{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T11:19:19Z","timestamp":1788175159134,"version":"build-2803163510"},"reference-count":58,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"vor","delay-in-days":21,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["P30 AI036214"],"award-info":[{"award-number":["P30 AI036214"]}],"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":[[2026,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Cluster randomized controlled trials where groups (or clusters) of individuals, rather than single individuals, are randomized are especially useful when individual\u2010level randomization is not feasible or when interventions are naturally delivered at the group level. Balanced randomization in the cluster randomized trial setting can pose logistical challenges and strain resources if subjects are randomized to a non\u2010optimal arm. We propose a Bayesian response\u2010adaptive randomization design for cluster randomized controlled trials based on Thompson sampling, which dynamically allocates clusters to the most efficacious treatment arm based on the interim posterior distributions of treatment effects using Markov chain Monte Carlo sampling. Our design also incorporates early stopping rules for efficacy and futility determined by prespecified posterior probability thresholds. The performance of the proposed design is evaluated across various operating characteristics under multiple settings, including varying intra\u2010cluster correlation coefficients, cluster sizes, and effect sizes. Our adaptive approach is also compared with a standard, parallel two\u2010arm cluster randomized controlled clinical trial design, highlighting improvements in both ethical considerations and efficiency. From our simulation studies based on an HIV behavioral trial, we demonstrate these improvements by preferentially assigning more clusters to the more efficacious intervention while maintaining robust statistical power and controlling false positive rates.<\/jats:p>","DOI":"10.1002\/sim.70386","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T09:19:22Z","timestamp":1769073562000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Response\u2010Adaptive Randomization for Cluster Randomized Controlled Trials"],"prefix":"10.1002","volume":"45","author":[{"given":"Yunyi","family":"Liu","sequence":"first","affiliation":[{"name":"Herbert Wertheim School of Public Health and Human Longevity Science University of California  San Diego California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maile","family":"Young Karris","sequence":"additional","affiliation":[{"name":"Department of Medicine University of California  San Diego California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8408-1247","authenticated-orcid":false,"given":"Sonia","family":"Jain","sequence":"additional","affiliation":[{"name":"Herbert Wertheim School of Public Health and Human Longevity Science University of California  San Diego California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/1471-0528.15199"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1038\/ijo.2016.239"},{"key":"e_1_2_12_4_1","first-page":"1","article-title":"Building on Existing Tools to Improve Chronic Disease Prevention and Screening in Public Health: A Cluster Randomized Trial","volume":"21","author":"Lofters A. K.","year":"2021","journal-title":"BMC Public Health"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amepre.2019.02.018"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.322.7286.583"},{"issue":"2","key":"e_1_2_12_7_1","article-title":"Cluster\u2010Randomized Studies in Educational Research: Principles and Methodological Aspects","volume":"34","author":"Dreyhaupt J.","year":"2017","journal-title":"GMS Journal for Medical Education"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa1701075"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2753.2005.00568.x"},{"key":"e_1_2_12_10_1","unstructured":"U.S. Food and Drug Administration \u201cGuidance for the Use of Bayesian Statistics in Medical Device Clinical Trials \u201d Guidance document U.S. Food and Drug Administration 2010. accessed November 23 2023 https:\/\/www.fda.gov\/regulatory\u2010information\/search\u2010fda\u2010guidance\u2010documents\/guidance\u2010use\u2010bayesian\u2010statistics\u2010medical\u2010device\u2010clinical\u2010trials"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-024-02235-0"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-024-02272-9"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph18020530"},{"key":"e_1_2_12_14_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12916-018-1017-7"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2022.11.002"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-019-4021-0"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1845"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-022-06664-4"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2289"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280220973697"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1177\/17407745231221438"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/sta4.487"},{"key":"e_1_2_12_23_1","doi-asserted-by":"publisher","DOI":"10.2307\/2332286"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v076.i01"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11904-025-00734-3"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.7448\/IAS.17.1.18719"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.2217\/pmt-2020-0004"},{"key":"e_1_2_12_28_1","doi-asserted-by":"publisher","DOI":"10.3389\/fphar.2021.653852"},{"key":"e_1_2_12_29_1","doi-asserted-by":"publisher","DOI":"10.1097\/j.pain.0000000000001369"},{"issue":"5","key":"e_1_2_12_30_1","first-page":"419","article-title":"Chronic Pain and Opioid Use in Older People With HIV","volume":"29","author":"Mandyam V. C.","year":"2022","journal-title":"Topics in Antiviral Medicine"},{"issue":"4","key":"e_1_2_12_31_1","article-title":"Opioids and HIV Infection: From Pain Management to Addiction Treatment","volume":"25","author":"Cunningham C. O.","year":"2018","journal-title":"Topics in Antiviral Medicine"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.beth.2009.08.002"},{"key":"e_1_2_12_33_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1352465808004700"},{"key":"e_1_2_12_34_1","doi-asserted-by":"publisher","DOI":"10.1080\/09602011.2010.540920"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cbpra.2014.05.006"},{"key":"e_1_2_12_36_1","doi-asserted-by":"publisher","DOI":"10.1002\/ejp.1762"},{"key":"e_1_2_12_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1130-8621(18)30046-9"},{"key":"e_1_2_12_38_1","doi-asserted-by":"publisher","DOI":"10.1080\/09540121.2021.1981819"},{"key":"e_1_2_12_39_1","doi-asserted-by":"publisher","DOI":"10.1097\/PSY.0000000000001172"},{"key":"e_1_2_12_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-23369-7"},{"key":"e_1_2_12_41_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-020-04269-3"},{"key":"e_1_2_12_42_1","doi-asserted-by":"publisher","DOI":"10.3102\/1076998615606113"},{"key":"e_1_2_12_43_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0258(20010215)20:3<435::AID-SIM804>3.0.CO;2-E"},{"key":"e_1_2_12_44_1","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA117A"},{"key":"e_1_2_12_45_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9871"},{"key":"e_1_2_12_46_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000070"},{"key":"e_1_2_12_47_1","doi-asserted-by":"crossref","unstructured":"M. B.Haugh \u201cA Tutorial on Markov Chain Monte\u2010Carlo and Bayesian Modeling \u201d2021 https:\/\/doi.org\/10.2139\/ssrn.3759243. SSRN 3759243.","DOI":"10.2139\/ssrn.3759243"},{"key":"e_1_2_12_48_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10474335"},{"key":"e_1_2_12_49_1","doi-asserted-by":"publisher","DOI":"10.1002\/wics.1546"},{"key":"e_1_2_12_50_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2010.00765.x"},{"key":"e_1_2_12_51_1","unstructured":"M.Betancourt \u201cA conceptual introduction to Hamiltonian Monte Carlo \u201d arXiv preprint; 2017. arXiv: 1701.02434."},{"issue":"1","key":"e_1_2_12_52_1","first-page":"1593","article-title":"The no\u2010U\u2010Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo","volume":"15","author":"Hoffman M. D.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_12_53_1","unstructured":"Stan Development Team \u201cRStan: The R Interface to Stan. R package version 2.19.1 \u201d2019 http:\/\/mc\u2010stan.org\/."},{"key":"e_1_2_12_54_1","doi-asserted-by":"publisher","DOI":"10.1080\/10543406.2017.1293077"},{"key":"e_1_2_12_55_1","doi-asserted-by":"crossref","unstructured":"E. Y. N.Tang S.Baas D.Kaddaj L.Pin D. S.Robertson andS. S.Villar \u201cA Burn\u2010in(g) Question: How Long Should an Initial Equal Randomization Stage be Before Bayesian Response\u2010Adaptive Randomization \u201d2025 https:\/\/doi.org\/10.48550\/arXiv.2503.19795. arXiv preprint.","DOI":"10.1177\/09622802251411538"},{"key":"e_1_2_12_56_1","doi-asserted-by":"publisher","DOI":"10.1093\/annonc\/mdv238"},{"key":"e_1_2_12_57_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3978"},{"key":"e_1_2_12_58_1","doi-asserted-by":"publisher","DOI":"10.1002\/047005588X"},{"key":"e_1_2_12_59_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-STS269"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70386","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70386","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T10:47:22Z","timestamp":1788173242000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70386"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":58,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10.1002\/sim.70386"],"URL":"https:\/\/doi.org\/10.1002\/sim.70386","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"2025-08-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-22","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-22","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70386"}}