{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T09:50:49Z","timestamp":1792144249166,"version":"4.4.0"},"reference-count":17,"publisher":"Wiley","issue":"30","license":[{"start":{"date-parts":[[2010,12,16]],"date-time":"2010-12-16T00:00:00Z","timestamp":1292457600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2010,12,30]]},"abstract":"Abstract<\/jats:title>Frailty models are encountered in many medical applications, yet little research has been devoted to develop measures that quantify the predictive ability of these models. In this paper, we elaborate on the concept of the concordance probability to clustered data, resulting in an \u2018Overall Conditional C\u2010index\u2019 or bfC<\/jats:italic>O<\/jats:bold>, C<\/jats:bold><\/jats:sub> and an \u2018Overall Marginal C\u2010index\u2019 or C<\/jats:bold>O<\/jats:bold>, M<\/jats:bold><\/jats:sub>. Both Overall C\u2010indices can be split up into a \u2018Between Conditional\u2019 or C<\/jats:bold>B<\/jats:bold>, C<\/jats:bold><\/jats:sub> and a \u2018Between Marginal C\u2010index\u2019 or C<\/jats:bold>B<\/jats:bold>, M<\/jats:bold><\/jats:sub> and into a \u2018Within Conditional\u2019 or C<\/jats:bold>W<\/jats:bold>, C<\/jats:bold><\/jats:sub> and a \u2018Within Marginal C\u2010index\u2019 or C<\/jats:bold>W<\/jats:bold>, M<\/jats:bold><\/jats:sub>. For PH frailty models of the power variance family, C<\/jats:bold>W<\/jats:bold>, C<\/jats:bold><\/jats:sub> and C<\/jats:bold>W<\/jats:bold>, M<\/jats:bold><\/jats:sub> are equivalent resulting in one \u2018Within C\u2010index\u2019 C<\/jats:bold>W<\/jats:bold><\/jats:sub>. We propose an application of Harrell's C\u2010index to estimate the proposed indices within a likelihood and a Bayesian context and the performances of their point estimates and confidence\/credible intervals are compared in an extensive simulation study. This simulation study shows that the point estimates of C<\/jats:bold>W<\/jats:bold><\/jats:sub> and C<\/jats:bold>B<\/jats:bold>, M<\/jats:bold><\/jats:sub> perform good within both a likelihood and Bayesian context but that the point estimates of C<\/jats:bold>B<\/jats:bold>, C<\/jats:bold><\/jats:sub> show less bias for the Bayesian approach than for the likelihood approach. The 95 per cent confidence\/credible intervals also possess good coverage properties, given that the point estimates perform good. The performance of the C\u2010indices is evaluated on a real data set. Copyright \u00a9 2010 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.4058","type":"journal-article","created":{"date-parts":[[2010,12,17]],"date-time":"2010-12-17T04:44:25Z","timestamp":1292561065000},"page":"3160-3171","source":"Crossref","is-referenced-by-count":37,"title":["An application of Harrell's C\u2010index to PH frailty models"],"prefix":"10.1002","volume":"29","author":[{"given":"R.","family":"Van Oirbeek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Lesaffre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2010,12,16]]},"reference":[{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1234\/12345678"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19990915\/30)18:17\/18<2529::AID-SIM274>3.0.CO;2-5"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1486."},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1001\/jama.1982.03320430047030"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1802"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3257."},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2427"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006\u2010341X.2005.030814.x."},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.4.965."},{"key":"e_1_2_9_11_2","volume-title":"The Frailty Model","author":"Duchateau L","year":"2008"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467\u20109868.2007.00593.x."},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345338."},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-4541-9"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1.1.64.7507"},{"key":"e_1_2_9_16_2","volume-title":"Modeling Survival Data","author":"Therneau TM","year":"2000"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0300\u20105712(98)00009\u20108."},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/92.2.351"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.4058","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.4058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T14:59:26Z","timestamp":1694617166000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.4058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,16]]},"references-count":17,"journal-issue":{"issue":"30","published-print":{"date-parts":[[2010,12,30]]}},"alternative-id":["10.1002\/sim.4058"],"URL":"https:\/\/doi.org\/10.1002\/sim.4058","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12,16]]}}}