{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T14:02:54Z","timestamp":1792159374793,"version":"4.4.0"},"reference-count":27,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T00:00:00Z","timestamp":1772236800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T00:00:00Z","timestamp":1772236800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100007301","name":"Harvard University Center for AIDS Research","doi-asserted-by":"publisher","award":["HU CFAR NIH\/NAIDS P30\u2010AI 060354"],"award-info":[{"award-number":["HU CFAR NIH\/NAIDS P30\u2010AI 060354"]}],"id":[{"id":"10.13039\/100007301","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012802","name":"Ragon Institute of MGH, MIT and Harvard","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012802","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Monitoring both immunological and virological outcome measures provides the most accurate and meaningful assessment of the human immunodeficiency virus (HIV) treatment effectiveness. However, evaluating treatment efficacy based solely on either measure, using commonly employed survival and hazard functions, can introduce bias. In addition, heterogeneity in treatment\u2010related recovery often results in skewed immunological and virological data. To address these challenges, we extend traditional survival analysis to the bivariate setting by introducing the bivariate median residual life function (MeRL) as a robust alternative for assessing treatment efficacy. In this framework, treatment efficacy is evaluated using the bivariate vector of time to immunological restoration and virological suppression. Unlike the mean residual life, the MeRL is less influenced by outliers and heavy\u2010tailed distributions, which are frequently encountered in clinical studies. This paper proposes novel estimators for the bivariate MeRL function under order restrictions, and establishes their strong consistency and asymptotic distributions. Simulation studies were conducted to evaluate the performance of the proposed estimators. Finally, we demonstrated the practical utility of our approach through an application to real\u2010world bivariate HIV data, offering valuable insights for both researchers and healthcare\u00a0practitioners.<\/jats:p>","DOI":"10.1002\/bimj.70112","type":"journal-article","created":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T16:59:14Z","timestamp":1772989154000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bivariate Quantile Residual Life Functions for Estimating Immunological and Virological Recovery in HIV Patients"],"prefix":"10.1002","volume":"68","author":[{"given":"Ruhul Ali","family":"Khan","sequence":"first","affiliation":[{"name":"Harvard Medical School Cambridge Massachusetts USA"},{"name":"The Ragon Institute of MGH MIT and Harvard Cambridge Massachusetts USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8572-1944","authenticated-orcid":false,"given":"Musie","family":"Ghebremichael","sequence":"additional","affiliation":[{"name":"Harvard Medical School Cambridge Massachusetts USA"},{"name":"The Ragon Institute of MGH MIT and Harvard Cambridge Massachusetts USA"},{"name":"MGH Biostatistics Somerville Massachusetts USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,2,28]]},"reference":[{"issue":"3","key":"e_1_2_9_2_1","first-page":"1129","article-title":"Semiparametric Inference for the Proportional Mean Residual Life Model With Right\u2010Censored Length\u2010Biased Data","volume":"26","author":"Bai F.","year":"2016","journal-title":"Statistica Sinica"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmjgh-2016-000227"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1001\/jama.2012.2001"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(06)68337-2"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201600068"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511802843"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2019.1710150"},{"key":"e_1_2_9_9_1","unstructured":"Ghebremichael M.2004. \u201cNonparametric Estimation of Bivariate Mean Residual Life Function.\u201d PhD diss Rice University."},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664763.2017.1420758"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1097\/OLQ.0b013e3181a866b8"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.3844\/jmssp.2019.55.64"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1258\/ijsa.2007.007248"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2007.00826.x"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00357-018-9300-z"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964818000128"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214502388618690"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/80.3.573"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.202200340"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.10076"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2007.07.005"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/02331888.2018.1470180"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2021.1947277"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00362-017-0905-9"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0130"},{"key":"e_1_2_9_26_1","volume-title":"Global AIDS Update 2016","author":"UNAIDS","year":"2016"},{"key":"e_1_2_9_27_1","volume-title":"Consolidated Guidelines on the Use of Antiretroviral Drugs for Treating and Preventing HIV Infection: Recommendations for a Public Health Approach","author":"WHO","year":"2016"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4110"}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70112","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/bimj.70112","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:19:26Z","timestamp":1776766766000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.70112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,28]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["10.1002\/bimj.70112"],"URL":"https:\/\/doi.org\/10.1002\/bimj.70112","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,28]]},"assertion":[{"value":"2024-11-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-28","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70112"}}