{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T02:56:03Z","timestamp":1774752963641,"version":"3.50.1"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2012,7,26]],"date-time":"2012-07-26T00:00:00Z","timestamp":1343260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Center for Statistical Science at Peking University","award":["11131002"],"award-info":[{"award-number":["11131002"]}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["11131002"],"award-info":[{"award-number":["11131002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001352","name":"National University of Singapore","doi-asserted-by":"publisher","award":["11131002"],"award-info":[{"award-number":["11131002"]}],"id":[{"id":"10.13039\/501100001352","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,1,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The conventional Wilcoxon or Mann\u2013Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann\u2013Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pretreatment variables. We also propose semiparametric extensions of the adjusted Mann\u2013Whitney test which lead to dimension reduction for high dimensional covariates. A novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations. Results from simulation studies and an economics observational study data analysis are presented to demonstrate the performance of the approach proposed.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2012.01036.x","type":"journal-article","created":{"date-parts":[[2012,7,27]],"date-time":"2012-07-27T03:25:13Z","timestamp":1343359513000},"page":"81-102","source":"Crossref","is-referenced-by-count":19,"title":["Mann\u2013Whitney Test with Adjustments to Pretreatment Variables for Missing Values and Observational Study"],"prefix":"10.1093","volume":"75","author":[{"given":"Song Xi","family":"Chen","sequence":"first","affiliation":[{"name":"Peking University , Beijing"},{"name":"People\u2019s Republic of China, and Iowa State University , Ames , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Qin","sequence":"additional","affiliation":[{"name":"National Institute of Allergy and Infectious Diseases , Bethesda , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng Yong","family":"Tang","sequence":"additional","affiliation":[{"name":"National University of Singapore , Singapore"},{"name":"University of Colorado , Denver , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2012,7,26]]},"reference":[{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"10","DOI":"10.2307\/2533140","article-title":"A semiparametric extension of the Mann-Whitney test for randomly truncated data","volume":"52","author":"Bilker","year":"1996","journal-title":"Biometrics"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/1541-0420.00001","article-title":"Are statistical contributions to medicine undervalued","volume":"59","author":"Breslow","year":"2003","journal-title":"Biometrics"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1080\/01621459.1994.10476448","article-title":"Nonparametric-estimation of mean functionals with data missing at random","volume":"89","author":"Cheng","year":"1994","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1111\/j.1541-0420.2005.00332.x","article-title":"Exact two-sample inference with missing data","volume":"61","author":"Cheung","year":"2005","journal-title":"Biometrics"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1093\/biomet\/82.2.315","article-title":"Nonparametric regression estimates using misspecified binary responses","volume":"82","author":"Chu","year":"1995","journal-title":"Biometrika"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1080\/01621459.1999.10473858","article-title":"Causal effects in nonexperimental studies: reevaluating the evaluation of training programs","volume":"94","author":"Dehejia","year":"1999","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109053361600_","volume-title":"Local Polynomial Modeling and Its Applications","author":"Fan","year":"1996"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"315","DOI":"10.2307\/2998560","article-title":"On the role of the propensity score in efficient semiparametric estimation of average treatment effects","volume":"66","author":"Hahn","year":"1998","journal-title":"Econometrica"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1198\/016214504000000548","article-title":"Cross-validation and the estimation of conditional probability densities","volume":"99","author":"Hall","year":"2004","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1404","DOI":"10.1214\/009053604000001282","article-title":"Approximating conditional distribution functions using dimension reduction","volume":"33","author":"Hall","year":"2005","journal-title":"Ann. Statist."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.2307\/1912775","article-title":"Large sample properties of generalized method of moments estimators","volume":"50","author":"Hansen","year":"1982","journal-title":"Econometrica"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","DOI":"10.1017\/CCOL0521382483","volume-title":"Applied Nonparametric Regression","author":"H\u00e4rdle","year":"1990"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1111\/1468-0262.00442","article-title":"Efficient estimation of average treatment effects using the estimated propensity score","volume":"71","author":"Hirano","year":"2003","journal-title":"Econometrica"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1214\/aoms\/1177730196","article-title":"A class of statistics with asymptotically normal distribution","volume":"19","author":"Hoeffding","year":"1948","journal-title":"Ann. Math. Statist."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1080\/01621459.1952.10483446","article-title":"A generalization of sampling without replacement from a finite universe","volume":"47","author":"Horvitz","year":"1952","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1093\/biomet\/asq005","article-title":"Semiparametric dimension reduction estimation for mean response with missing data","volume":"97","author":"Hu","year":"2010","journal-title":"Biometrika"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"3084","DOI":"10.1016\/j.jspi.2011.03.030","article-title":"Dimension reducted kernel estimation for distribution function with incomplete data","volume":"141","author":"Hu","year":"2011","journal-title":"J. Statist. Planng Inf."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1162\/003465304323023651","article-title":"Nonparametric estimation of average treatment effects under exogeneity: a review","volume":"86","author":"Imbens","year":"2004","journal-title":"Rev. Econ. Statist."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1214\/ss\/1028905885","article-title":"Clinician preferences and the estimation of causal treatment differences","volume":"13","author":"Korn","year":"1998","journal-title":"Statist. Sci."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-3515-5","volume-title":"Theory of U-statistics","author":"Koroljuk","year":"1994"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1093\/biomet\/80.2.385","article-title":"A kernel method for estimating finite population functions using auxiliary information","volume":"80","author":"Kuk","year":"1993","journal-title":"Biometrika"},{"key":"2023031109053361600_","first-page":"604","article-title":"Evaluating the econometric evaluations of training programs with experimental data","volume":"76","author":"Lalonde","year":"1986","journal-title":"Am. Econ. Rev."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","DOI":"10.1002\/9781119013563","volume-title":"Statistical Analysis with Missing Data","author":"Little","year":"2002"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1093\/biomet\/68.3.685","article-title":"Use of regression functions for improved estimation of means","volume":"68","author":"Matloff","year":"1981","journal-title":"Biometrika"},{"key":"2023031109053361600_","volume-title":"Handbook of Econometrics","author":"Newey","year":"1994"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1198\/016214508000000238","article-title":"Efficient and doubly robust imputation for covariate-dependent missing responses","volume":"103","author":"Qin","year":"2008","journal-title":"J. Am. Statist. Ass."},{"key":"2023031109053361600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3692-2","volume-title":"Observational Studies","author":"Rosenbaum","year":"2002"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","article-title":"The central role of the propensity score in observational studies for causal effects","volume":"70","author":"Rosenbaum","year":"1983","journal-title":"Biometrika"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1093\/biomet\/63.3.581","article-title":"Inference and missing values (with discussion)","volume":"63","author":"Rubin","year":"1976","journal-title":"Biometrika"},{"key":"2023031109053361600_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316481","volume-title":"Approximation Theorems of Mathematical Statistics","author":"Serfling","year":"1980"},{"key":"2023031109053361600_","volume-title":"Semiparametric Theory and Missing Data","author":"Tsiatis","year":"2006"},{"key":"2023031109053361600_","first-page":"1028","article-title":"Local linear regression for generalized linear models with missing data","volume":"26","author":"Wang","year":"1998","journal-title":"Ann. Statist."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2012.01036.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/75\/1\/81\/49509711\/jrsssb_75_1_81.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/75\/1\/81\/49509711\/jrsssb_75_1_81.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,27]],"date-time":"2024-04-27T14:31:08Z","timestamp":1714228268000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/75\/1\/81\/7075417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7,26]]},"references-count":32,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,7,26]]},"published-print":{"date-parts":[[2013,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2012.01036.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2013,1]]},"published":{"date-parts":[[2012,7,26]]}}}