Date of Award

Spring 2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Sundarraman Subramanian

Second Advisor

Manish Chandra Bhattacharjee

Third Advisor

Sunil Kumar Dhar

Fourth Advisor

Wenge Guo

Fifth Advisor

Kaifeng Lu

Abstract

In medical reports point estimates and pointwise confidence intervals of parameters are usually displayed. When the parameter is a survival function, however, the approach of joining the upper end points of individual interval estimates obtained at several points and likewise for the lower end points would not produce bands that include the entire survival curve with a given confidence. Simultaneous confidence bands, which allow confidence statements to be valid for the entire survival curve,would be more meaningful

This dissertation focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is model- based, relying on a parametric model for the conditional expectation of the censoring indicator given the observed minimum, and derives its chief strength from easy access to a good-fitting model among a plethora of choices currently available for binary response data. The substantive methodological contribution is in exploiting an available semiparametric estimator of the survival function for the one-sample case to produce improved simultaneous confidence bands. Since the relevant limiting distribution cannot be transformed to a Brownian Bridge unlike for the normalized Kaplan{Meier process, a two-stage bootstrap approach that combines the classical bootstrap with the more recent model-based regeneration of censoring indicators is proposed and a justification of its asymptotic validity is also provided. Several different confidence bands are studied using the proposed approach. Numerical studies, including robustness of the proposed bands to misspecification, are carriedout to check efficacy. The method is illustrated using two lung cancer data sets.

Included in

Mathematics Commons

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