{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T23:04:10Z","timestamp":1789340650176,"version":"build-2803163510"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T00:00:00Z","timestamp":1780012800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T00:00:00Z","timestamp":1780012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Universit\u00e0 degli Studi di Roma La Sapienza"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Eur J Epidemiol"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The methodological objective of the present study is to extend Rothman\u2019s additive interaction framework from two factors to three or more factors considered simultaneously, while preserving its original causal interpretation and operational simplicity. we propose a generalized Synergy Index (\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>p<\/jats:italic>\n                    <\/jats:sub>\n                    ) that retains the additive logic of Rothman\u2019s original formulation while extending it to an arbitrary number of dichotomous factors. For the analysis we used a database of a previous work in which the synergistic factor was calculated for each couples of two factors (alcohol, tobacco smoke and other risk factors) for age-related macular degeneration. The proposed three-factor\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>p<\/jats:italic>\n                    <\/jats:sub>\n                    is sensitive to the underlying structure of the risk factors considered. When a strong susceptibility component such as family history is included, the combined exposure exhibits clear super-additive behavior (\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>p<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20091.783). Conversely, when hypercholesterolemia replaces family history, the joint effect remains substantial but does not exceed additivity (\n                    <jats:italic>S<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>p<\/jats:italic>\n                    <\/jats:sub>\n                    \u2009=\u20090.756). The generalized multi-factor Synergy Index represents a valuable conceptual and analytical tool for investigating higher-order interactions. It is particularly well suited for the study of complex diseases, where multiple exposures co-occur and interact. It enables the identification of exposure constellations characterized by true superadditivity, with potential implications for etiological research, risk stratification, and targeted prevention strategies.\n                  <\/jats:p>","DOI":"10.1007\/s10654-026-01405-2","type":"journal-article","created":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T04:33:49Z","timestamp":1780029229000},"page":"819-827","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Evaluating synergistic effects among multiple factors in disease causation: a new approach using a generalized synergy index"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1233-2040","authenticated-orcid":false,"given":"Giuseppe","family":"La Torre","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7406-6411","authenticated-orcid":false,"given":"Pierpaolo","family":"D\u2019Urso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,29]]},"reference":[{"key":"1405_CR1","unstructured":"CCOHS. Synergism and related terms. 2019. Available at https:\/\/www.ccohs.ca\/oshanswers\/chemicals\/synergism.pdf, Accessed 15 Jan 2026."},{"key":"1405_CR2","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1093\/oxfordjournals.aje.a112335","volume":"104","author":"KJ Rothman","year":"1976","unstructured":"Rothman KJ. Causes. Am J Epidemiol. 1976;104:587\u201392.","journal-title":"Causes Am J Epidemiol"},{"issue":"6","key":"1405_CR3","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1093\/oxfordjournals.aje.a121626","volume":"99","author":"KJ Rothman","year":"1974","unstructured":"Rothman KJ. Synergy and antagonism in cause-effect relationships. Am J Epidemiol. 1974;99(6):385\u20138.","journal-title":"Am J Epidemiol"},{"issue":"5","key":"1405_CR4","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1093\/oxfordjournals.aje.a112252","volume":"103","author":"KJ Rothman","year":"1976","unstructured":"Rothman KJ. The estimation of synergy or antagonism. Am J Epidemiol. 1976;103(5):506\u201311.","journal-title":"Am J Epidemiol"},{"issue":"4","key":"1405_CR5","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1093\/oxfordjournals.aje.a113015","volume":"112","author":"KJ Rothman","year":"1980","unstructured":"Rothman KJ, Greenland S, Walker AM. Concepts of Interaction. Am J Epidemiol. 1980;112(4):467\u201370.","journal-title":"Am J Epidemiol"},{"key":"1405_CR6","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1186\/1756-0500-2-105","volume":"2","author":"M Cortina-Borja","year":"2009","unstructured":"Cortina-Borja M, Smith AD, Combarros O, et al. The synergy factor: a statistic to measure interactions in complex diseases. BMC Res Notes. 2009;2:105.","journal-title":"BMC Res Notes"},{"key":"1405_CR7","unstructured":"Rothman KJ. Epidemiology: An Introduction. Oxford University Press; 2002."},{"issue":"5","key":"1405_CR8","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/s10654-013-9798-7","volume":"28","author":"G La Torre","year":"2013","unstructured":"La Torre G, Pacella E, Saulle R, Giraldi G, Pacella F, Lenzi T, Mastrangelo O, Mirra F, Aloe G, Turchetti P, Brillante C, De Paolis G, Boccia A, Giustolisi R. The synergistic effect of exposure to alcohol, tobacco smoke and other risk factors for age-related macular degeneration. Eur J Epidemiol. 2013;28(5):445\u20136.","journal-title":"Eur J Epidemiol"},{"issue":"1","key":"1405_CR9","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1093\/aje\/kwj011","volume":"163","author":"K Hoffmann","year":"2006","unstructured":"Hoffmann K, Heidemann C, Weikert C, Schulze MB, Boeing H. Estimating the proportion of disease due to classes of sufficient causes. Am J Epidemiol. 2006;163(1):76\u201383. https:\/\/doi.org\/10.1093\/aje\/kwj011. Epub 2005 Nov 17. 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At that time the study investigation adhered to the Declaration of Helsinki and was approved by the local Ethics Committee.","order":2,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}}]}}