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Its growing popularity stems from its ability to accommodate a hierarchy of event types within a composite primary endpoint in an RCT. However, as a relatively new measure, the WR exhibits some surprising properties. Oakes and other authors have noted that for a given triplet of participants, there are realizations of event times and hierarchy of event types when \u201cwins\u201d form a loop. They term this property \u201cintransitivity.\u201d In this paper, we report and study a different phenomenon, a violation of long\u2010run transitivity of WRs, for example, when in the long run ,  and paradoxically , where  denote the time\u2010to\u2010event in trial arms A, B, and C (or placebo, standard of care and novel treatment, respectively). We refer to it as Efron\u2010type \u201cnon\u2010transitivity.\u201d Unlike Oakes\u2010type intransitivity, Efron\u2010type non\u2010transitivity is an inherent property of the underlying random variables. As such, it cannot be resolved by a longer observation period or larger sample size. Lumley and Gillen showed that transitivity can be guaranteed only for univariate statistics (e.g., mean, median, etc.), whereas head\u2010to\u2010head comparisons can be non\u2010transitive. WR and win proportion (WP) are head\u2010to\u2010head comparisons and may be non\u2010transitive, in which case the best treatment cannot be determined. Therefore, the non\u2010transitivity property challenges the utility of all head\u2010to\u2010head comparisons as efficacy measures in RCTs. In this paper, we explore the scope of this problem, focusing on identifying conditions that rule out non\u2010transitivity for WR, WP, and hazard ratio (HR). We apply our findings to establish transitivity in two case studies using published RCTs. This work highlights an important phenomenon that must be recognized when the WR is used as an efficacy measure in randomized controlled trials.<\/jats:p>","DOI":"10.1002\/sim.70581","type":"journal-article","created":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T09:48:56Z","timestamp":1787132936000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Long Run Non\u2010Transitivity of Win Ratio and How to Rule It Out"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3355-3210","authenticated-orcid":false,"given":"Olga V.","family":"Demler","sequence":"first","affiliation":[{"name":"Computer Science Department ETH Zurich  Zurich Switzerland"},{"name":"Brigham and Women's Hospital\/Harvard Medical School  Boston Massachusetts USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-8477-5141","authenticated-orcid":false,"given":"Anna","family":"Gy\u0151rffy\u2010Kerekes","sequence":"additional","affiliation":[{"name":"Computer Science Department ETH Zurich  Zurich Switzerland"},{"name":"Max Planck ETH Center for Learning Systems  T\u00fcbingen Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,19]]},"reference":[{"key":"e_1_2_13_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19990615)18:11<1341::AID-SIM129>3.0.CO;2-7"},{"key":"e_1_2_13_3_1","doi-asserted-by":"publisher","DOI":"10.1093\/eurheartj\/ehr352"},{"key":"e_1_2_13_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jchf.2020.02.010"},{"key":"e_1_2_13_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201800255"},{"key":"e_1_2_13_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2006.06.001"},{"key":"e_1_2_13_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41591-021-01659-1"},{"key":"e_1_2_13_8_1","doi-asserted-by":"publisher","DOI":"10.1055\/s-0043-1769612"},{"key":"e_1_2_13_9_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa2206286"},{"key":"e_1_2_13_10_1","doi-asserted-by":"publisher","DOI":"10.1097\/CCM.0000000000004104"},{"key":"e_1_2_13_11_1","doi-asserted-by":"publisher","DOI":"10.1212\/WNL.0000000000004960"},{"key":"e_1_2_13_12_1","doi-asserted-by":"publisher","DOI":"10.1093\/eurheartj\/ehae647"},{"key":"e_1_2_13_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asw026"},{"key":"e_1_2_13_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2024.110267"},{"key":"e_1_2_13_15_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxv032"},{"key":"e_1_2_13_16_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1270-110"},{"key":"e_1_2_13_17_1","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0574-120"},{"key":"e_1_2_13_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40879-023-00618-z"},{"key":"e_1_2_13_19_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0005117919060055"},{"key":"e_1_2_13_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2015.11.005"},{"key":"e_1_2_13_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.2251"},{"key":"e_1_2_13_22_1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400829460"},{"key":"e_1_2_13_23_1","doi-asserted-by":"publisher","DOI":"10.1086\/256963"},{"key":"e_1_2_13_24_1","volume-title":"Trans Iain McLean and Fiona Hewitt","author":"Condorcet M.","year":"1994"},{"key":"e_1_2_13_25_1","unstructured":"G.H\u00e4geleandF.Pukelsheim \u201cLulls' Writings on Electoral Systems \u201d2001."},{"key":"e_1_2_13_26_1","doi-asserted-by":"crossref","unstructured":"R. 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