The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	Dependent censoring in survival analysis
Author:	Lin, Zhongcheng
View Online:	njit-etd2021-096 (ix, 40 pages ~ 0.6 MB pdf)
Department:	Department of Mathematical Sciences
Degree:	Doctor of Philosophy
Program:	Mathematical Sciences
Document Type:	Dissertation
Advisory Committee:	Wang, Antai (Committee chair) Guo, Wenge (Committee member) Fang, Yixin (Committee member) Subramanian, Sundarraman (Committee member) Wei, Zhi (Committee member)
Date:	2021-12
Keywords:	Archimedean copula Copula-Graphic estimator Left censoring Left Kaplan-Meier estimator Survival analysis
Availability:	Unrestricted
Abstract:	This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is proposed as well, and some simulation studies are performed to demonstrate our parameter estimation method. The second part is relevant to a new statistic proposed to estimate the survival function where left censoring exists. The derivation of this estimator is a little similar to that of the well-known copula-graphic estimator. The simulation results indicate the difference of performance between it and Left Kaplan Meier estimator when dependent censoring occurs.