{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T17:08:26Z","timestamp":1792084106427,"version":"4.4.0"},"reference-count":21,"publisher":"Wiley","issue":"10-12","license":[{"start":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:00:00Z","timestamp":1776988800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T00:00:00Z","timestamp":1776988800000},"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":[[2026,5]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>When the proportional hazards assumption does not hold, the hazard ratio can misrepresent treatment effects in survival analysis. We evaluate the win ratio, originally proposed for prioritizing multiple outcomes, as an effect size measure for a single survival outcome under non\u2010proportional hazards, and compare it with the difference in restricted mean survival time (RMST). We perform bootstrap\u2010based inference for the win ratio under both right\u2010 and interval\u2010censoring using plug\u2010in estimators based on nonparametric maximum likelihood estimators or spline\u2010based sieve maximum likelihood estimators of the survival functions. We also study stratified win ratio to mitigate confounding. Extensive simulations are conducted to assess and compare the performances of the win ratio and the difference in RMST under various types of alternatives encountered in practice. The simulation results show that the win ratio\u2010based tests outperform RMST\u2010based tests when treatment benefits arise early, whereas RMST is more sensitive to late\u2010onset effects, and stratified win ratio maintains nominal type I error in the presence of confounding, unlike unstratified win ratio. As an illustration, we analyze right\u2010censored and interval\u2010censored progression\u2010free survival in patients with multiple myeloma treated with two different regimens. The results of this article support reporting the win ratio, along with the difference in RMST, when the proportional hazards assumption is doubtful, offering complementary clinical interpretability and robustness across censoring mechanisms and treatment effect patterns.<\/jats:p>","DOI":"10.1002\/sim.70554","type":"journal-article","created":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T22:54:33Z","timestamp":1777071273000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Win Ratio as an Effect Size Measure Under Non\u2010Proportional Hazards: A Comparison With Difference in Restricted Mean Survival"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8925-555X","authenticated-orcid":false,"given":"Yuan","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9975-6005","authenticated-orcid":false,"given":"Zhiguo","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Bioinformatics Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,4,24]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4274"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2288-13-152"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1200\/JCO.2014.55.2208"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1093\/eurheartj\/ehr352"},{"issue":"1","key":"e_1_2_10_6_1","first-page":"135","article-title":"Generalized Pairwise Comparisons of Prioritized Outcomes in the Two\u2010Sample Problem","volume":"11","author":"Buyse M.","year":"2010","journal-title":"Biostatistics"},{"issue":"1","key":"e_1_2_10_7_1","first-page":"178","article-title":"Large Sample Inference for a Win Ratio Analysis of a Composite Outcome Based on Prioritized Components","volume":"72","author":"Bebu 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