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Nonparametric maximum likelihood estimation in cure-rate models based on uncensored and censored data

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Nonparametric maximum likelihood estimation in cure-rate models based on uncensored and censored data

Tan, Fang (2006) Nonparametric maximum likelihood estimation in cure-rate models based on uncensored and censored data. Masters thesis, Concordia University.

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Abstract

In this thesis, we shall attempt to give the NPMLE of the event time distribution and cure-rate based on different types of uncensored and censored data. Cure-mixture model and hidden model are used extensively. We address the non-estimability of the cure-rate when no cures are actually observed, in the uncensored case and some important censoring models. A proof is also given for the almost sure convergence of [Special characters omitted.] F ( x ) to (1 - s), where [Special characters omitted.] F ( x ) is the supremum of the MLE of the underlying distribution function, and s is the true underlying cure-rate, for random censoring and interval censoring (case-1). We describe and illustrate the "max-min formula" derived by Groeneboom and Wellner (1992) for interval censoring (case-1), then modify it to get the MLE of the cure-rate under a cure-mixture model, when some cures are observed. We perform a simulation study to give some numerical results as well. Finally, we discuss a probable approach to find the NPMLE in interval censoring (case-2), as a problem for further research.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Tan, Fang
Pagination:vii, 52 leaves ; 29 cm.
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics and Statistics
Date:2006
Thesis Supervisor(s):Sen, Arusharka
ID Code:8900
Deposited By:Concordia University Libraries
Deposited On:18 Aug 2011 14:38
Last Modified:18 Aug 2011 14:39
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