{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T19:47:17Z","timestamp":1768679237499,"version":"3.49.0"},"reference-count":37,"publisher":"Wiley","issue":"13-14","license":[{"start":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T00:00:00Z","timestamp":1749254400000},"content-version":"vor","delay-in-days":6,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>ABSTRACT<\/jats:title><jats:p>Randomized controlled trials (RCTs) are the gold standard for causal inference and are widely used. However, valid analyses of RCTs are often complicated by non\u2010compliance, which can lead to confounding bias and biased causal effect estimation. The main challenge comes from compliance datasets in both the treatment and control groups both following two\u2010component mixture models. The maximum nonparametric likelihood estimator is inconsistent in a two\u2010component mixture model even if the mixture proportion and one of the components are completely known, but the other component is unknown. In this paper, we instead assume parametric models for the ratios of risks among compliers assigned treatment, never\u2010takers and always\u2010takers, and leave the baseline compliers not assigned treatment unspecified. We develop a novel two\u2010step maximum likelihood estimation procedure by making full use of the observed covariates and latent compliance classes, which theoretically can produce asymptotic root  consistent estimators. In particular, our proposed estimator for the conditional local risk ratio always lies within the range of the parameter. Our numerical results show that the proposed method is generally more reliable than existing alternatives.<\/jats:p>","DOI":"10.1002\/sim.70153","type":"journal-article","created":{"date-parts":[[2025,6,7]],"date-time":"2025-06-07T07:05:04Z","timestamp":1749279904000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semiparametric Estimation of Relative Causal Effects in Randomized Controlled Trials With Noncompliance"],"prefix":"10.1002","volume":"44","author":[{"given":"Wenli","family":"Liu","sequence":"first","affiliation":[{"name":"KLATASDS\u2010MOE School of Statistics, East China Normal University  Shanghai China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2817-6326","authenticated-orcid":false,"given":"Jing","family":"Qin","sequence":"additional","affiliation":[{"name":"National Institute of Allergy and Infectious Diseases National Institutes of Health  Bethesda Maryland USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9743-9276","authenticated-orcid":false,"given":"Yukun","family":"Liu","sequence":"additional","affiliation":[{"name":"KLATASDS\u2010MOE School of Statistics, East China Normal University  Shanghai China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,6,7]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.2134\/jeq1991.00472425002000030029x"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200410193"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.2165\/00003495-198325010-00004"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0277-9536(92)90206-6"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19970515)16:9<1017::AID-SIM508>3.0.CO;2-V"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753381887"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12191"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780101011"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2008.01066.x"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.4103\/2229-3485.83221"},{"key":"e_1_2_9_12_1","volume-title":"The Tariff on Animal and Vegetable Oils","author":"Wright P.","year":"1928"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177731868"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780080608"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(97)81890-3"},{"key":"e_1_2_9_16_1","volume-title":"Econometric Analysis of Cross Section and Panel Data","author":"Wooldridge J. 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