Flexible Association Methods for Bivariate Survival Data Open Access

Yang, Jing (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/gq67jr33c?locale=en


Biomedical follow-up studies often involve multiple event times. The inter-relationship among these event times is often of great scientific interest. In this dissertation, we focus on two scenarios involving multiple event times, semi-competing risks (Fine et al., 2001) and recurrent events. The first project is to study the dependence structure between the nonterminal event and the terminal event in the semi-competing risks setting. We propose a new robust dependence measure without requiring distributional assumption, which can accommodate the exploration of the potential changing pattern of the dependence in the identifiable region of semi-competing risks data. We develop a nonparametric estimation procedure for the proposed measure by adopting a quantile regression framework. The estimation method can be readily extended to adjust for covariates. The proposed methods are evaluated by extensive simulation studies and an application to the Denmark diabetes registry data. The second project is to develop a new nonparametric estimator of the dependence measure proposed in the first project. The new estimator can accommodate left truncation that occurs in semi-competing risks settings, requiring weaker constraints on the truncation mechanism. Asymptotic properties and inference procedures are established for the resulting estimator. We conduct simulation studies to assess the finite-sample performance of the new estimator. We also apply it to a Denmark diabetes registry dataset. The third project is to explore the association between bivariate recurrent event processes under an observation window structure, which is motivated by the US Cystic Fibrosis Foundation Patient Registry (CFFPR) study. We propose a novel measure which can flexibly depict the association between two recurrent event processes. We further develop a regression framework for the proposed measure to allow for assessing whether and how the association is influenced by covariates. We establish the estimation procedure, which show promising results by some preliminary simulation studies. We also apply the proposed method to the CFFPR study.

Table of Contents

1 Introduction. 1

1.1 Background. 2

1.2 Literature Review. 4

1.2.1 Existing work on dependence for semi-competing risks data. 4

1.2.2 Existing work on association for bivariate survival data. 6

1.3 Outline. 8

2 A New Flexible Dependence Measure for Semi-competing Risks Data. 9

2.1 Proposed Dependence Measure. 10

2.2 Estimation and Inference Procedures. 11

2.2.1 Data and notation. 11

2.2.2 The proposed estimator. 12

2.2.3 Asymptotic results. 15

2.2.4 Inference procedures. 16

2.3 An Extension to Adjusting for Covariates. 19

2.4 Simulation Studies. 21

2.5 An Application to Denmark Diabetes Registry Data. 28

2.6 Remarks. 32

2.7 Appendix. 35

2.7.1 Proof of Theorem 2.2.1. 35

2.7.2 Proof of Theorem 2.2.2. 36

2.7.3 Justication for the proposed covariance estimate. 39

3 Estimation of the New Dependence Measure for Semi-competing Risks Data under the General Truncation Scheme. 40

3.1 Estimation and Inference Procedures. 41

3.1.1 The proposed estimator. 41

3.1.2 Asymptotic results. 44

3.1.3 Inference. 45

3.2 An Extension to Covariates Adjustment. 47

3.3 Simulation Studies. 47

3.4 Denmark Diabetes Registry Data Analysis. 51

3.5 Remarks. 53

3.6 Appendix. 55

3.6.1 Proof of Theorem 3.1.1. 55

3.6.2 Proof of Theorem 3.1.2. 59

4 Semiparametric Regression Procedures for the Association between Bivariate Recurrent Processes. 64

4.1 Association Measure and Model. 65

4.1.1 Data and notation. 65

4.1.2 Proposed association measure for bivariate recurrent event data. 65

4.1.3 Proposed regression model for PZ(u; v). 68

4.2 Estimation Procedure. 69

4.2.1 Estimation of Bk0(). 69

4.2.2 Proposed estimation procedure for a0(; ). 70

4.2.3 Algorithm to obtain the estimator of a0(; ). 71

4.2.4 Inference. 72

4.3 Simulation Studies. 73

4.4 An Application to CFFPR Data. 74

5 Summary and Future Work 88 5.1 Summary. 89

5.2 Future Work. 90

Bibliography. 90

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