Keywords

Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic, Statistical hypothesis testing, Survival analysis (Biometry), Bootstrap, Confidence interval, Cox model, Doubly censored data, Empirical likelihood function, Goodness of fit test, Maximum likelihood, Partly interval censored data, Proportional hazards model, Right censored data, Survival analysis

Abstract

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 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.

Notes

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Graduation Date

2006

Semester

Spring

Advisor

Ren, Jian-Jian

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0001099

URL

http://purl.fcla.edu/fcla/etd/CFE0001099

Language

English

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Included in

Mathematics Commons

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