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Estimation for the Cox Model with Various Types of Censored Data

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Date Issued:
2011
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,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.
Title: Estimation for the Cox Model with Various Types of Censored Data.
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Name(s): Riddlesworth, Tonya, Author
Ren, Joan, Committee Chair
Mohapatra, Ram, Committee Member
Richardson, Gary, Committee Member
Ni, Liqiang, Committee Member
Schott, James, Committee Member
, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2011
Publisher: University of Central Florida
Language(s): English
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,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.
Identifier: CFE0004158 (IID), ucf:49051 (fedora)
Note(s): 2011-12-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): Bivariate Maximum Likelihood Distribution Estimator -- Conditional Survival Probability -- Cox Model -- Doubly Censored Data -- Interval Censored Data -- Maximum Likelihood Estimator -- Partly Interval-Censored Data -- Right Censored Data -- Weighted Empirical Likelihood
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0004158
Restrictions on Access: public 2011-12-15
Host Institution: UCF

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