Survival Analysis with Covariate Measurement Error Open Access

Abstract

In many medical research studies, survival time is typically the primary outcome
of interest. The Cox proportional hazards model and the accelerated failure time
model are two popular methods to investigate the relationship between covariates
and survival time. However, in many clinical trials, the true
covariates may not always be accurately measured. For regression analysis, naively analysis using mismeasured covariates may incur substantial estimation bias.
In this research, we aim to resolve several issues in survival data analysis
with covariate measurement error.
The first topic focuses on the analysis of recurrent events data. We proposes an estimation procedure under the
accelerated failure time model.
With replicated mismeasured covariates available, the proposed estimation procedure
requires no distributional assumptions on either the true covariates or the error. The regression coefficient estimators are
shown to be consistent and asymptotically normal. The performance of the proposed
procedure is investigated by numerical studies with practical sample size.
The second topic considers the Cox model for univariate
survival data. In the presence of measurement error, several functional
modeling methods have been proposed when the erro distribution is known. Among them are parametric corrected score
and conditional score. Although both methods are consistent, each suffers from severe problem of multiple roots or absence
of appropriate root when the measurement error is substantial. The problem persists
even when the sample size is practically large. We conduct a detailed investigation on
the pathological behaviors of parametric corrected score and propose an approach of
incorporating additional estimating functions to remedy these pathological behaviors.
Extensive simulation studies are conducted to evaluate the performance of
proposed method.
In the third topic, we consider the Cox model when the error distribution is completely unspecified, but
replicated mismeasured covariates are available instead. A consistent nonparametric corrected score has been proposed for Cox model with replicated mismeasured covariates. But it also suffers from pathological behaviors similar to that of the parametric corrected score. To address this issue, we develop a similar technique for the nonparametric corrected score and evaluate
its performance by simulation study.

Table of Contents

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivating Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Nutritional Prevention of Cancer (NPC) Trial . . . . . . . . . 3
1.2.2 AIDS Clinical Trial Group (ACTG) 175 Study . . . . . . . . . 5
1.3 Covariate Measurement Error . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Functional Modeling and Structural Modeling . . . . . . . . . . . . . 9
1.5 Measurement Error Techniques in Survival Analysis . . . . . . . . . . 12
1.5.1 Recurrent Events Data . . . . . . . . . . . . . . . . . . . . . . 12
1.5.2 Univariate Survival Data . . . . . . . . . . . . . . . . . . . . . 13
1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Accelerated Failure Time Model for Recurrent Events With Errors
in Covariates 16
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Inference Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 The Model and Data . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Proposed Estimation Procedure . . . . . . . . . . . . . . . . . 19
2.2.3 Asymptotic Properties . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Illustration with the NPC Trial Data . . . . . . . . . . . . . . 29
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Appendix: Technical Details . . . . . . . . . . . . . . . . . . . . . . . 32
2.5.1 Proof of the Asymptotic Theory . . . . . . . . . . . . . . . . . 32
2.5.2 Asymptotic Variance of Estimating Function . . . . . . . . . . 37
3 Augmented Parametric Corrected Score for Proportional Hazards
Model with Covariate Measurement Error 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Parametric Corrected Score and Conditional Score and Their Pathological
Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Parametric corrected score and conditional score . . . . . . . . 43
3.2.2 Pathological behaviors . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Improving Corrected Score . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Augmented Estimation Method . . . . . . . . . . . . . . . . . 51
3.3.2 Estimation and inference . . . . . . . . . . . . . . . . . . . . . 55
3.4 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Application to ACTG 175 data . . . . . . . . . . . . . . . . . 69
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Appendix: Asymptotic Variance of Estimating Function . . . . . . . 72
4 Augmented Nonparametric Corrected Score for Proportional Haz-
ards Model with Covariate Measurement Error 74
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2 Nonparametric Corrected Score and Pathological Behaviors . . . . . . 76
4.2.1 Nonparametric Corrected Score . . . . . . . . . . . . . . . . . 76
4.2.2 Pathological Behaviors . . . . . . . . . . . . . . . . . . . . . . 77
4.3 Improving Nonparametric Corrected Score . . . . . . . . . . . . . . . 80
4.4 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.2 Application to ACTG 175 data . . . . . . . . . . . . . . . . . 88
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5 Summary and Future Work 93
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics Statistics
Keyword	covariate measurement error estimating function proportional hazards model survival analysis accelerated failure time model recurrent events
Committee Chair / Thesis Advisor	Huang, Eugene, Emory University
Committee Members	Johnson, Brent, Emory University Lyles, Robert, Emory University Kutner, Nancy, Emory University

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