Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Zhou, Qian

Committee Member

Chen, Xinyuan

Committee Member

Patil, Prakash

Committee Member

Shi, Jingyi

Committee Member

Wu, Tung-Lung; Yuan, Yan

Date of Degree

12-13-2024

Original embargo terms

Worldwide

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy (Ph.D.)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

This dissertation has three parts. The first part proposes a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the nonterminal event is subject to dependent censoring by the terminal event. Under a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and a parametric copula function specifies the between-event dependence. The parameters associated with the marginal of the terminal event are first estimated, and the marginal parameters for the non-terminal event time and the copula parameter are second estimated via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. We showed that our approach leads to consistent estimates with less computational cost and more robustness compared to the one-stage procedure developed by Chen (2012). In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed by Zhu et al. (2021). The second part develops a goodness-of-fit t est f or t he copula specification under semi-parametric copula models with semi-competing risks data. We constructed an information ratio (IR) statistic by comparing consistent estimates of the two information matrices, the sensitivity matrix and the variability matrix. The information matrices are derived from the log-likelihood function, which is a function of the marginal distribution of the terminal event time, the marginal distribution of the time to the first event, and the copula parameter. We established the asymptotic distribution of the IR statistic and examined the finite-sample performance of the IR test via a simulation study. The third part develops a class of models to characterize the effects of factors that vary with the age at baseline and the age at the event. This project is motivated by the Childhood Cancer Survivor Study. The age-specific effects of the covariates are estimated via an inverse probability weighted kernel smoothing method. We conducted simulation studies to evaluate the performance of the proposed estimator.

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