{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T14:02:30Z","timestamp":1791986550333,"version":"4.4.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T00:00:00Z","timestamp":1559001600000},"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\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006462","name":"City University of New York","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006462","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We present a procedure that divides a set of experimental units into two groups that are similar on a prespecified set of covariates and are almost as random as with a complete randomization. Under complete randomization, the difference in the standardized average between treatment and control is $O_{\\rm p}(n^{-1\/2})$, which may be material in small samples. We present an algorithm that reduces imbalance to $O_{\\rm p}(n^{-3})$ for one covariate and $O_{\\rm p}\\{n^{-(1 + 2\/p)}\\}$ for $p$ covariates, but whose assignments are, strictly speaking, nonrandom. In addition to the metric of maximum eigenvalue of allocation variance, we introduce two metrics that capture departures from randomization and show that our assignments are nearly as random as complete randomization in terms of all measures. Simulations illustrate the results, and inference is discussed. An R package to generate designs according to our algorithm and other popular designs is available.<\/jats:p>","DOI":"10.1093\/biomet\/asz026","type":"journal-article","created":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T19:11:17Z","timestamp":1557256277000},"page":"695-701","source":"Crossref","is-referenced-by-count":25,"title":["Nearly random designs with greatly improved balance"],"prefix":"10.1093","volume":"106","author":[{"given":"A M","family":"Krieger","sequence":"first","affiliation":[{"name":"Department of Statistics, The Wharton School of the University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D","family":"Azriel","sequence":"additional","affiliation":[{"name":"Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Technion City, Haifa 3200003, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A","family":"Kapelner","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Queens College, City University of New York, 65\u201330 Kissena Blvd, Queens, New York 11367, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,5,28]]},"reference":[{"key":"2019091012125342700_B1","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1093\/biomet\/asr021","article-title":"The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors","volume":"98","author":"Baldi Antognini,","year":"2011","journal-title":"Biometrika"},{"key":"2019091012125342700_B2","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1287\/opre.2015.1361","article-title":"The power of optimization over randomization in designing experiments involving small samples","volume":"63","author":"Bertsimas,","year":"2015","journal-title":"Oper. Res."},{"key":"2019091012125342700_B3","article-title":"Randomization tests that condition on non-categorical covariate balance","author":"Branson,","year":"2018"},{"key":"2019091012125342700_B4","first-page":"240","article-title":"Principles of research","volume":"64","author":"Cornfield,","year":"1959","journal-title":"Am. J. Ment. Def."},{"key":"2019091012125342700_B5","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1093\/biomet\/58.3.403","article-title":"Forcing a sequential experiment to be balanced","volume":"58","author":"Efron,","year":"1971","journal-title":"Biometrika"},{"key":"2019091012125342700_B6","author":"Fisher,","edition":"1st"},{"key":"2019091012125342700_B7","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.aam.2006.12.003","article-title":"On regression adjustments to experimental data","volume":"40","author":"Freedman,","year":"2008","journal-title":"Adv. Appl. Math."},{"key":"2019091012125342700_B8","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1093\/biostatistics\/5.2.263","article-title":"Optimal multivariate matching before randomization","volume":"5","author":"Greevy,","year":"2004","journal-title":"Biostatistics"},{"key":"2019091012125342700_B9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1751-5823.2007.00024.x","article-title":"Econometric causality","volume":"76","author":"Heckman,","year":"2008","journal-title":"Int. Statist. Rev."},{"key":"2019091012125342700_B10","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1111\/rssb.12240","article-title":"Optimal a priori balance in the design of controlled experiments","volume":"80","author":"Kallus,","year":"2018","journal-title":"J. R. Statist. Soc. B"},{"key":"2019091012125342700_B11","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1111\/biom.12148","article-title":"Matching on-the-fly: Sequential allocation with higher power and efficiency","volume":"70","author":"Kapelner,","year":"2014","journal-title":"Biometrics"},{"key":"2019091012125342700_B12","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/0197-2456(88)90046-3","article-title":"Properties of simple randomization in clinical trials","volume":"9","author":"Lachin,","year":"1988","journal-title":"Contr. Clin. Trials"},{"key":"2019091012125342700_B13","doi-asserted-by":"crossref","first-page":"9157","DOI":"10.1073\/pnas.1808191115","article-title":"Asymptotic theory of rerandomization in treatment\u2013control experiments","volume":"115","author":"Li,","year":"2018","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2019091012125342700_B14","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1214\/12-AOAS583","article-title":"Agnostic notes on regression adjustments to experimental data: Reexamining Freedman\u2019s critique","volume":"7","author":"Lin,","year":"2013","journal-title":"Ann. Appl. Statist."},{"key":"2019091012125342700_B15","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1214\/12-AOS1008","article-title":"Rerandomization to improve covariate balance in experiments","volume":"40","author":"Morgan,","year":"2012","journal-title":"Ann. Statist."},{"key":"2019091012125342700_B16","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719109","volume-title":"Optimal Design of Experiments","author":"Pukelsheim,","year":"2006"},{"key":"2019091012125342700_B17","article-title":"R Foundation for Statistical Computing","volume-title":"R: A Language and Environment for Statistical Computing","year":"2019"},{"key":"2019091012125342700_B18","doi-asserted-by":"crossref","DOI":"10.1002\/9781118742112","volume-title":"Randomization in Clinical Trials: Theory and Practice","author":"Rosenberger,","year":"2016","edition":"2nd"},{"key":"2019091012125342700_B19","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1111\/1467-9884.00227","article-title":"Consensus and controversy in pharmaceutical statistics","volume":"49","author":"Senn,","year":"2000","journal-title":"Statistician"},{"key":"2019091012125342700_B20","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1093\/biomet\/29.3-4.363","article-title":"Comparison between balanced and random arrangements of field plots","volume":"29","year":"1938","journal-title":"Biometrika"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asz026\/28708906\/asz026.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/biomet\/article-pdf\/106\/3\/695\/29133138\/asz026.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,16]],"date-time":"2023-09-16T09:50:55Z","timestamp":1694857855000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/106\/3\/695\/5499316"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,28]]},"references-count":20,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,5,28]]},"published-print":{"date-parts":[[2019,9,1]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asz026","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2019,9]]},"published":{"date-parts":[[2019,5,28]]}}}