{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T15:35:19Z","timestamp":1785857719882,"version":"3.56.0"},"reference-count":21,"publisher":"Wiley","issue":"20-22","license":[{"start":{"date-parts":[[2025,9,14]],"date-time":"2025-09-14T00:00:00Z","timestamp":1757808000000},"content-version":"vor","delay-in-days":13,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000049","name":"National Institute on Aging","doi-asserted-by":"publisher","award":["R01AG064803"],"award-info":[{"award-number":["R01AG064803"]}],"id":[{"id":"10.13039\/100000049","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000049","name":"National Institute on Aging","doi-asserted-by":"publisher","award":["P30AG072958"],"award-info":[{"award-number":["P30AG072958"]}],"id":[{"id":"10.13039\/100000049","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":[[2025,9]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Neurodegenerative diseases such as Alzheimer's and Parkinson's often exhibit complex, multivariate longitudinal outcomes that require advanced statistical methods to comprehensively evaluate treatment efficacy. The Longitudinal Rank Sum Test (LRST) offers a nonparametric framework to assess global treatment effects across multiple longitudinal endpoints without requiring multiplicity corrections. This study develops a robust methodology for power and sample size estimation specific to the LRST, integrating theoretical derivations, asymptotic properties, and practical estimation techniques under large sample conditions. Validation through numerical simulations demonstrates the accuracy of the proposed methods, while real\u2010world applications to clinical trials in Alzheimer's disease (AD) and Parkinson's disease (PD) highlight their practical significance. This framework facilitates the design of efficient, well\u2010powered trials, advancing the evaluation of treatments for complex diseases with multivariate longitudinal outcomes.<\/jats:p>","DOI":"10.1002\/sim.70261","type":"journal-article","created":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T02:04:18Z","timestamp":1757901858000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Power and Sample Size Calculation for Multivariate Longitudinal Trials Using the Longitudinal Rank Sum Test"],"prefix":"10.1002","volume":"44","author":[{"given":"Dhrubajyoti","family":"Ghosh","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoming","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4214-5809","authenticated-orcid":false,"given":"Sheng","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"for the CPP Integrated Parkinson's Database","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,9,14]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa1304839"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1961.tb00410.x"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697723"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2009.01.017"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2012.07.016"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531158"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(96)00177-2"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(02)00269-0"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12222"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2010.ap09114"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2010.02.019"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2018.12.005"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.3390\/sym14020244"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802211046389"},{"key":"e_1_2_8_16_1","first-page":"1","article-title":"A Novel Longitudinal Rank\u2010Sum Test for Multiple Primary Endpoints in Clinical Trials: Applications to Neurodegenerative Disorders","author":"Xu X.","year":"2025","journal-title":"Statistics in Biopharmaceutical Research"},{"key":"e_1_2_8_17_1","volume-title":"Nonparametric Analysis of Longitudinal Data in Factorial Experiments","author":"Brunner E.","year":"2002"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2025.105447"},{"key":"e_1_2_8_19_1","volume-title":"LRST: An R Package for Longitudinal Rank Sum Test (LRST). 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