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Estimation for the Cox Model with Various Types of Censored Data
Title
Estimation for the Cox Model with Various Types of Censored Data.
Creator
Riddlesworth, Tonya, Ren, Joan, Mohapatra, Ram, Richardson, Gary, Ni, Liqiang, Schott, James, University of Central Florida
Abstract / Description
In survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) Fn(t...
Show moreIn survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) Fn(t,z) for joint distribution function Fo(t,z) of survival time T and covariate Z, where T is subject to right censoring, noting that such BNPMLE Fn has not been studied in statistical literature. Then, based on this BNPMLE Fn we derive empirical likelihood-based (Owen, 1988) confidence interval for the conditional survival probabilities, which is an important and difficult problem in statistical analysis, and also has not been studied in literature. Finally, with this BNPMLE Fn as a starting point, we extend the weighted empirical likelihood method (Ren, 2001 and 2008a) to the multivariate case, and obtain a weighted empirical likelihood-based estimation method for the Cox model. Such estimation method is given in a unified form, and is applicable to various types of censored data aforementioned.
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Date Issued
2011
Identifier
CFE0004158, ucf:49051
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004158
APPLICATION OF THE EMPIRICAL LIKELIHOOD METHOD IN PROPORTIONAL HAZARDS MODEL
Title
APPLICATION OF THE EMPIRICAL LIKELIHOOD METHOD IN PROPORTIONAL HAZARDS MODEL.
Creator
HE, BIN, Ren, Jian-Jian, University of Central Florida
Abstract / Description
In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment...
Show moreIn survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) approach to construct goodness-of-fit test and provide estimates for the Cox model with various types of censored data.Specifically, the problems under consideration are the two-sample Cox model and stratified Cox model with right censored data, doubly censored data and partly interval-censored data. Related computational issues are discussed, and some simulation results are presented. The procedures developed in the work are applied to several real data sets with some discussion.
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Date Issued
2006
Identifier
CFE0001099, ucf:46780
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001099