Thesis (M.Sc.). / Written for the Dept. of Mathematics and Statistics. Title from title page of PDF (viewed 2008/12/07). Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 96-98). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 96-98). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 46-54). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 46-54). Also available on the Internet.

Thesis (M.A.)--The University of North Carolina at Greensboro, 2008. / Title from PDF t.p. (viewed Aug. 17, 2009). Directed by Kirsten Doehler; submitted to the Dept. of Mathematical Sciences. Includes bibliographical references (p. 56-57).

Thesis (M.A.S.)--Memorial University of Newfoundland, 2003. / Bibliography: leaves 48-50. Also available online.

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.

no abstract provided by author / Master of Science

Survival analysis pertains to a statistical approach designed to take into account the amount of time an experimental unit contributes to a study. A Mayo Clinic study of 418 Primary Biliary Cirrhosis patients during a ten year period was used. The Kaplan-Meier Estimator, a non-parametric statistic, and the Cox Proportional Hazard methods were the tools applied. Kaplan-Meier results include total values/censored values.