Author

Shujie Chen

Date of Award

Spring 2023

Document Type

Open Access Dissertation

Department

Statistics

First Advisor

Jiajia Zhang

Abstract

In this dissertation, we focus on studying three mixture cure models with background mortality. With the development of treatment, patients may be cured and suffer from other cause of death. The cure model with background mortality can measure the population cure which refers to the patients with comparable mortality with their counterpart in general population. Three types of survival models are investigated, including generalized odds rate (GOR) model, cure model with background mortality for right censoring and interval censoring, and extended illness death model via incorporating “cure” fraction. All methods are validated via comprehensive simulation studies and real data application. The first project focuses on studying the mortality rate among breast cancer patients with the stage at regional. The second project studies the risk factors for mortality on the interval censored women with breast cancer data. In the third project, we investigate the progression to AIDS onset among people living with HIV (PLWH) and the mortality rate for PLWH with or without AIDS. The first two projects are motivated by the SEER database and the third project is based on the South Carolina (SC) HIV datasets.

We list the specific projects as follow. In the first project, we extend the background mortality proportional hazards (PH) cure model to the background mortality model with GOR model, which includes the background mortality with PH cure model as a special case. We develop the two estimation methods based on 1) Multiple imputation (MI) method and 2) Expectation and Maximization (EM) algorithm, where spline function is employed for estimating the unknown baseline hazard function. These two proposed methods are evaluated via the comprehensive simulation studies and further being applied to SEER female breast cancer dataset in Chapter 2.

In the second project, we consider PH cure model with background mortality for interval censored data. There is an existing mixture cure PH model with background mortality (MCPH+BM) improving the estimation of the cure rate compared to the mixture cure PH model. However, there is a knowledge gap how to extend the estimation method to mixture cure PH model with background mortality for survival data with interval censoring. To handle the interval censoring, we incorporate additional latent variable to simplify the likelihood and develop the EM algorithm with monotone spline function. The proposed methods is evaluated via the comprehensive simulation studies and further being applied to SEER breast cancer data set in Chapter 3.

In the third project, we extend the knowledge of illness death model to the situation with potential cure and background mortality. First, we modified the illness death model via allowing the latent cure status which indicate potential patients with illness free. Second, we incorporate the background mortality as a competing event for all cause mortality to the multistate cure model. The estimated model could provide the survival probability and also identify the significant risk factors on each pathway. EM algorithm is used to estimate the proposed model. The performance of the methods is evaluated with simulation under different cure rate and sample sizes. We apply the proposed model to the SC HIV data to investigate the probability of AIDS and mortality rate among PLWH in Chapter 4.

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