Joint Modeling Approaches for Clustered Survival Data with Random Cluster Size 公开

Liu, Shuling (2015)

Permanent URL: https://etd.library.emory.edu/concern/etds/ff365622m?locale=zh
Published

Abstract

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

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

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