{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:36:36Z","timestamp":1767339396155,"version":"3.37.3"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,1,16]],"date-time":"2024-01-16T00:00:00Z","timestamp":1705363200000},"content-version":"vor","delay-in-days":444,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,11,23]],"date-time":"2022-11-23T00:00:00Z","timestamp":1669161600000},"content-version":"vor","delay-in-days":25,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000272","name":"National Institute for Health Research","doi-asserted-by":"publisher","award":["RMOFS 2012\/05"],"award-info":[{"award-number":["RMOFS 2012\/05"]}],"id":[{"id":"10.13039\/501100000272","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000272","name":"National Institute for Health Research","doi-asserted-by":"publisher","award":["RMOFS 2012\/05"],"award-info":[{"award-number":["RMOFS 2012\/05"]}],"id":[{"id":"10.13039\/501100000272","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Complete case analyses of complete crossover designs provide an opportunity to make comparisons based on patients who can tolerate all treatments. It is argued that this provides a means of estimating a principal stratum strategy estimand, something which is difficult to do in parallel group trials. While some trial users will consider this a relevant aim, others may be interested in hypothetical strategy estimands, that is, the effect that would be found if all patients completed the trial. Whether these estimands differ importantly is a question of interest to the different users of the trial results. This paper derives the difference between principal stratum strategy and hypothetical strategy estimands, where the former is estimated by a complete-case analysis of the crossover design, and a model for the dropout process is assumed. Complete crossover designs, that is, those where all treatments appear in all sequences, and which compare t treatments over p periods with respect to a continuous outcome are considered. Numerical results are presented for Williams designs with four and six periods. Results from a trial of obstructive sleep apnoea-hypopnoea (TOMADO) are also used for illustration. The results demonstrate that the percentage difference between the estimands is modest, exceeding 5% only when the trial has been severely affected by dropouts or if the within-subject correlation is low.<\/jats:p>","DOI":"10.1111\/biom.13777","type":"journal-article","created":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T07:14:50Z","timestamp":1667027690000},"page":"1896-1907","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Contrasting Principal Stratum and Hypothetical Strategy Estimands in Multi-Period Crossover Trials with Incomplete Data"],"prefix":"10.1093","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2559-037X","authenticated-orcid":false,"given":"John N.S.","family":"Matthews","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics & Physics, Newcastle University , Newcastle upon Tyne , UK"},{"name":"Public Health Sciences Institute, Newcastle University , Newcastle upon Tyne , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sofia","family":"Bazakou","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics & Physics, Newcastle University , Newcastle upon Tyne , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robin","family":"Henderson","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics & Physics, Newcastle University , Newcastle upon Tyne , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linda D.","family":"Sharples","sequence":"additional","affiliation":[{"name":"Department of Medical Statistics, London School of Hygiene and Tropical Medicine , London , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,10,29]]},"reference":[{"key":"2024011603473341600_biom13777-bib-0001","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1016\/j.jspi.2010.03.006","article-title":"A joint model for incomplete data in crossover trials","volume":"140","author":"Basu","year":"2010","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2024011603473341600_biom13777-bib-0002","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1016\/j.csda.2007.05.002","article-title":"Choosing cross-over designs when few subjects are available","volume":"52","author":"Bate","year":"2008","journal-title":"Computational Statistics & Data Analysis"},{"key":"2024011603473341600_biom13777-bib-0003","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1093\/ije\/31.1.140","article-title":"Meta-analyses involving cross-over trials: methodological issues","volume":"31","author":"Elbourne","year":"2002","journal-title":"International Journal of Epidemiology"},{"key":"2024011603473341600_biom13777-bib-0004","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1016\/j.csda.2005.12.003","article-title":"The specification of rank reducing observation sets in experimental design","volume":"51","author":"Godolphin","year":"2006","journal-title":"Computational Statistics & Data Analysis"},{"key":"2024011603473341600_biom13777-bib-0005","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1177\/0962280217736541","article-title":"Robustness of crossover trials against subject drop-out\u2014examples of perpetually connected designs","volume":"28","author":"Godolphin","year":"2019","journal-title":"Statistical Methods in Medical Research"},{"key":"2024011603473341600_biom13777-bib-0006","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1201\/9780203492000.ch2","article-title":"The closed skew-normal distribution","volume-title":"Skew-elliptical distributions and their applications: a journey beyond normality","author":"Gonz\u00e1lez-Far\u00edas","year":"2004"},{"key":"2024011603473341600_biom13777-bib-0007","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1002\/sim.4497","article-title":"Dropouts in the AB\/BA crossover design","volume":"31","author":"Ho","year":"2012","journal-title":"Statistics in Medicine"},{"volume-title":"International Council for Harmonisation. 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