{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T05:07:22Z","timestamp":1790140042122,"version":"4.0.1"},"reference-count":17,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T00:00:00Z","timestamp":1789948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider sequential monitoring in early-phase clinical trial designs with patient noncompliance. Unlike most existing methods that focus on modeling a single endpoint, we consider the entire outcome distribution and propose a Bayesian causal effect estimation method based on the Wasserstein distance. Using a principal stratification framework and random forest to classify patient compliance statuses, we quantify a distributional causal-effect magnitude among Compliers by calculating the Wasserstein distance between the barycenters of their potential outcome distributions. The proposed method also adaptively determines early trial termination based on accumulated outcomes. Simulation results show favorable operating characteristics under the scenarios investigated, with the proposed analysis remaining close to the oracle benchmark as noncompliance increases.<\/jats:p>","DOI":"10.3390\/e28091040","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T14:12:09Z","timestamp":1789999929000},"page":"1040","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Clinical Trial Design for Distributional Outcomes with Noncompliance"],"prefix":"10.3390","volume":"28","author":[{"given":"Xin","family":"Guo","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Shanghai University of Finance and Economics, Shanghai 200433, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siyuan","family":"Li","sequence":"additional","affiliation":[{"name":"Santa Margarita Catholic High School, Irvine, CA 92688, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3137-1085","authenticated-orcid":false,"given":"Weining","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Statistics, Donald Bren School of Information and Computer Sciences, University of California, Irvine, CA 92697, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/0021-9681(61)90060-1","article-title":"The determination of the number of patients required in a preliminary and a follow-up trial of a new chemotherapeutic agent","volume":"13","author":"Gehan","year":"1961","journal-title":"J. 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