Date on Master's Thesis/Doctoral Dissertation

8-2022

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Bioinformatics and Biostatistics

Degree Program

Biostatistics, PhD

Committee Chair

Zheng, Qi

Committee Co-Chair (if applicable)

Kulasekera, KB

Committee Member

Kong, Maiying

Committee Member

Mitra, Riten

Committee Member

Garbett, Nicholas

Author's Keywords

Functional data; conditional kaplan-meier; observational studies; personalized treatments; propensity scores; survival data

Abstract

Due to the wide availability of functional data from multiple disciplines, the studies of functional data analysis have become popular in the recent literature. However, the related development in censored survival data has been relatively sparse. In Chapter 2, we consider the problem of analyzing time-to-event data in the presence of functional predictors. We develop a conditional generalized Kaplan Meier (KM) estimator that incorporates functional predictors using kernel weights and rigorously establishes its asymptotic properties. In addition, we propose to select the optimal bandwidth based on a time-dependent Brier score. We then carry out extensive numerical studies to examine the finite sample performance of the proposed functional KM estimator and bandwidth selector. We also illustrated the practical usage of our proposed method by using a data set from Alzheimer's Disease Neuroimaging Initiative data. Estimating the optimal treatment regime based on individual patient characteristics has been discussed in many forums. Advanced computational power has added momentum to this discussion over the last two decades, and practitioners have advocated using new methods to determine the best treatment. Treatments geared towards the "best" outcome for a patient based on their genetic markers and characteristics are highly important. In Chapter 3, we develop an approach to predict the optimal personalized treatment based on observational data. We have used inverse probability of treatment weighted machine learning methods to obtain score functions to predict the optimal treatment. Extensive simulation studies showed that our proposed method has desirable performance in selecting the optimal treatment. We provided a case study to examine the statin use on cognitive function to illustrate the use of our proposed method. Personalized treatment selection methods that assign individuals to treatments based on patients' characteristics have been widely recognized in modern medicine. Survivorship is considered the most representative of clinical effectiveness among many clinical outcomes. As a result, in personalized treatment selection, survival time is arguably a better choice for a patient's outcome. Many methods have been developed for randomized experimental data, which may not be suitable for observational data due to the confounding between treatment assignment and outcome variable. In Chapter 4, we propose a penalized semiparametric modeling approach to estimate the optimal treatment regime, which is suitable for both randomized experimental and observational data. The proposed method has a variable selection feature so that it can handle high-dimensional covariates as well as censored observations. The proposed method has been developed to identify the optimal treatment in multiple treatment settings. Extensive simulation studies showed that our proposed method has desirable performance in selecting the optimal treatment. We demonstrated the application of the proposed method using data obtained from the Kentucky Medicaid database on patients diagnosed with cirrhosis.

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