{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,6]],"date-time":"2026-09-06T02:45:36Z","timestamp":1788662736511,"version":"build-2803163510"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:00:00Z","timestamp":1706659200000},"content-version":"vor","delay-in-days":216,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF-14301618"],"award-info":[{"award-number":["GRF-14301618"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF-14301920"],"award-info":[{"award-number":["GRF-14301920"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF-14307221"],"award-info":[{"award-number":["GRF-14307221"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF\u201014301618"],"award-info":[{"award-number":["GRF\u201014301618"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF\u201014301920"],"award-info":[{"award-number":["GRF\u201014301920"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["GRF\u201014307221"],"award-info":[{"award-number":["GRF\u201014307221"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non-smooth components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self-contradicting conclusions. We propose an estimating equation-based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap-based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite-sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and so forth.<\/jats:p>","DOI":"10.1111\/biom.13892","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T14:14:13Z","timestamp":1688048053000},"page":"3549-3563","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Interquantile Smoothness of Censored Quantile Regression with Induced Smoothing"],"prefix":"10.1093","volume":"79","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0253-8045","authenticated-orcid":false,"given":"Zexi","family":"Cai","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Columbia University , New York, New York , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5006-1838","authenticated-orcid":false,"given":"Tony","family":"Sit","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong , Shatin, Hong Kong SAR , China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"2024020107191625800_biom13892-bib-0001","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1093\/biomet\/92.1.149","article-title":"Standard errors and covariance matrices for smoothed rank estimators","volume":"92","author":"Brown","year":"2005","journal-title":"Biometrika"},{"key":"2024020107191625800_biom13892-bib-0002","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/978-1-4613-3030-1_74","article-title":"The veterans administration study of chemoprophylaxis for recurrent stage I bladder tumours: comparisons of placebo, pyridoxine and topical thiotepa","volume-title":"Bladder Tumors and other Topics in Urological Oncology","author":"Byar","year":"1980"},{"key":"2024020107191625800_biom13892-bib-0003","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1111\/biom.13230","article-title":"Censored quantile regression model with time-varying covariates under length-biased sampling","volume":"76","author":"Cai","year":"2020","journal-title":"Biometrics"},{"key":"2024020107191625800_biom13892-bib-0004","doi-asserted-by":"crossref","first-page":"1495","DOI":"10.1002\/sim.6415","article-title":"Rank-based estimating equations with general weight for accelerated failure time models: an induced smoothing approach","volume":"34","author":"Chiou","year":"2015","journal-title":"Statistics in Medicine"},{"key":"2024020107191625800_biom13892-bib-0005","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s11222-016-9634-5","article-title":"Rank-based estimation for semiparametric accelerated failure time model under length-biased sampling","volume":"27","author":"Chiou","year":"2017","journal-title":"Statistics and Computing"},{"key":"2024020107191625800_biom13892-bib-0006","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1080\/01621459.2019.1695623","article-title":"Transformed dynamic quantile regression on censored data","volume":"116","author":"Chu","year":"2021","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0007","volume-title":"Counting processes and survival analysis","author":"Fleming","year":"1991"},{"key":"2024020107191625800_biom13892-bib-0008","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1093\/biostatistics\/kxw036","article-title":"A quantile regression model for failure-time data with time-dependent covariates","volume":"18","author":"Gorfine","year":"2017","journal-title":"Biostatistics"},{"key":"2024020107191625800_biom13892-bib-0009","doi-asserted-by":"crossref","first-page":"2899","DOI":"10.1214\/22-AOS2214","article-title":"Scalable estimation and inference for censored quantile regression process","volume":"50","author":"He","year":"2022","journal-title":"The Annals of Statistics"},{"key":"2024020107191625800_biom13892-bib-0010","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1198\/016214506000001257","article-title":"Smoothed rank regression with censored data","volume":"102","author":"Heller","year":"2007","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0011","volume-title":"Applied survival analysis: regression modeling of time-to-event data","author":"Hosmer","year":"1999"},{"key":"2024020107191625800_biom13892-bib-0012","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1080\/01621459.2019.1602047","article-title":"Functional censored quantile regression","volume":"115","author":"Jiang","year":"2020","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0013","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1093\/biomet\/90.2.341","article-title":"Rank-based inference for the accelerated failure time model","volume":"90","author":"Jin","year":"2003","journal-title":"Biometrika"},{"key":"2024020107191625800_biom13892-bib-0014","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1093\/biomet\/asp025","article-title":"Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data","volume":"96","author":"Johnson","year":"2009","journal-title":"Biometrika"},{"key":"2024020107191625800_biom13892-bib-0015","doi-asserted-by":"crossref","first-page":"33","DOI":"10.2307\/1913643","article-title":"Regression quantiles","volume":"46","author":"Koenker","year":"1978","journal-title":"Econometrica"},{"key":"2024020107191625800_biom13892-bib-0016","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1111\/biom.12847","article-title":"Generalized accelerated recurrence time model for multivariate recurrent event data with missing event type","volume":"74","author":"Ma","year":"2018","journal-title":"Biometrics"},{"key":"2024020107191625800_biom13892-bib-0017","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1016\/j.csda.2010.10.018","article-title":"Variance estimation in censored quantile regression via induced smoothing","volume":"56","author":"Pang","year":"2012","journal-title":"Computational Statistics & Data Analysis"},{"key":"2024020107191625800_biom13892-bib-0018","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1198\/016214508000000355","article-title":"Survival analysis with quantile regression models","volume":"103","author":"Peng","year":"2008","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0019","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1198\/016214503000000954","article-title":"Censored regression quantiles","volume":"98","author":"Portnoy","year":"2003","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0020","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(84)90004-6","article-title":"Least absolute deviations estimation for the censored regression model","volume":"25","author":"Powell","year":"1984","journal-title":"Journal of Econometrics"},{"key":"2024020107191625800_biom13892-bib-0021","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0304-4076(86)90016-3","article-title":"Censored regression quantiles","volume":"32","author":"Powell","year":"1986","journal-title":"Journal of Econometrics"},{"key":"2024020107191625800_biom13892-bib-0022","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/01621459.2014.995795","article-title":"Generalizing quantile regression for counting processes with applications to recurrent events","volume":"111","author":"Sun","year":"2016","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0023","doi-asserted-by":"crossref","first-page":"3696","DOI":"10.1016\/j.csda.2009.03.012","article-title":"Quantile regression without the curse of unsmoothness","volume":"53","author":"Wang","year":"2009","journal-title":"Computational Statistics & Data Analysis"},{"key":"2024020107191625800_biom13892-bib-0024","doi-asserted-by":"crossref","first-page":"1670","DOI":"10.1080\/01621459.2014.989323","article-title":"Smoothed and corrected score approach to censored quantile regression with measurement errors","volume":"110","author":"Wu","year":"2015","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0025","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.1080\/01621459.2013.837368","article-title":"Cure rate quantile regression for censored data with a survival fraction","volume":"108","author":"Wu","year":"2013","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0026","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1080\/01621459.2016.1222286","article-title":"Estimation and inference of quantile regression for survival data under biased sampling","volume":"112","author":"Xu","year":"2017","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0027","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1080\/01621459.1995.10476500","article-title":"Survival analysis with median regression models","volume":"90","author":"Ying","year":"1995","journal-title":"Journal of the American Statistical Association"},{"key":"2024020107191625800_biom13892-bib-0028","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1093\/biostatistics\/kxm034","article-title":"Efficient resampling methods for nonsmooth estimating functions","volume":"9","author":"Zeng","year":"2008","journal-title":"Biostatistics"}],"container-title":["Biometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/79\/4\/3549\/56383537\/biometrics_79_4_3549.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/79\/4\/3549\/56383537\/biometrics_79_4_3549.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T07:22:15Z","timestamp":1706772135000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biometrics\/article\/79\/4\/3549\/7587584"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,29]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,6,29]]},"published-print":{"date-parts":[[2023,12,1]]}},"URL":"https:\/\/doi.org\/10.1111\/biom.13892","relation":{},"ISSN":["0006-341X","1541-0420"],"issn-type":[{"value":"0006-341X","type":"print"},{"value":"1541-0420","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,12]]},"published":{"date-parts":[[2023,6,29]]},"assertion":[{"value":"2022-02-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-04-24","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-06-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}