Date of Award

12-16-2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Gengsheng Qin

Second Advisor

Yi Jiang

Third Advisor

Jing Zhang

Fourth Advisor

Ruiyan Luo

Abstract

Recent studies show that appropriate statistical analysis of cost data may lead to more cost-effective medical treatments, resulting in substantial cost savings. Even though the mean value is publicly accepted as a summary of medical costs, however, due to heavy censoring and heavy skewness, mean will be affected much by missing or extremely large values. Therefore, quantiles of medical costs like the median cost are more reasonable summaries of the cost data. In the first part of this dissertation, we first propose to use empirical likelihood (EL) methods based on influence function and jackknife techniques to construct confidence regions for regression parameters in median cost regression models with censored data. We further propose EL-based confidence intervals for the median cost with given covariates. Compared with existing normal approximation-based confidence intervals, our proposed intervals have better coverage accuracy.

In the real world, there is a large proportion of patients having zero costs. In the second part, we propose to use fiducial quantity and EL-based inference for the mean of zero-inflated censored medical costs applying the method of variance estimates recovery (MOVER). We also provide EL-based confidence intervals for the upper quantile censored medical costs with many zero observations. Simulation studies are conducted to compare the performance between proposed EL-based methods and the existing normal approximation-based methods in terms of coverage probability. The novel EL-based methods are observed to have better finite sample performances than existing methods, especially when the censoring proportion is high.

In the third part of this dissertation, we focus on evaluating breast cancer recurrence risk. For early-stage cancer tumor recurrence study, existing methods do not have an overall powerful survival prediction ability. Preliminary studies show that centrosome amplification has a strong latent correlation with tumor progression. As a result, we propose to construct a novel quantitative centrosome amplification score to stratify patients' cancer recurrence risk. We prove that patients with higher centrosome amplification score will have a significantly higher probability to experience cancer recurrence given all demographic conditions, which could provide a potent reference for the future developing trend of early-stage breast cancer.

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