{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T11:06:01Z","timestamp":1791198361244,"version":"4.1.0"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2003,4,25]],"date-time":"2003-04-25T00:00:00Z","timestamp":1051228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003,5,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The maximum likelihood estimator (MLE) for the proportional hazards model with partly interval-censored data is studied. Under appropriate regularity conditions, the MLEs of the regression parameter and the cumulative hazard function are shown to be consistent and asymptotically normal. Two methods to estimate the variance\u2013covariance matrix of the MLE of the regression parameter are considered, based on a generalized missing information principle and on a generalized profile information procedure. Simulation studies show that both methods work well in terms of the bias and variance for samples of moderate size. An example illustrates the methods.<\/jats:p>","DOI":"10.1111\/1467-9868.00398","type":"journal-article","created":{"date-parts":[[2004,12,28]],"date-time":"2004-12-28T14:38:40Z","timestamp":1104244720000},"page":"489-502","source":"Crossref","is-referenced-by-count":66,"title":["Maximum Likelihood Estimation for the Proportional Hazards Model with Partly Interval-Censored Data"],"prefix":"10.1093","volume":"65","author":[{"given":"Jong S.","family":"Kim","sequence":"first","affiliation":[{"name":"Portland State University , Portland , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,4,25]]},"reference":[{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1214\/aos\/1176345976","article-title":"Cox\u2019s regression model for counting processes: a large sample study","volume":"10","author":"Andersen","year":"1982","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1007\/BF00281993","article-title":"The effect of proteinuria on relative mortality in Type I (insulin-dependent) diabetes mellitus","volume":"28","author":"Borch-Johnsen","year":"1985","journal-title":"Diabetologia"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1214\/aos\/1176347506","article-title":"Weak convergence of a self-consistent estimator of the survival function with doubly censored data","volume":"18","author":"Chang","year":"1990","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.1214\/aos\/1176350608","article-title":"Strong consistency of a nonparametric estimator of the survival function with doubly censored data","volume":"15","author":"Chang","year":"1987","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1093\/biomet\/62.2.269","article-title":"Partial likelihood","volume":"62","author":"Cox","year":"1975","journal-title":"Biometrika"},{"key":"2023032908214706900_","first-page":"76","article-title":"Estimation of morbid risk and age at onset with missing information","volume":"49","author":"Cupples","year":"1991","journal-title":"Am. J. Hum. Genet."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8621-5","volume-title":"Information Bounds and Nonparametric Maximum Likelihood Estimation","author":"Groeneboom","year":"1992"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1214\/aos\/1176349140","article-title":"Asymptotic properties of self-consistent estimator based on doubly censored data","volume":"21","author":"Gu","year":"1993","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1214\/aos\/1032894452","article-title":"Efficient estimation for the proportional hazards model with interval censoring","volume":"24","author":"Huang","year":"1996","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","first-page":"501","article-title":"Asymptotic properties of nonparametric estimation based on partly interval-censored data","volume":"9","author":"Huang","year":"1999","journal-title":"Statist. Sin."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1080\/01621459.1997.10474050","article-title":"Sieve estimation for the proportional odds failure-time regression model with interval censoring","volume":"92","author":"Huang","year":"1997","journal-title":"J. Am. Statist. Ass."},{"key":"2023032908214706900_","article-title":"Efficient estimation for the proportional hazards model with \u2018\u2018Case 2\u2019\u2019 interval censoring","volume-title":"Technical Report 290","author":"Huang","year":"1995"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"685","DOI":"10.2307\/2530049","article-title":"Covariate analysis of survival data: a small-sample study of Cox\u2019s model","volume":"38","author":"Johnson","year":"1982","journal-title":"Biometrics"},{"key":"2023032908214706900_","volume-title":"Functional Analysis","author":"Kantorovich","year":"1982"},{"key":"2023032908214706900_","volume-title":"The proportional hazards model based on arbitrarily censored data","author":"Kim","year":"1999"},{"key":"2023032908214706900_","first-page":"1569","volume-title":"Statist. Med.","author":"Law","year":"1992"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/2531007","article-title":"A comparison of test statistics for assessing the effects of concomitant variables in survival analysis","volume":"39","author":"Lee","year":"1983","journal-title":"Biometrics"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1111\/j.2517-6161.1982.tb01203.x","article-title":"Finding observed information when using the EM algorithm","volume":"44","author":"Louis","year":"1982","journal-title":"J. R. Statist. Soc. B"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"381","DOI":"10.2307\/3318710","article-title":"Observed information in semi-parametric models","volume":"5","author":"Murphy","year":"1999","journal-title":"Bernoulli"},{"key":"2023032908214706900_","first-page":"25","article-title":"A counting process approach to maximum likelihood estimation in frailty models","volume":"19","author":"Nielsen","year":"1992","journal-title":"Scand. J. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"951","DOI":"10.2307\/2532360","article-title":"Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model","volume":"48","author":"Odell","year":"1992","journal-title":"Biometrics"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/01621459.1978.10480015","article-title":"Size and power assessments of tests of hypotheses on survival parameters","volume":"73","author":"Peace","year":"1978","journal-title":"J. Am. Statist. Ass."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"185","DOI":"10.2307\/2344317","article-title":"Asymptotically efficient rank invariant test procedures (with discussion)","volume":"135","author":"Peto","year":"1972","journal-title":"J. R. Statist. Soc. A"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/03461238.1987.10413814","article-title":"Life insurance for insulin-dependent diabetics","volume":"39","author":"Ramlau-Hansen","year":"1987","journal-title":"Scand. Act. J."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"929","DOI":"10.2307\/2531328","article-title":"Estimating morbidity risks with variable age of onset: review of methods and a maximum likelihood approach","volume":"39","author":"Risch","year":"1983","journal-title":"Biometrics"},{"key":"2023032908214706900_","first-page":"76","article-title":"Relative risk of Alzheimer disease and age-at-onset distributions based on APOE genotype among elderly African American Caucaisians, and Hispanics in New York City","volume":"49","author":"Tang","year":"1995","journal-title":"Am. J. Hum. Genet."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1214\/aos\/1176345335","article-title":"A large sample study of Cox\u2019s regression model","volume":"9","author":"Tsiatis","year":"1981","journal-title":"Ann. Statist."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/01621459.1974.10480146","article-title":"Nonparametric estimation of a survivorship function with doubly censored data","volume":"69","author":"Turnbull","year":"1974","journal-title":"J. Am. Statist. Ass."},{"key":"2023032908214706900_","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1111\/j.2517-6161.1976.tb01597.x","article-title":"The empirical distribution function with arbitrarily grouped, censored and truncated data","volume":"38","author":"Turnbull","year":"1976","journal-title":"J. R. Statist. Soc. B"},{"key":"2023032908214706900_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2545-2","volume-title":"Weak Convergence and Empirical Processes with Applications to Statistics","author":"Vaart","year":"1996"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00398","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00398","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/2\/489\/49684519\/jrsssb_65_2_489.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/2\/489\/49684519\/jrsssb_65_2_489.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,21]],"date-time":"2024-12-21T16:14:05Z","timestamp":1734797645000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/65\/2\/489\/7092860"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4,25]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2003,4,25]]},"published-print":{"date-parts":[[2003,5,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00398","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2003,5]]},"published":{"date-parts":[[2003,4,25]]}}}