{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T07:55:49Z","timestamp":1790754949460,"version":"4.1.0"},"reference-count":38,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"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":["Biometrical J"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time\u2010to\u2010event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl, respectively), as well as use the single\u2010world intervention graph to show mathematically that the hazard function has causal interpretations under all three frameworks. In addition, we argue that the hazard ratio over time can provide a useful interpretation in practical\u00a0settings.<\/jats:p>","DOI":"10.1002\/bimj.70187","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T06:58:00Z","timestamp":1790751480000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Defense of the Hazard Ratio"],"prefix":"10.1002","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0124-1856","authenticated-orcid":false,"given":"Andrew","family":"Ying","sequence":"first","affiliation":[{"name":"Irvine California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronghui","family":"Xu","sequence":"additional","affiliation":[{"name":"Herbert Wertheim School of Public Health Department of Mathematics, and Halicioglu Data Science Institute University of California San Diego La Jolla California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"issue":"4","key":"e_1_2_9_2_1","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s10985-015-9335-y","article-title":"Does Cox Analysis of a Randomized Survival Study Yield a Causal Treatment Effect?","volume":"21","author":"Aalen O. 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