Varying-coefficient Regression Analyses for Semi-competing Risks Data Open Access
Li, Ruosha (2011)
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 94About this Dissertation
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