Flexible and Robust Methods for Evaluating Covariate Effects on Biomedical Outcomes Restricted; Files Only
Cui, Ying (Spring 2023)
Published
Abstract
In practice, it is often of scientific interest to evaluate covariate effects on biomedical outcomes. This task can be complicated by the presence of dynamic (or varying) variable effects that often manifest meaningful scientific mechanisms. Appropriately accounting for possible dynamic effects is crucial to avoid depreciating some important variables. Moreover, with technology advancement, modern biomedical studies often collect a huge number of variables, posing ultra-high dimensional data settings. Furthermore, important contributors of biomedical outcomes may evolve over time, posing time-dependent covariates. The overall objective of my dissertation is to develop statistical methods that can provide robust and flexible assessment of covariate effects that can address the limitations of existing approaches while leading to meaningful scientific discovery.
In the first dissertation project, we adopt the device of globally concerned quantile regression, and propose a flexible testing framework suited to assess either constant or dynamic covariate effects on outcomes subject to random censoring. We study the powerful Kolmogorov-Smirnov (K-S) and Cramer-Von-Mises (C-V) type test statistics and develop a resampling procedure to tackle their complicated limit distributions. We provide rigorous theoretical results, including the limit null distributions, consistency under a general class of alternative hypotheses of the proposed tests, and the justifications for the presented resampling procedure. Extensive numerical studies demonstrate the utility of the new testing procedures and their advantages over existing approaches.
In the second dissertation project, we propose a model-free testing and screening framework by adopting a global view pertaining to the concept of interval quantile independence. The new framework not only permits robust identification of variables dynamically associated with an outcome, but also offers the flexibility to evaluate multiple covariates simultaneously, where the covariates under consideration can be either continuous or discrete. The key testing strategy naturally evolves into unconditional and conditional screening procedures for ultra-high dimensional settings that enjoys the desirable sure screening property. We demonstrate good practical utility of the proposed methods via extensive simulation studies and a real application to a microarray data set.
In the third dissertation project, utilizing the interval-quantile index, we propose a new model-free globally-concerned test statistic for evaluating the impact of time-dependent covariates on time-to-event outcomes. Additionally, we develop a resampling procedure based on perturbation resampling. We establish the limit null distributions and consistency under a general class of alternative hypotheses of the proposed tests and provide justification for the resampling procedure. The proposed methods are demonstrated through extensive simulation studies, as well as an application to the Feeding Infants Right... from the STart (FIRST) study.
Table of Contents
1 Introduction 1
1.1 A Brief Overview 2
1.2 Literature Review 3
1.3 The Proposed Methods 7
1.4 Outline 13
2 Assessing Dynamic Covariate Effects with Survival Data 15
2.1 The Proposed Testing Procedures 16
2.2 Numerical Studies 27
2.3 Real Example with Dialysis Data 31
2.4 Remarks 35
2.5 Appendix 37
3 Global Group Testing and Screening With Dynamic Effects 46
3.1 Problem and Motivation 47
3.2 The Proposed Global Testing Framework 48
3.3 Variable Screening in Ultra-high Dimensional Setting 52
3.4 Numerical Studies 58
3.5 Real Example with Microarray Data 70
3.6 Remarks 75
3.7 Appendix 77
4 Non-parametric Testing for Survival Data With Time-dependent Covariates 102
4.1 The Proposed Testing Framework 103
4.2 Numerical Studies 111
4.3 Real Example with FIRST Data 125
4.4 Remarks 129
4.5 Appendix 134
5 Summary and Future Work 147
5.1 Summary 148
5.2 Future work 149
Bibliography 150
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File download under embargo until 22 May 2025 | 2023-04-28 14:31:45 -0400 | File download under embargo until 22 May 2025 |
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