Mathematics Commons^™

Dependent Censoring In Survival Analysis, Zhongcheng Lin

Dissertations

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 …

Asymmetric Multivariate Archimedean Copula Models And Semi-Competing Risks Data Analysis, Ziyan Guo

Dissertations

Many multivariate models have been proposed and developed to model high dimensional data when the dimension of a data set is greater than 2 (d ≥ 3). The existing multivariate models often force the “exchangeable” structure for part or the whole model, are not very flexible which tends to be of limited use in practice. There is a demand for developing and studying multivariate models with any pre-specified bivariate margins.

Suppose there exists such a class of flexible models with any pre-specified bivariate margins. Given a multivariate data, what is the distribution function and how to easily estimate the parameters …