Varying-coefficient Regression Analyses for Semi-competing Risks Data Public

Abstract

Abstract
Biomedical studies for chronic diseases often involve multiple event times. In this
dissertation, we focus on a scenario where one terminating event can dependently
censor a nonterminating event, but not vice versa. Such data structure was termed
as semi-competing risks data by Fine et al. (2001). We concern regression analyses of
semi-competing risks data under the modeling frameworks that accommodate vary-
ing covariate effects, including quantile regression (Koenker and Bassett, 1978) and
temporal regression (Fine et al., 2004). The two modeling frameworks are gaining
increased popularity in survival analysis for their flexibilities and ease of interpreta-
tions.
In the ï¬rst project, we propose quantile regression methods for left-truncated semi-
competing risks data. The project is motivated by the Denmark diabetes registry
study, where the nonterminating event time of interest, time to diabetic nephropathy
(DN), is subject to the dependent censoring by time to death. Biological interests
are centered on regression analysis of time to DN, without removing the effect of
death. A notable complication in this dataset is the administrative left truncation to
death, which greatly complicates the analysis. We propose inference procedures for
the conditional quantiles of the cumulative incidence function of DN, by appropriately
handling left-truncation via the technique of inverse probability of censoring weight-
ing. We show that the proposed estimator has nice asymptotic properties including
uniform consistency and weak convergence. We illustrate the practical utility of the
proposed method via simulation studies and an application to the Denmark diabetes
registry data.
In the second project, we study quantile regression on the marginal distribution of
the nonterminating event. The project is motivated by the AIDS Clinical Trial Group
(ACTG) 364 study, where a study endpoint, time to ï¬rst virologic failure, is subject
to censoring by patients dropouts. We develop a quantile regression method which
focuses on the marginal conditional quantiles of the study endpoint, while providing
information on the association between the study endpoint and the patient dropout.
The proposed estimating equations well utilize the special semi-competing risks data
structure, and can be solved by an efficient iterative algorithm. We derive the asymp-
totic properties of the resulting estimator, including uniform consistency and weak
convergence. Simulation studies demonstrate the proposed method performs well
with moderate sample size. We applied the proposed methods to the ACTG 364
study for analyses of the virologic endpoint.
In the third project, we study the same data structure as that in the ï¬rst project
from a different perspective. Speciï¬cally, we develop temporal regression methods for
the cumulative incidence function of DN in the Denmark diabetes registry study, to
evaluate the temporal relationship between covariates and DN progression. We pro-
pose estimation and inference procedures for the time-varying regression coefficients.
Furthermore, some preliminary simulation results show that the proposed methods
perform well with realistic sample sizes.

Varying-coefficient Regression Analyses for Semi-competing
Risks Data
By
Ruosha Li
B.S., Peking University, 2006
M.S., Emory University, 2010
Advisor: Limin Peng, Ph.D.
A dissertation submitted to the Faculty of the
James T. Laney School of Graduate Studies of Emory University
in partial fulï¬llment of the requirements for the degree of
Doctor of Philosophy
in Biostatistics
2011

Table of Contents

Contents

1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 First Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Denmark Diabetes Registry Study . . . . . . . . . . . . . . . . 4 1.2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Second Motivating Example . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 AIDS Clinical Trial Group 364 study . . . . . . . . . . . . . . 6 1.3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Quantile Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Temporal Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Quantile Regression for Left-truncated Semi-competing Risks Data 15 2.1 Regression Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Data and Model . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.2 Estimation of 0(τ ) . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.3 Asymptotic Results . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.4 Covariance Estimation . . . . . . . . . . . . . . . . . . . . . . 21 2.1.5 Other Inferences . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.2 Denmark Diabetes Registry Data Analysis . . . . . . . . . . . 28 2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4.1 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4.2 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4.3 Justification for the Proposed Covariance Matrix Estimate . . 42 2.4.4 The Form of ξi(t, z) under the Cox Proportional Hazard Model 42 3 Quantile Regression adjusting for Dependent Censoring 44 3.1 Regression Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.1 Data and Model . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.2 Estimating Equations . . . . . . . . . . . . . . . . . . . . . . . 47 3.1.3 Computational Algorithm . . . . . . . . . . . . . . . . . . . . 49 3.1.4 Asymptotic Results . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.5 Inferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.2 Aids Clinical Trial Group 364 Data Analysis . . . . . . . . . . 60 3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4.1 Regularity Conditions . . . . . . . . . . . . . . . . . . . . . . 64 3.4.2 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.3 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5 Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4 Temporal Regression for Left-truncated Semi-competing Risks Data 82 4.1 Regression Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.1.1 Data and Model . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.1.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.1.3 Second Stage Inferences . . . . . . . . . . . . . . . . . . . . . 86 4.2 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.2.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.2.2 Analysis of Denmark Diabetes Registry Study . . . . . . . . . 89 5 Summary and Future Work 92 5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Bibliography 94

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics
Mot-clé	Semi-competing Risks Data Temporal Regression Left-truncation Dependent Censoring Quantile Regression
Committee Chair / Thesis Advisor	Peng, Limin, Emory University
Committee Members	Benatar, Michael, Emory University Huang, Eugene, Emory University Manatunga, Amita, Emory University

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