Unit University College London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2020,2,14]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12136"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40273-014-0193-3"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774517711442"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/1912352"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986113"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011180"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6902"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.2307\/146317"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00236"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1515\/jem-2013-0008"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12136"},{"key":"e_1_2_10_13_1","first-page":"643","article-title":"On the testability of models with missing data","volume":"33","author":"Mohan K","year":"2014","journal-title":"Proceedings of Artificial Intelligence and Statistics"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-6419.00104"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119013563"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1201\/b17622"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.3310\/hta17220"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/hec.3173"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-8510(90)90421-9"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177010269"},{"key":"e_1_2_10_21_1","volume-title":"Statistics in Practice","author":"Carpenter J","year":"2013"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316696"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4067"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7988"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1186\/1477-7525-2-49"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/hec.2930"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssc.12028"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280212448721"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v027.i07"},{"key":"e_1_2_10_30_1","first-page":"279","article-title":"Strategy for modelling nonrandom missing data mechanisms in observational studies using Bayesian methods","volume":"28","author":"Mason A","year":"2012","journal-title":"J Off Stat"},{"key":"e_1_2_10_31_1","unstructured":"PlummerM. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. Paper presented at: Proceedings of the 3rd International Workshop on Distributed Statistical Computing; 2003:1\u201010."},{"key":"e_1_2_10_32_1","doi-asserted-by":"publisher","DOI":"10.1191\/1471082X06st113oa"},{"key":"e_1_2_10_33_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2012.656011"},{"key":"e_1_2_10_34_1","doi-asserted-by":"publisher","DOI":"10.1097\/EDE.0000000000000218"},{"key":"e_1_2_10_35_1","unstructured":"ClarkeS HouleB. Evaluation of Heckman selection model method for correcting estimates of HIV prevalence from sample surveys. Center for Statistics and the Social Sciences Working Paper no. 120. 2012."},{"key":"e_1_2_10_36_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19981215)17:23<2723::AID-SIM38>3.0.CO;2-5"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.8504","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8504","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.8504","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.8504","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T09:59:29Z","timestamp":1693821569000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.8504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,14]]},"references-count":35,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2020,5,20]]}},"alternative-id":["10.1002\/sim.8504"],"URL":"https:\/\/doi.org\/10.1002\/sim.8504","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,14]]},"assertion":[{"value":"2018-04-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-01-20","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-02-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}