{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:47:05Z","timestamp":1792601225819,"version":"4.5.0"},"reference-count":70,"publisher":"Wiley","issue":"23-24","license":[{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T00:00:00Z","timestamp":1790294400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Externally controlled single\u2010arm trials are increasingly popular because they do not require randomized controls, thereby substantially reducing financial costs; however, valid causal inference in this setting relies critically on transportability between the trial and external populations, an assumption that is untestable. Frequentist semiparametrically efficient estimators, such as the doubly robust estimator, are typically analyzed under first\u2010order asymptotics and are designed to mitigate nuisance\u2010estimation bias under correct specification; however, this framework does not account for structural bias arising under local transportability violations, where bias and stochastic fluctuation occur at the same parametric rate. We propose a reliable Bayesian framework for estimating the average treatment effect on the treated (ATT) that combines synthetic outcome construction with residualized power\u2010prior borrowing. Flexible machine learning is first used to construct covariate\u2010aligned synthetic controls, after which Bayesian inference on residualized outcomes allows external borrowing to modulate uncertainty without distorting covariate\u2010driven heterogeneity. The posterior admits a heavy\u2010tailed distribution\u2014unlike classical Wald procedures\u2014and the resulting estimator lies outside the class of regular asymptotically linear estimators, thereby revealing behavior beyond first\u2010order semiparametric asymptotics. We establish a reliability\u2013efficiency trade\u2010off under local transportability violations. Simulations and a case study on schizophrenia trial design demonstrate the theoretical findings and practical utility.<\/jats:p>","DOI":"10.1002\/sim.70748","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T08:37:59Z","timestamp":1790325479000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reliable Bayesian Causal Inference for Externally Controlled Single\u2010Arm Trials Under Transportability Violations"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9551-5562","authenticated-orcid":false,"given":"Se Yoon","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Statistics Texas A&amp;M University  College Station Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,25]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v25i1.7861"},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-STS313"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13009"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/23-STS889"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13609"},{"key":"e_1_2_13_7_1","first-page":"1","article-title":"Power Priors and Type I Error Control: Constrained Borrowing of External Control Data","volume":"36","author":"Lee S. 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