{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T10:19:42Z","timestamp":1783937982727,"version":"3.55.0"},"reference-count":21,"publisher":"Wiley","issue":"13","license":[{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007155","name":"Medical Research Council Canada","doi-asserted-by":"publisher","award":["MC_UU_12023\/29"],"award-info":[{"award-number":["MC_UU_12023\/29"]}],"id":[{"id":"10.13039\/501100007155","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000925","name":"National Health and Medical Research Council","doi-asserted-by":"publisher","award":["1108283"],"award-info":[{"award-number":["1108283"]}],"id":[{"id":"10.13039\/501100000925","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2020,6,15]]},"abstract":"<jats:p>When calculating sample size or power for stepped wedge or other types of longitudinal cluster randomized trials, it is critical that the planned sampling structure be accurately specified. One common assumption is that participants will provide measurements in each trial period, that is, a closed cohort, and another is that each participant provides only one measurement during the course of the trial. However some studies have an \u201copen cohort\u201d sampling structure, where participants may provide measurements in variable numbers of periods. To date, sample size calculations for longitudinal cluster randomized trials have not accommodated open cohorts. Feldman and McKinlay (1994) provided some guidance, stating that the participant\u2010level autocorrelation could be varied to account for the degree of overlap in different periods of the study, but did not indicate precisely how to do so. We present sample size and power formulas that allow for open cohorts and discuss the impact of the degree of \u201copenness\u201d on sample size and power. We consider designs where the number of participants in each cluster will be maintained throughout the trial, but individual participants may provide differing numbers of measurements. Our results are a unification of closed cohort and repeated cross\u2010sectional sample results of Hooper et al (2016), and indicate precisely how participant autocorrelation of Feldman and McKinlay should be varied to account for an open cohort sampling structure. We discuss different types of open cohort sampling schemes and how open cohort sampling structure impacts on power in the presence of decaying within\u2010cluster correlations and autoregressive participant\u2010level errors.<\/jats:p>","DOI":"10.1002\/sim.8519","type":"journal-article","created":{"date-parts":[[2020,3,5]],"date-time":"2020-03-05T03:45:00Z","timestamp":1583379900000},"page":"1871-1883","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Sample size and power calculations for open cohort longitudinal cluster randomized trials"],"prefix":"10.1002","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8940-0136","authenticated-orcid":false,"given":"Jessica","family":"Kasza","sequence":"first","affiliation":[{"name":"School of Public Health and Preventive Medicine Monash University  Melbourne Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1063-0917","authenticated-orcid":false,"given":"Richard","family":"Hooper","sequence":"additional","affiliation":[{"name":"Centre for Primary Care and Public Health Queen Mary University of London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Copas","sequence":"additional","affiliation":[{"name":"MRC Clinical Trials Unit University College London  London UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew B.","family":"Forbes","sequence":"additional","affiliation":[{"name":"School of Public Health and Preventive Medicine Monash University  Melbourne Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2020,3,4]]},"reference":[{"key":"e_1_2_8_2_1","volume-title":"Design and Analysis of Group\u2010Randomized Trials","author":"Murray DM","year":"1998"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7028"},{"key":"e_1_2_8_4_1","article-title":"A tutorial on sample size calculation for cluster randomised multiple\u2010period parallel, cross\u2010over and stepped\u2010wedge trials and introduction to the Shiny CRT calculator","author":"Hemming K","year":"2019","journal-title":"Int J Epidemiol"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-017-2113-2"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cct.2006.05.007"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.7403"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-015-0842-7"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-019-3534-x"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13063-015-0839-2"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2018.11.013"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4780130108"},{"key":"e_1_2_8_13_1","unstructured":"ChangW ChengJ AllaireJJ XieY Mc PhersonJ. 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