{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T13:04:33Z","timestamp":1789995873671,"version":"4.0.1"},"reference-count":34,"publisher":"Wiley","issue":"6-7","license":[{"start":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T00:00:00Z","timestamp":1773360000000},"content-version":"vor","delay-in-days":12,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>This paper proposes a propensity score (PS)\u2010based stratified win ratio method to address challenges of small patient populations in clinical trials, especially for rare or pediatric diseases, by incorporating external control data. Our approach enhances traditional win ratio analysis by leveraging PS stratification to account for heterogeneity between the current and external studies. Additionally, down\u2010weighting based on the overlapping coefficient of PS distributions of current treatment and external control groups further mitigates the patient bias due to heterogeneity. Simulations show significant improvements in statistical power for detecting treatment effects within the composite endpoint combining continuous and time\u2010to\u2010event components, over nonborrowing and pooling methods, with utilizing Mantel\u2010Haenszel (MH)\u2010type weights achieving the highest power. The proposed methods are also applied to an amyotrophic lateral sclerosis (ALS) study incorporating the external control arm from a prior ALS trial. The proposed PS\u2010based stratified win ratio method thus provides a rigorous framework for borrowing external data and analyzing composite endpoints with limited patient availability.<\/jats:p>","DOI":"10.1002\/sim.70487","type":"journal-article","created":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:57:45Z","timestamp":1773467865000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Propensity Score\u2010Based Stratified Win Ratio for Augmented Control Designs"],"prefix":"10.1002","volume":"45","author":[{"given":"Yurong","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Statistical Science Baylor University  Waco Texas USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingdong","family":"Feng","sequence":"additional","affiliation":[{"name":"Eli Lilly and Company  Indianapolis Indiana 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