{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T16:46:29Z","timestamp":1792601189487,"version":"4.5.0"},"reference-count":44,"publisher":"Wiley","issue":"23-24","license":[{"start":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000},"content-version":"vor","delay-in-days":8,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100006093","name":"Patient-Centered Outcomes Research Institute","doi-asserted-by":"publisher","award":["ME\u20102022C2\u201027676"],"award-info":[{"award-number":["ME\u20102022C2\u201027676"]}],"id":[{"id":"10.13039\/100006093","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006108","name":"National Center for Advancing Translational Sciences","doi-asserted-by":"publisher","award":["U24TR004437"],"award-info":[{"award-number":["U24TR004437"]}],"id":[{"id":"10.13039\/100006108","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MC_UU_00004\/07"],"award-info":[{"award-number":["MC_UU_00004\/07"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MC_UU_00004\/09"],"award-info":[{"award-number":["MC_UU_00004\/09"]}],"id":[{"id":"10.13039\/501100000265","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":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In cluster randomized trials, the individual\u2010average treatment effect (i\u2010ATE) can be different from the cluster\u2010average treatment effect (c\u2010ATE) when informative cluster size (ICS) is present, that is, when treatment effects or participant outcomes depend on cluster size. In such scenarios, mixed\u2010effects models and generalized estimating equations (GEEs) with exchangeable correlation structure are biased for both the i\u2010ATE and c\u2010ATE estimands, whereas GEEs with an independence correlation structure or analyses of cluster\u2010level summaries are recommended in practice. However, when cluster size is non\u2010informative, mixed\u2010effects models and GEEs with exchangeable correlation structure can provide unbiased estimation and notable efficiency gains over other methods. Thus, hypothesis tests for ICS would be useful to assess this key phenomenon under cluster randomization. In this work, we develop model\u2010based, model\u2010assisted, and randomization\u2010based tests for ICS in cluster randomized trials. We conduct simulation studies to examine the operating characteristics of these tests, show they have appropriate Type I error rate control and meaningful power, and contrast them to existing model\u2010based tests used in the observational study setting. The proposed tests are then applied to data from a recent cluster randomized trial, and practical recommendations for using these tests are discussed.<\/jats:p>","DOI":"10.1002\/sim.70762","type":"journal-article","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T13:05:57Z","timestamp":1791551157000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Evaluating Informative Cluster Size in Cluster Randomized Trials"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3121-7718","authenticated-orcid":false,"given":"Bryan S.","family":"Blette","sequence":"first","affiliation":[{"name":"Department of Biostatistics Vanderbilt University Medical Center  Nashville Tennessee USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7737-8915","authenticated-orcid":false,"given":"Zhe","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Informatics University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9957-0844","authenticated-orcid":false,"given":"Brennan C.","family":"Kahan","sequence":"additional","affiliation":[{"name":"MRC Clinical Trial Unit, Institute of Clinical Trials and Methodology University College London  UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4269-914X","authenticated-orcid":false,"given":"Andrew","family":"Forbes","sequence":"additional","affiliation":[{"name":"Division of Quantitative Research Methodology Monash University  Melbourne Victoria Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0553-674X","authenticated-orcid":false,"given":"Michael O.","family":"Harhay","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Informatics University of Pennsylvania  Philadelphia Pennsylvania USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-1893","authenticated-orcid":false,"given":"Fan","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics Yale School of Public Health  New Haven Connecticut USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"key":"e_1_2_13_2_1","volume-title":"Design and Analysis of Group\u2010Randomized Trials","author":"Murray D. 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