{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T08:11:12Z","timestamp":1790151072016,"version":"4.0.1"},"reference-count":17,"publisher":"Wiley","issue":"20-22","license":[{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T00:00:00Z","timestamp":1787616000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Bayesian estimation implemented via OpenBUGS is used to establish the novelty and practical relevance of the log\u2010Cauchy distribution within a mixture cure fraction modeling framework. Mixture cure fraction models are widely used in survival analysis to accommodate the presence of long\u2010term survivors; however, standard parametric assumptions often fail when survival data exhibit heavy\u2010tailed behavior and substantial right censoring. In such settings, conventional distributions such as the exponential, Weibull, gamma, and lognormal may lead to biased estimation and inadequate uncertainty quantification. In this paper, we propose a Bayesian mixture cure fraction model based on the log\u2010Cauchy distribution to flexibly model survival times of uncured subjects in the presence of extreme observations. Bayesian inference is conducted using Markov chain Monte Carlo (MCMC) methods implemented in OpenBUGS, allowing full posterior inference for model parameters through explicit specification of the log\u2010Cauchy likelihood. A comprehensive simulation study is performed to assess the finite\u2010sample performance of the proposed model under varying cure fractions and censoring levels. The results demonstrate accurate parameter estimation, stable MCMC convergence, and reliable posterior coverage, even in challenging scenarios characterized by high censoring and long\u2010term survival. Comparative analyses further show that the proposed model consistently outperforms competing parametric cure models in terms of estimation accuracy and model fit, particularly under heavy\u2010tailed survival settings. The practical utility of the model is further illustrated through application to a real breast cancer dataset, where the proposed approach provides improved model fit and interpretable inference compared with conventional parametric alternatives. Overall, the results confirm that the Bayesian log\u2010Cauchy mixture cure model, implemented via OpenBUGS, provides a robust, flexible, and computationally efficient framework for analyzing survival data with cure fractions and heavy\u2010tailed characteristics, with clear relevance for medical and epidemiological research.<\/jats:p>","DOI":"10.1002\/sim.70721","type":"journal-article","created":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T06:14:05Z","timestamp":1787724845000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Bayesian Log\u2010Cauchy Mixture Cure Fraction Model for Heavy\u2010Tailed Survival Data: Implementation via\n                    <scp>OpenBUGS<\/scp>"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9893-8379","authenticated-orcid":false,"given":"Khalid","family":"Salah","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science &amp; Technology Al\u2010Quds University  Jerusalem Palestine"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,25]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1949.tb00020.x"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1952.10501187"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(93)90008-X"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1999.10474196"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2014.07.011"},{"issue":"1","key":"e_1_2_11_7_1","first-page":"113","article-title":"Cure Fraction Modeling and Estimation in a Population\u2010Based Cancer Survival Analysis","volume":"2","author":"Abu Bakar M. R.","year":"2008","journal-title":"Malaysian Journal of Mathematical Sciences"},{"issue":"1","key":"e_1_2_11_8_1","first-page":"75","article-title":"Bayesian Approach for Joint Longitudinal and Time\u2010To\u2010Event Data With Survival Fraction","volume":"32","author":"Abu Bakar M. R.","year":"2009","journal-title":"Bulletin of the Malaysian Mathematical Sciences Society"},{"key":"e_1_2_11_9_1","first-page":"48","article-title":"A Stochastic Joint Model for Longitudinal and Survival Data With Cured Patients","volume":"11","author":"Abu Bakar M. R.","year":"2009","journal-title":"International Journal of Tomography and Statistics"},{"key":"e_1_2_11_10_1","volume-title":"Survival Analysis With Long\u2010Term Survivors","author":"Maller R. A.","year":"1996"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2000.00237.x"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3447-8"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008929526011"},{"issue":"2","key":"e_1_2_11_14_1","first-page":"3","article-title":"On Maximum Likelihood Estimation of Mixed Cure Fraction Model Assuming Stable Distribution","volume":"34","author":"Salah K. A.","year":"2021","journal-title":"International Journal of Tomography and Simulation"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.23937\/2469\u20105831\/1510020"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1515\/tmmp\u20102016\u20100025"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10477003"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12062"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70721","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70721","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70721","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T07:44:06Z","timestamp":1790149446000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,25]]},"references-count":17,"journal-issue":{"issue":"20-22","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["10.1002\/sim.70721"],"URL":"https:\/\/doi.org\/10.1002\/sim.70721","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,25]]},"assertion":[{"value":"2026-01-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-18","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70721"}}