{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T04:40:02Z","timestamp":1789274402835,"version":"build-2803163510"},"reference-count":30,"publisher":"Wiley","issue":"9","license":[{"start":{"date-parts":[[2022,2,6]],"date-time":"2022-02-06T00:00:00Z","timestamp":1644105600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["R61NS120240"],"award-info":[{"award-number":["R61NS120240"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000027","name":"National Institute on Alcohol Abuse and Alcoholism","doi-asserted-by":"publisher","award":["R21AA027571"],"award-info":[{"award-number":["R21AA027571"]}],"id":[{"id":"10.13039\/100000027","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000026","name":"National Institute on Drug Abuse","doi-asserted-by":"publisher","award":["R01DA048764"],"award-info":[{"award-number":["R01DA048764"]}],"id":[{"id":"10.13039\/100000026","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":[[2022,4,30]]},"abstract":"<jats:p>Sequential, multiple assignment, randomized trials (SMARTs) compare sequences of treatment decision rules called dynamic treatment regimes (DTRs). In particular, the Adaptive Treatment for Alcohol and Cocaine Dependence (ENGAGE) SMART aimed to determine the best DTRs for patients with a substance use disorder. While many authors have focused on a single pairwise comparison, addressing the main goal involves comparisons of &gt;2 DTRs. For complex comparisons, there is a paucity of methods for binary outcomes. We fill this gap by extending the multiple comparisons with the best (MCB) methodology to the Bayesian binary outcome setting. The set of best is constructed based on simultaneous credible intervals. A substantial challenge for power analysis is the correlation between outcome estimators for distinct DTRs embedded in SMARTs due to overlapping subjects. We address this using Robins' G\u2010computation formula to take a weighted average of parameter draws obtained via simulation from the parameter posteriors. We use non\u2010informative priors and work with the exact distribution of parameters avoiding unnecessary normality assumptions and specification of the correlation matrix of DTR outcome summary statistics. We conduct simulation studies for both the construction of a set of optimal DTRs using the Bayesian MCB procedure and the sample size calculation for two common SMART designs. We illustrate our method on the ENGAGE SMART. The <jats:styled-content>R<\/jats:styled-content> package <jats:styled-content>SMARTbayesR<\/jats:styled-content> for power calculations is freely available on the Comprehensive <jats:styled-content>R<\/jats:styled-content> Archive Network (CRAN) repository. An <jats:styled-content>RShiny<\/jats:styled-content> app is available at \n<jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/wilart.shinyapps.io\/shinysmartbayesr\/\">https:\/\/wilart.shinyapps.io\/shinysmartbayesr\/<\/jats:ext-link>.<\/jats:p>","DOI":"10.1002\/sim.9323","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T00:04:07Z","timestamp":1644192247000},"page":"1688-1708","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian set of best dynamic treatment regimes: Construction and sample size calculation for SMARTs\u00a0with\u00a0binary outcomes"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0576-3686","authenticated-orcid":false,"given":"William J.","family":"Artman","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Computational Biology University of Rochester Medical Center  Rochester New\u00a0York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brent A.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology University of Rochester Medical Center  Rochester New\u00a0York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin G.","family":"Lynch","sequence":"additional","affiliation":[{"name":"Center for Clinical Epidemiology and Biostatistics (CCEB) and Department of Psychiatry University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James R.","family":"McKay","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Perelman School of Medicine University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashkan","family":"Ertefaie","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology University of Rochester Medical Center  Rochester New\u00a0York USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,2,6]]},"reference":[{"key":"e_1_2_12_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsat.2008.10.004"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11920-012-0296-5"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/08897077.2014.925029"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/acer.12800"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3223(00)00946-X"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2022"},{"key":"e_1_2_12_8_1","first-page":"189","volume-title":"Optimal Structural Nested Models for Optimal Sequential Decisions","author":"Robins JM","year":"2004"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0029372"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-statistics-022513-115553"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1177\/1740774514525691"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13142-014-0265-0"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/15374416.2015.1105138"},{"key":"e_1_2_12_14_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0039534"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.3109\/16066359.2015.1017570"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/add.13743"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2017.1386773"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0270-0255(86)90088-6"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxv025"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345582"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346732"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-7180-7"},{"key":"e_1_2_12_23_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxy064"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11123-005-2215-9"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2007.07.005"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201900364"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1201\/b16018"},{"key":"e_1_2_12_28_1","unstructured":"RoseEJ LaberEB DavidianM TsiatisAA ZhaoYQ KosorokMR.Sample size calculations for SMARTs; 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