The GMLE based Buckley–James estimator with modified case–cohort data
ABSTRACT We consider the estimation problem under the linear regression model with the modified case–cohort design. The extensions
of the Buckley–James estimator (BJE) under the case–cohort designs have been studied under an additional assumption that the
censoring variable and the covariate are independent. If this assumption is violated, as is the case in a typical real data
set in the literature, our simulation results suggest that those extensions are not consistent and we propose a new extension.
Our estimator is based on the generalized maximum likelihood estimator (GMLE) of the underlying distributions. We propose
a self-consistent algorithm, which is quite different from the one for multivariate interval-censored data. We also show that
under certain regularity conditions, the GMLE and the BJE are consistent and asymptotically normally distributed. Some simulation
results are presented. The BJE is also applied to the real data set in the literature.
KeywordsRight-censorship-Linear regression model-Self-consistent algorithm-Generalized MLE-Consistency-Asymptotic normality
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ABSTRACT: Case-cohort sampling aims at reducing the data sampling and costs of large cohort studies. It is therefore important to estimate the parameters of interest as efficiently as possible. We present a maximum likelihood estimator (MLE) for a case-cohort study based on the proportional hazards assumption. The estimator shows finite sample properties that improve on those by the Self & Prentice [Ann. Statist. 16 (1988)] estimator. The size of the gain by the MLE varies with the level of the disease incidence and the variability of the relative risk over the considered population. The gain tends to be small when the disease incidence is low. The MLE is found by a simple EM algorithm that is easy to implement. Standard errors are estimated by a profile likelihood approach based on EM-aided differentiation. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..Scandinavian Journal of Statistics 06/2004; 31(2):283-293. DOI:10.1111/j.1467-9469.2004.02-064.x · 1.06 Impact Factor
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ABSTRACT: Buckley and James proposed an extension of the classical least squares estimator to the censored regression model. It has been found in some empirical and Monte Carlo studies that their approach provides satisfactory results and seems to be superior to other extensions of the least squares estimator in the literature. To develop a complete asymptotic theory for this approach, we introduce herein a slight modification of the Buckley-James estimator to get around the difficulties caused by the instability at the upper tail of the associated Kaplan-Meier estimate of the underlying error distribution and show that the modified Buckley-James estimator is consistent and asymptotically normal under certain regularity conditions. A simple formula for the asymptotic variance of the modified Buckley-James estimator is also derived and is used to study the asymptotic efficiency of the estimator. Extensions of these results to the multiple regression model are also given.The Annals of Statistics 09/1991; 19(3). DOI:10.1214/aos/1176348253 · 2.44 Impact Factor
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