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In these trials, the average causal effects of treatments within principal strata of compliance behaviour are of interest for better understanding the effect of the treatment. Unfortunately, even with the usual assumptions, the average causal effects of treatments within principal strata are not point identified. However, the observable data do provide useful information on the bounds of the identification regions of the parameters of interest. Under two sets of assumptions, we derive sharp bounds for the causal effects within principal strata for binary outcomes and construct confidence intervals to cover the identification regions. The methods are illustrated by an analysis of data from a randomized study of treatments for alcohol dependence.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00568.x","type":"journal-article","created":{"date-parts":[[2006,10,24]],"date-time":"2006-10-24T15:34:04Z","timestamp":1161704044000},"page":"815-836","source":"Crossref","is-referenced-by-count":86,"title":["Bounds on Causal Effects in Three-Arm Trials With Non-Compliance"],"prefix":"10.1093","volume":"68","author":[{"given":"Jing","family":"Cheng","sequence":"first","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dylan S.","family":"Small","sequence":"additional","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2006,10,24]]},"reference":[{"key":"2023040708371391800_","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","article-title":"Identification of causal effects using instrumental variables","volume":"91","author":"Angrist","year":"1996","journal-title":"J. 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