{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T00:25:50Z","timestamp":1787185550755,"version":"build-2736575974"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71991471"],"award-info":[{"award-number":["71991471"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72442027"],"award-info":[{"award-number":["72442027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002338","name":"Ministry of Education of China","doi-asserted-by":"publisher","award":["E5820801"],"award-info":[{"award-number":["E5820801"]}],"id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Identifying patient subgroups is increasingly vital for advancing personalized and precision medicine, where patient heterogeneity plays a central role. Subgroups can be revealed by examining how predictors depend on each other. However, traditional global dependence measures, such as Kendall\u2019s \u03c4, often overlook localized and nonlinear relationships, potentially missing critical patterns that define subpopulations. Existing local dependence measures are typically constrained to linear structures or lack flexibility in capturing complex local behaviors. We propose a novel, intuitive, and highly flexible framework, the Generalized Local Kendall\u2019s \u03c4, for assessing nonlinear local dependence. This method allows local regions to take diverse shapes (e.g., rectangles, squares, extreme-value neighborhoods), thereby unifying global, local, and tail dependence within a flexible and interpretable structure. The framework includes U-statistic-based and copula model-based estimators, introducing four new quantile dependence measures and novel tail dependence coefficients. We develop two visualization tools\u2014Type I and Type II local Kendall\u2019s \u03c4 surfaces\u2014applied to Archimedean copulas to aid interpretation. Comparisons show that global Kendall\u2019s \u03c4 often differs markedly from its local versions, emphasizing the added value of local analysis. Simulation results indicate that when the model is correctly specified, the copula-based estimator exhibits significantly superior performance. We illustrate the framework\u2019s practical utility using Parkinson\u2019s disease and COVID-19 datasets, showing its ability to detect subgroup-specific dependence patterns vital for precision medicine.<\/jats:p>","DOI":"10.1093\/biomtc\/ujag132","type":"journal-article","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T11:12:02Z","timestamp":1785323522000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized Local Kendall\u2019s \u03c4: a novel framework for uncovering nonlinear local dependence"],"prefix":"10.1093","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5389-4963","authenticated-orcid":false,"given":"Zaixin","family":"Huang","sequence":"first","affiliation":[{"name":"School of Information Management and Engineering, Shanghai University of Finance and Economics , Shanghai 200433 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