Joint Modeling Approaches for Clustered Survival Data with Random Cluster Size Open Access

Liu, Shuling (2015)

Permanent URL:


The first part of this dissertation focuses on the development of copula based joint modeling approaches for the clustered survival data with a random cluster size. We propose to adopt Clayton-Oakes model (Clayton, 1978; Oakes, 1989) for measurements within a cluster and the cluster size is modeled via a discrete survival model. The methods are motivated by the Mount Sinai Study of Women Office Workers (MSSWOW) where women were prospectively followed for one year for studying fertility. For each woman, menstrual cycle lengths (MCLs) are recorded until time-to-pregnancy (TTP) or the end of study. We first consider specifying a parametric distribution as the marginal survival distribution in the Clayton-Oakes model and TTP is modeled using a grouped version of the usual continuous time Cox regression model (Scheike and Jensen, 1997). Second, we consider a semiparametric linear transformation model (Cheng et al., 1995) for the marginal distribution of the Clayton-Oakes model. We develop an EM algorithm to derive an approximate generalized maximum likelihood estimator. We also provide a computationally simple estimation procedure known as the "two-stage" approach. Asymptotic theory for the "two-stage" estimators is established. Simulation studies are conducted to evaluate the performance of the proposed joint model and estimation procedures. The proposed methods are also applied to the MSSWOW data. In the second part of this dissertation, we consider the problem of testing whether a repeatedly measured quantitative biomarker is associated with a subsequent time-to-event process. We propose a nonparametric testing procedure to evaluate the null hypothesis by adopting a linear mixed model for repeated measures, but without imposing modeling assumptions on the time to event. The proposed test can utilize all the information provided by the random effects and is not sensitive to the model misspecification of the time-to-event process. We show that the proposed test statistic is asymptotically consistent and normally distributed under both null and alternative hypotheses. We demonstrate the validity of the new nonparametric test using simulation studies and compare the proposed method to a model-based score test. We finally apply the proposed method to a real data from epidemiological study to illustrate its practical utility.

Table of Contents

Abstract iii

1 Introduction 1

1.1 Background 1

1.2 The Mount Sinai Study of Women Oce Workers 3

1.3 Discrete Survival Models for TTP 4

1.4 Modeling Menstrual Cycle Lengths 7

1.5 Copula Models 10

1.6 Joint Modeling of Longitudinal and Survival Data 13

1.6.1 Shared Random Eects Joint Models 15

1.6.2 Mixture and Selection Joint Models 17

1.6.3 Other Joint Models 18

1.6.4 Testing Whether Repeated Measured Biomarker Associated with Time To Event 20

1.7 Outline 20

2 Joint Models with Marginal Parametric Assumptions 23

2.1 Introduction 23

2.2 The Model 27

2.2.1 Notation 27

2.2.2 General Framework 28

2.2.3 The Model Specication 29

2.3 Parameter Estimation 33

2.3.1 Maximum Likelihood Estimators 33

2.3.2 Estimation of Standard Errors 35

2.4 Simulation Studies 35

2.5 MSSWOW Data 36

2.6 Remarks 41

3 Semiparametric Joint Models 46

3.1 Introduction 46

3.2 The Models 49

3.3 Parameter Estimation 52

3.3.1 Likelihood Construction 53

3.3.2 EM algorithm 57

3.4 Simulation Studies 59

3.5 Application to MSSWOW Study 61

3.6 Discussion 64

4 A Two-Stage Estimation Approach 68

4.1 Introduction 68

4.2 Model Specications 70

4.2.1 Marginal models for repeated measurements 71

4.2.2 Dierent copula models 71

4.2.3 Discrete model for the random length 73

4.3 Parameter Estimation Procedure 75

4.3.1 First stage: estimation parameters under working independence assumption 75

4.3.2 Second stage: estimation of association parameter 78

4.4 Simulation Studies 79

4.5 Application to MSSWOW Data 82

4.6 Discussion 87

5 Nonparametric Test for the Conditional Independence between a Biomarker and Time-to-Event Data 101

5.1 Introduction 101

5.2 The Joint Modeling Framework 104

5.3 Model Based Score Test 105

5.4 Nonparametric Testing Procedure 107

5.4.1 Derivation of the nonparametric test statistic 107

5.4.2 Asymptotic property of the nonparametric test statistic 108

5.5 Simulation Studies 109

5.6 A Real Data Example 113

5.7 Discussion 115

6 Conclusions and Future Work 121

6.1 Conclusions 121

6.2 Future Work 123

List of Figures viii

List of Tables ix

About this Dissertation

Rights statement
  • Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
  • English
Research Field
Committee Chair / Thesis Advisor
Committee Members
Last modified

Primary PDF

Supplemental Files