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Joint Modeling of Longitudinal and Survival Data, and Robust Nonparametric Regression

Gao, Xiaotian (2020) Joint Modeling of Longitudinal and Survival Data, and Robust Nonparametric Regression. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This dissertation covers two areas: joint modeling of longitudinal and survival data, and robust nonparametric regression. For joint modeling, the first chapter focuses on developing a statistical inference tool to estimate mean quality adjusted lifetime (QAL). QAL is traditionally calculated based on discrete health status. We proposed to incorporate continuous quality of life scores in calculating QAL and use joint models with inverse probability weighting to estimate mean QAL. Asymptotic properties of the estimator were studied, and finite sample performance was evaluated via simulations. The method was also applied to the Virahep-C data set. We continue to develop a joint model that can handle multiple longitudinal outcomes and semi-competing risk survival data in the third chapter.
In the second chapter of the dissertation, we developed a robust method for the nonparametric additive regression. The goal of this chapter is to develop a robust nonparametric additive model that produces stable estimates even when the errors have asymmetric and heavy-tail distributions. This is accomplished using an adaptive Huber loss function, with the value of its parameter increasing with the sample size at a certain rate. Compared with traditional robust regressions, the proposed method balances the robustness-to-unbiasedness trade-off and produces stable and consistent estimates. Non-asymptotic deviation results are studied, and stable algorithms are developed under both low and high dimension regimes. The method is applied to the NCI-60 data set to explore the relationship of expression levels between proteins (heavy-tail) and genes.
Public Health Significance: In this dissertation, the chapter on quality- adjusted lifetime provides useful tools to compare treatments with side effects. Incorporating continuous quality of life scores, the proposed method together with its sensitivity analysis could potentially help clinicians make individualized recommendations to different patients with different preferences over treatment effects and tolerance of side effects. The chapter on robust nonparametric regression is focused on analyzing the outcomes with heavy-tail distributions, such as protein expression levels. The proposed method is able to identify weaker signals while maintain a similar false discovery rate comparing with traditional methods. This will help clinical researchers identify key but weak genes or biomarkers with more confidence.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Gao, Xiaotianxig31@pitt.eduxig31
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWahed, Abduswahed@pitt.eduwahed
Committee CoChairKang, Chaeryoncrkang@pitt.educrkang
Committee MemberRen, Zhaozren@pitt.eduzren
Committee MemberTang, Gonggot1@pitt.edugot1
Date: 23 September 2020
Date Type: Publication
Defense Date: 18 June 2020
Approval Date: 23 September 2020
Submission Date: 20 August 2020
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 97
Institution: University of Pittsburgh
Schools and Programs: Graduate School of Public Health > Biostatistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Joint model of longitudinal and survival data, quality-adjusted lifetime, robust nonparametric regression, Huber's loss, semi-competing risk data, multivariate longitudinal processes
Date Deposited: 23 Sep 2020 13:22
Last Modified: 23 Sep 2020 13:22
URI: http://d-scholarship.pitt.edu/id/eprint/39661

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