{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:10:41Z","timestamp":1773249041845,"version":"3.50.1"},"reference-count":41,"publisher":"Wiley","issue":"15","license":[{"start":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T00:00:00Z","timestamp":1681084800000},"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"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2023,7,10]]},"abstract":"<jats:p>Existing methods for estimating the mean outcome under a given sequential treatment rule often rely on intention\u2010to\u2010treat analyses, which estimate the effect of following a certain treatment rule regardless of compliance behavior of patients. There are two major concerns with intention\u2010to\u2010treat analyses: (1) the estimated effects are often biased toward the null effect; (2) the results are not generalizable and reproducible due to the potentially differential compliance behavior. These are particularly problematic in settings with a high level of non\u2010compliance, such as substance use disorder studies. Our work is motivated by the Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE), which is a multi\u2010stage trial that aimed to construct optimal treatment strategies to engage patients in therapy. Due to the relatively low level of compliance in this trial, intention\u2010to\u2010treat analyses essentially estimate the effect of being randomized to a certain treatment, instead of the actual effect of the treatment. We obviate this challenge by defining the target parameter as the mean outcome under a dynamic treatment regime conditional on a potential compliance stratum. We propose a flexible non\u2010parametric Bayesian approach based on principal stratification, which consists of a Gaussian copula model for the joint distribution of the potential compliances, and a Dirichlet process mixture model for the treatment sequence specific outcomes. We conduct extensive simulation studies which highlight the utility of our approach in the context of multi\u2010stage randomized trials. We show robustness of our estimator to non\u2010linear and non\u2010Gaussian settings as well.<\/jats:p>","DOI":"10.1002\/sim.9742","type":"journal-article","created":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T00:49:31Z","timestamp":1681174171000},"page":"2661-2691","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A non\u2010parametric Bayesian approach for adjusting partial compliance in sequential decision making"],"prefix":"10.1002","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4567-0027","authenticated-orcid":false,"given":"Indrabati","family":"Bhattacharya","sequence":"first","affiliation":[{"name":"Department of Statistics Florida State University  Tallahassee Florida USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brent A.","family":"Johnson","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Computational Biology University of 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