Statistics PhD Defense - 10/17/24

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 non-terminal 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 test for the 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 studies the age-varying effects of cancer treatments on non-surgical primary ovarian insufficiency (POI) among young female cancer survivors. This project is motivated by the Childhood Cancer Survivor Study. We proposed a class of models that allow the treatment effects to vary with two ages: the age at diagnosis and the age at POI. 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.