{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T18:07:12Z","timestamp":1792692432625,"version":"4.5.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T00:00:00Z","timestamp":1614729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,2,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Covariate-adaptive randomization schemes such as minimization and stratified permuted blocks are often applied in clinical trials to balance treatment assignments across prognostic factors. The existing theory for inference after covariate-adaptive randomization is mostly limited to situations where a correct model between the response and covariates can be specified or the randomization method has well-understood properties. Based on stratification with covariate levels utilized in randomization and a further adjustment for covariates not used in randomization, we propose several model-free estimators of the average treatment effect. We establish the asymptotic normality of the proposed estimators under all popular covariate-adaptive randomization schemes, including the minimization method, and we show that the asymptotic distributions are invariant with respect to covariate-adaptive randomization methods. Consistent variance estimators are constructed for asymptotic inference. Asymptotic relative efficiencies and finite-sample properties of estimators are also studied. We recommend using one of our proposed estimators for valid and model-free inference after covariate-adaptive randomization.<\/jats:p>","DOI":"10.1093\/biomet\/asab015","type":"journal-article","created":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T15:10:36Z","timestamp":1614352236000},"page":"33-47","source":"Crossref","is-referenced-by-count":40,"title":["Inference on the average treatment effect under minimization and other covariate-adaptive randomization methods"],"prefix":"10.1093","volume":"109","author":[{"given":"Ting","family":"Ye","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanyao","family":"Yi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Shao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,3,3]]},"reference":[{"key":"2022020204423292900_B1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1093\/biomet\/69.1.61","article-title":"Optimum biased coin designs for sequential clinical trials with prognostic factors","volume":"69","author":"Atkinson,","year":"1982","journal-title":"Biometrika"},{"key":"2022020204423292900_B2","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.1002\/(SICI)1097-0258(19990730)18:14<1741::AID-SIM210>3.0.CO;2-F","article-title":"Optimum biased-coin designs for sequential treatment allocation with covariate information","volume":"18","author":"Atkinson,","year":"1999","journal-title":"Statist. 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