{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T10:49:04Z","timestamp":1782211744497,"version":"3.54.5"},"reference-count":47,"publisher":"Wiley","issue":"13-14","license":[{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100006093","name":"Patient-Centered Outcomes Research Institute","doi-asserted-by":"publisher","award":["ME\u20102020C1\u201019220"],"award-info":[{"award-number":["ME\u20102020C1\u201019220"]}],"id":[{"id":"10.13039\/100006093","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006093","name":"Patient-Centered Outcomes Research Institute","doi-asserted-by":"publisher","award":["ME\u20102020C3\u201021072"],"award-info":[{"award-number":["ME\u20102020C3\u201021072"]}],"id":[{"id":"10.13039\/100006093","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01\u2010HL168202"],"award-info":[{"award-number":["R01\u2010HL168202"]}],"id":[{"id":"10.13039\/100000002","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":[[2026,6]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Cluster\u2010randomized trials (CRTs) on fragile populations frequently encounter complex attrition problems where the reasons for missing outcomes can be heterogeneous, with participants who are known alive, known to have died, or with unknown survival status, and with complex and distinct missing data mechanisms for each group. Although existing methods have been developed to address death truncation in CRTs, no existing methods can jointly accommodate participants who drop out for reasons unrelated to mortality or serious illnesses, or those with an unknown survival status. This paper proposes a Bayesian framework for estimating survivor average causal effects in CRTs while accounting for different types of incomplete data. Our approach uses a multivariate outcome that jointly estimates the causal effects, and in the posterior estimates, we distinguish the individual\u2010level and the cluster\u2010level survivor average causal effect. We perform simulation studies to evaluate the performance of our model and found low bias and high coverage on key parameters across several different scenarios. We use data from a geriatric CRT to illustrate the use of our model. Although our illustration focuses on the case of a bivariate continuous outcome, our model is straightforwardly extended to accommodate more than two endpoints as well as other types of endpoints (e.g., binary). Thus, this work provides a general modeling framework for handling complex missingness in CRTs and can be applied to a wide range of settings with aging and palliative care populations.<\/jats:p>","DOI":"10.1002\/sim.70588","type":"journal-article","created":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T11:37:07Z","timestamp":1779709027000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Inference for Cluster\u2010Randomized Trials With Multivariate Outcomes Subject to Both Truncation by Death and Missingness"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7697-5029","authenticated-orcid":false,"given":"Guangyu","family":"Tong","sequence":"first","affiliation":[{"name":"Department of Internal Medicine, Section of Cardiovascular Medicine Yale School of Medicine  New Haven Connecticut USA"},{"name":"Department of Biostatistics Yale School of Public Health  New Haven Connecticut USA"},{"name":"Cardiovascular Medicine Analytics Center Yale School of Medicine  New Haven Connecticut USA"},{"name":"Center for Methods in Implementation and Prevention Science Yale University  New Haven Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenxi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics &amp; Bioinformatics Duke School of Medicine  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eric","family":"Velazquez","sequence":"additional","affiliation":[{"name":"Department of Internal Medicine, Section of Cardiovascular Medicine Yale School of Medicine  New Haven Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0553-674X","authenticated-orcid":false,"given":"Michael O.","family":"Harhay","sequence":"additional","affiliation":[{"name":"Clinical Trials Methods and Outcomes Lab, Palliative and Advanced Illness Research (PAIR) Center, Perelman School of Medicine University of Pennsylvania  Philadelphia Pennsylvania USA"},{"name":"Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-1893","authenticated-orcid":false,"given":"Fan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Internal Medicine, Section of Cardiovascular Medicine Yale School of Medicine  New Haven Connecticut USA"},{"name":"Department of Biostatistics Yale School of Public Health  New Haven Connecticut USA"},{"name":"Center for Methods in Implementation and Prevention Science Yale University  New Haven Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,5,25]]},"reference":[{"key":"e_1_2_12_2_1","volume-title":"Design and Analysis of Group\u2010Randomized Trials","author":"Murray D. M.","year":"1998"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.2105\/AJPH.2017.303706"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.2105\/AJPH.2017.303707"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.j5748"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-016-1201-z"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1214\/088342306000000114"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-52636-2_117"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280219859915"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1186\/1477-7525-6-57"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280214545121"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1097\/MLR.0000000000001059"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1001\/jama.289.19.2554"},{"key":"e_1_2_12_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2023.2289693"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyac131"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2002.00021.x"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0012"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2011.tm10265"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.3102\/10769986028004353"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12113"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6181"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"issue":"4","key":"e_1_2_12_23_1","first-page":"558","article-title":"On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection","volume":"97","author":"Neyman J.","year":"1934","journal-title":"Journal of the Royal Statistical Society. Series A, Statistics in Society"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/kwad038"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9939"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1177\/17407745211046672"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2021.12.006"},{"key":"e_1_2_12_28_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13692"},{"key":"e_1_2_12_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11256"},{"key":"e_1_2_12_30_1","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOAS674"},{"key":"e_1_2_12_31_1","doi-asserted-by":"publisher","DOI":"10.1093\/ageing\/aft185"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476902"},{"key":"e_1_2_12_33_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12191"},{"key":"e_1_2_12_34_1","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/kwq418"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000706"},{"key":"e_1_2_12_36_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802241254197"},{"key":"e_1_2_12_37_1","doi-asserted-by":"publisher","DOI":"10.1080\/07350015.2020.1862672"},{"key":"e_1_2_12_38_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/3.2.147"},{"key":"e_1_2_12_39_1","article-title":"Consort 2010 Statement: Extension to Cluster Randomised Trials","volume":"345","author":"Campbell M. K.","year":"2012","journal-title":"BMJ (Clinical Research Ed.)"},{"key":"e_1_2_12_40_1","doi-asserted-by":"publisher","DOI":"10.1186\/1472-6963-12-403"},{"key":"e_1_2_12_41_1","volume-title":"User's Manual for the SF\u201012v2 Health Survey (With a Supplement Documenting SF\u201012 Health Survey)","author":"Ware J.","year":"2002"},{"key":"e_1_2_12_42_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9401"},{"key":"e_1_2_12_43_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2005.030227.x"},{"issue":"1","key":"e_1_2_12_44_1","article-title":"Semiparametric Principal Stratification Analysis Beyond Monotonicity","volume":"38","author":"Tong J.","year":"2025","journal-title":"Statistica Sinica"},{"key":"e_1_2_12_45_1","doi-asserted-by":"publisher","DOI":"10.1214\/23-AOAS1792"},{"key":"e_1_2_12_46_1","doi-asserted-by":"publisher","DOI":"10.2307\/2533322"},{"key":"e_1_2_12_47_1","doi-asserted-by":"publisher","DOI":"10.2307\/2986113"},{"key":"e_1_2_12_48_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011180"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70588","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70588","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70588","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T10:18:56Z","timestamp":1782209936000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,25]]},"references-count":47,"journal-issue":{"issue":"13-14","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["10.1002\/sim.70588"],"URL":"https:\/\/doi.org\/10.1002\/sim.70588","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,25]]},"assertion":[{"value":"2025-04-03","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-05-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-05-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70588"}}