{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T00:07:17Z","timestamp":1787962037406,"version":"build-2784847793"},"reference-count":39,"publisher":"SAGE Publications","issue":"10-11","license":[{"start":{"date-parts":[[2018,10,15]],"date-time":"2018-10-15T00:00:00Z","timestamp":1539561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme","award":["682540 - TransMID"],"award-info":[{"award-number":["682540 - TransMID"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Stat Methods Med Res"],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:p> Frailty models have been developed to quantify both heterogeneity as well as association in multivariate time-to-event data. In recent years, numerous shared and correlated frailty models have been proposed in the survival literature allowing for different association structures and frailty distributions. A bivariate correlated gamma frailty model with an additive decomposition of the frailty variables into a sum of independent gamma components was introduced before. Although this model has a very convenient closed-form representation for the bivariate survival function, the correlation among event- or subject-specific frailties is bounded above which becomes a severe limitation when the values of the two frailty variances differ substantially. In this article, we review existing correlated gamma frailty models and propose novel ones based on bivariate gamma frailty distributions. Such models are found to be useful for the analysis of bivariate survival time data regardless of the censoring type involved. The frailty methodology was applied to right-censored and left-truncated Danish twins mortality data and serological survey current status data on varicella zoster virus and parvovirus B19 infections in Belgium. From our analyses, it has been shown that fitting more flexible correlated gamma frailty models in terms of the imposed association and correlation structure outperforms existing frailty models including the one with an additive decomposition. <\/jats:p>","DOI":"10.1177\/0962280218803127","type":"journal-article","created":{"date-parts":[[2019,9,12]],"date-time":"2019-09-12T04:26:10Z","timestamp":1568262370000},"page":"3437-3450","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["Correlated gamma frailty models for bivariate survival time data"],"prefix":"10.1177","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4565-4572","authenticated-orcid":false,"given":"Adelino","family":"Martins","sequence":"first","affiliation":[{"name":"Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium"},{"name":"Department of Mathematics and Informatics, Eduardo Mondlane University, Maputo, Mozambique"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1803-9072","authenticated-orcid":false,"given":"Marc","family":"Aerts","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Niel","family":"Hens","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium"},{"name":"Centre for Health Economics Research and Modelling Infectious Diseases, Centre for the Evaluation of Vaccination, Vaccine & Infectious Disease Institute (WHO Collaborating Centre), University of Antwerp, Wilrijk, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Wienke","sequence":"additional","affiliation":[{"name":"Institute of Medical Epidemiology, Biostatistics and Informatics, Martin Luther University of Halle-Wittenberg, Halle, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven","family":"Abrams","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2018,10,15]]},"reference":[{"key":"bibr1-0962280218803127","volume-title":"Frailty models in survival analysis","author":"Wienke A","year":"2011"},{"key":"bibr2-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-6646-9"},{"key":"bibr3-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2004.11.010"},{"key":"bibr4-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1002\/9781118307656"},{"key":"bibr5-0962280218803127","doi-asserted-by":"publisher","DOI":"10.2307\/2061224"},{"key":"bibr6-0962280218803127","doi-asserted-by":"publisher","DOI":"10.2307\/1914140"},{"key":"bibr7-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.1.141"},{"key":"bibr8-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/61.1.17"},{"key":"bibr9-0962280218803127","doi-asserted-by":"publisher","DOI":"10.2307\/2530458"},{"key":"bibr10-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1080\/08898489509525394"},{"key":"bibr11-0962280218803127","doi-asserted-by":"publisher","DOI":"10.4054\/DemRes.2014.30.58"},{"key":"bibr12-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(99)00119-3"},{"key":"bibr13-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3660"},{"key":"bibr14-0962280218803127","first-page":"137","volume":"5","author":"Kibble WF","year":"1941","journal-title":"Sankhya"},{"key":"bibr15-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/25.1-2.121"},{"key":"bibr16-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2004.11.008"},{"key":"bibr17-0962280218803127","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2011.633202"},{"key":"bibr18-0962280218803127","unstructured":"Hauge M. 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