{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:21:01Z","timestamp":1787505661688,"version":"build-2736575974"},"reference-count":33,"publisher":"Wiley","issue":"18-19","license":[{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100020595","name":"National Science and Technology Council","doi-asserted-by":"publisher","award":["113\u20102118\u2010M\u2010001\u2010013\u2010MY3"],"award-info":[{"award-number":["113\u20102118\u2010M\u2010001\u2010013\u2010MY3"]}],"id":[{"id":"10.13039\/100020595","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001869","name":"Academia Sinica","doi-asserted-by":"publisher","award":["AS\u2010IV\u2010114\u2010M05"],"award-info":[{"award-number":["AS\u2010IV\u2010114\u2010M05"]}],"id":[{"id":"10.13039\/501100001869","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":[[2026,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>The illness\u2010death model is widely used to characterize disease progression over time. Previous work focuses either on estimation without causal interpretation or on causal interpretation under a strong Markov assumption where the terminal event depends on the status but not the timing of the intermediate event. To bridge the research gap, we propose a new definition of counterfactual hazard that relaxes the Markov assumption by considering the entire history of the intermediate event. We derive an identification formula that involves an integral with respect to the probability density function of the intermediate event time. Direct and indirect effects refer to the influence of an exposure on the terminal event not mediated by, and mediated through, the intermediate event, respectively. We propose non\u2010parametric kernel estimators for the two effects and study their asymptotic properties. We conduct numerical simulations to examine the proposed estimators' finite\u2010sample performance. Applying the method to a hepatitis study where the Markov assumption is violated, we show that the effect of hepatitis C on mortality is not mediated through septicemia during the first 15 years of follow\u2010up.<\/jats:p>","DOI":"10.1002\/sim.70685","type":"journal-article","created":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T03:18:42Z","timestamp":1785554322000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non\u2010Parametric Mediation Analysis of Non\u2010Markov Illness\u2010Death Model"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6020-4448","authenticated-orcid":false,"given":"Li\u2010Sheng","family":"Zhuang","sequence":"first","affiliation":[{"name":"Institute of Statistics and Data Science National Tsing Hua University  Hsinchu Taiwan"},{"name":"Institute of Statistical Science Academia Sinica  Taipei Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-1743-5427","authenticated-orcid":false,"given":"Jih\u2010Chang","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Statistics National Taipei University  New Taipei Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7657-0040","authenticated-orcid":false,"given":"Yen\u2010Tsung","family":"Huang","sequence":"additional","affiliation":[{"name":"Institute of Statistical Science Academia Sinica  Taipei Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4348-9"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009672031531"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1200\/JCO.2011.36.2335"},{"issue":"3","key":"e_1_2_10_5_1","first-page":"141","article-title":"An Empirical Transition Matrix for Non\u2010Homogeneous Markov Chains Based on Censored Observations","volume":"5","author":"Aalen O. 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