{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:21:38Z","timestamp":1787505698075,"version":"build-2736575974"},"reference-count":34,"publisher":"Wiley","issue":"18-19","license":[{"start":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:00:00Z","timestamp":1786579200000},"content-version":"vor","delay-in-days":12,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100021171","name":"Guangdong Basic and Applied Basic Research Foundation","doi-asserted-by":"publisher","award":["2026A1515010197"],"award-info":[{"award-number":["2026A1515010197"]}],"id":[{"id":"10.13039\/501100021171","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":[[2026,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Estimation of optimal individualized treatment rules (ITRs) tailored to patient characteristics is a crucial component of precision medicine. When such problems arise in multicenter randomized trials with known treatment assignment probabilities, the optimal ITR may vary across sites because of site\u2010level heterogeneity, and directly pooling data across centers can lead to biased ITR estimation. Meanwhile, privacy constraints often prevent investigators from accessing individual\u2010level data from all centers. We therefore propose Heterogeneous Distributed Learning (HD\u2010learning) to estimate optimal site\u2010specific ITRs using only summary\u2010level data from each site in a single communication round. The method uses a distributed mixed\u2010effects model to accommodate common fixed effects and site\u2010specific random effects. We further develop Shrinkage HD\u2010learning (SHD\u2010learning) for moderate\u2010 or high\u2010dimensional covariates. Under suitable conditions, we establish asymptotic properties of the proposed estimators. Simulations show that our methods are lossless relative to the corresponding pooled estimator and outperform methods that ignore heterogeneity. We illustrate the proposed methods using the acute upper respiratory tract infections (AURTIs) study and the opioid withdrawal study.<\/jats:p>","DOI":"10.1002\/sim.70696","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:37:41Z","timestamp":1786621061000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Estimating Optimal Site\u2010Specific Individualized Treatment Rules With Limited Data Sharing"],"prefix":"10.1002","volume":"45","author":[{"given":"Nan","family":"Qiao","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics Beijing University of Technology  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1597-3951","authenticated-orcid":false,"given":"Jingxiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Statistics Renmin University of China  Beijing China"},{"name":"Center for Applied Statistics Renmin University of China  Beijing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1837-5253","authenticated-orcid":false,"given":"Zishu","family":"Zhan","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, State Key Laboratory of Multi\u2010organ Injury Prevention and Treatment, Guangdong Provincial Key Laboratory of Tropical Disease Research, School of Public Health Southern Medical University  Guangzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,13]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2020.1865167"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOS864"},{"issue":"3","key":"e_1_2_10_4_1","first-page":"901","article-title":"Penalized Q\u2010Learning for Dynamic Treatment Regimens","volume":"25","author":"Song R.","year":"2015","journal-title":"Statistica Sinica"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/17-AOS1570"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asaa076"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802221144326"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-50690-1"},{"issue":"1","key":"e_1_2_10_9_1","first-page":"D933","article-title":"GWAS Central: A Comprehensive Resource for the Discovery and Comparison of Genotype and Phenotype Data From Genome\u2010Wide Association Studies","volume":"48","author":"Beck T.","year":"2020","journal-title":"Nucleic Acids Research"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyq111"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-29160-4"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxac006"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asab007"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9318"},{"key":"e_1_2_10_15_1","first-page":"171","volume-title":"Meta\u2010Analysis of Individualized Treatment Rules via Sign\u2010Coherency","author":"Cheng J. J.","year":"2022"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1214\/18-EJS1480"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1214\/25-AOAS2017"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2012.02.005"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/54.1-2.93"},{"key":"e_1_2_10_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729893"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2006.11.016"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781315119281"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.951443"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2021.1923517"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214507000000509"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxz036"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asm037"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13818"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1198\/106186006X100515"},{"key":"e_1_2_10_30_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.c2096"},{"key":"e_1_2_10_31_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780429246593"},{"key":"e_1_2_10_32_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj-2023-078276"},{"key":"e_1_2_10_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2013.03.018"},{"key":"e_1_2_10_34_1","doi-asserted-by":"publisher","DOI":"10.1515\/2156\u20106674.1021"},{"key":"e_1_2_10_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2012.09.003"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70696","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70696","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70696","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:31:02Z","timestamp":1787502662000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70696"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":34,"journal-issue":{"issue":"18-19","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["10.1002\/sim.70696"],"URL":"https:\/\/doi.org\/10.1002\/sim.70696","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"2025-03-11","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70696"}}