Keywords

Censored observations (Statistics), Nonparametric statistics, Survival analysis (Biometry)

Abstract

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) F[subscript n](t,z) for joint distribution function F[sub 0](t,z) of survival time T and covariate Z, where T is subject to right censoring, noting that such BNPMLE F[subscript n] has not been studied in statistical literature. Then, based on this BNPMLE F[subscript n] 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 F[subscript n] 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.

Notes

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Graduation Date

2011

Semester

Fall

Advisor

Ren, Jian-Jian (Joan)

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0004158

URL

http://purl.fcla.edu/fcla/etd/CFE0004158

Language

English

Release Date

December 2011

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Subjects

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic

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Included in

Mathematics Commons

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