{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:37:12Z","timestamp":1740141432328,"version":"3.37.3"},"reference-count":10,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,24]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>A general framework is set up to study the asymptotic properties of the intent-to-treat Wilcoxon\u2013Mann\u2013Whitney test in randomized experiments with nonignorable noncompliance. Under location-shift alternatives, the Pitman efficiencies of the intent-to-treat Wilcoxon\u2013Mann\u2013Whitney and $t$ tests are derived. It is shown that the former is superior if the compliers are more likely to be found in high-density regions of the outcome distribution or, equivalently, if the noncompliers tend to reside in the tails. By logical extension, the relative efficiency of the two tests is sharply bounded by least and most favourable scenarios in which the compliers are segregated into regions of lowest and highest density, respectively. Such bounds can be derived analytically as a function of the compliance rate for common location families such as Gaussian, Laplace, logistic and $t$ distributions. These results can help empirical researchers choose the more efficient test for existing data, and calculate sample size for future trials in anticipation of noncompliance. Results for nonadditive alternatives and other tests follow along similar lines.<\/jats:p>","DOI":"10.1093\/biomet\/asab053","type":"journal-article","created":{"date-parts":[[2021,10,22]],"date-time":"2021-10-22T03:15:59Z","timestamp":1634872559000},"page":"873-880","source":"Crossref","is-referenced-by-count":2,"title":["On the relative efficiency of the intent-to-treat Wilcoxon\u2013Mann\u2013Whitney test in the presence of noncompliance"],"prefix":"10.1093","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8626-9822","authenticated-orcid":false,"given":"Lu","family":"Mao","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison , Madison, Wisconsin 53726, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"2022102500073607900_B1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/1468-0262.00270","article-title":"Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings","volume":"70","author":"Abadie,","year":"2002","journal-title":"Econometrica"},{"key":"2022102500073607900_B2","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. Am. Statist. Assoc."},{"key":"2022102500073607900_B3","doi-asserted-by":"crossref","first-page":"109","DOI":"10.4103\/2229-3485.83221","article-title":"Intention-to-treat concept: A review","volume":"2","author":"Gupta,","year":"2011","journal-title":"Perspect. Clin. Res."},{"key":"2022102500073607900_B4","doi-asserted-by":"crossref","first-page":"555","DOI":"10.2307\/2971731","article-title":"Estimating outcome distributions for compliers in instrumental variables models","volume":"64","author":"Imbens,","year":"1997","journal-title":"Rev. Econ. Stud."},{"key":"2022102500073607900_B5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal Inference in Statistics, Social, and Biomedical Sciences","author":"Imbens,","year":"2015"},{"key":"2022102500073607900_B6","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1214\/aoms\/1177730491","article-title":"On a test of whether one of two random variables is stochastically larger than the other","volume":"18","author":"Mann,","year":"1947","journal-title":"Ann. Math. Statist."},{"key":"2022102500073607900_B7","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1214\/aos\/1176344064","article-title":"Bayesian inference for causal effects: The role of randomization","volume":"6","author":"Rubin,","year":"1978","journal-title":"Ann. Statist."},{"volume-title":"Theory of Rank Tests","year":"1999","author":"Sidak,","key":"2022102500073607900_B8"},{"key":"2022102500073607900_B9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","author":"van der Vaart,","year":"1998"},{"key":"2022102500073607900_B10","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2307\/3001968","article-title":"Individual comparisons by ranking methods","volume":"1","author":"Wilcoxon,","year":"1945","journal-title":"Biomet. Bull."}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asab053\/42114198\/asab053.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/873\/45512129\/asab053.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/873\/45512129\/asab053.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T00:08:32Z","timestamp":1666656512000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/109\/3\/873\/6409853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,25]]},"references-count":10,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,10,25]]},"published-print":{"date-parts":[[2022,8,24]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asab053","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"type":"print","value":"0006-3444"},{"type":"electronic","value":"1464-3510"}],"subject":[],"published-other":{"date-parts":[[2022,9,1]]},"published":{"date-parts":[[2021,10,25]]}}}