Flexible Semiparametric Regression Methods for Observational Follow-up Studies Open Access
Sun, Xiaoyan (2014)
Abstract
Observational follow-up studies often present various challenges that can complicate statistical analysis, such as complex censoring mechanism, missing observations, and highly skewed measurements. In my dissertation, we have developed flexible semiparametric regression methods for three different complex data scenarios.
The first one is recurrent events setting subject to window observation, which arises when the observation of recurrent event is not available before the follow-up starts and after the follow-up ends. We adopt the accelerated recurrent time model (Huang and Peng, 2009), and develop two estimators for window observed recurrent event data. We illustrate our method via an analysis of the time to expected frequency of pseudomonas aeruginosa (PA) infection in Cystic Fibrosis (CF) children through the use of the US CF Foundation Patient Registry (CFFPR).
The second project is about longitudinal data with skewed outcome subject to left censoring and following an informative intermittent missing pattern, which is motivated by the Michigan Long-Term Polybrominated Biphenyls (PBB's) Study. In this work, we consider quantile regression modeling for the data from such longitudinal studies. We adopt an appropriate censored quantile regression technique to handle left censoring and employ the idea of inverse probability weighting to tackle the issue associated with informative intermittent missing data. We evaluate our method by simulation studies. The proposed method is applied to the Michigan PBB study to investigate the PBB decay profile.
The third data scenario is longitudinal data with skewed outcome subject to left censoring and irregular outcome-dependent follow-up. For example, in the Michigan PBB study, serum samples were not taken at a set of common time points but at irregular time intervals. In this work, we propose an inverse intensity-ratio weighted least absolute deviation estimator in censored quantile regression. This approach yields consistent estimates of the quantile regression parameters provided that the model for the follow-up visit process has been correctly specified. The proposed method is also applied to the Michigan PBB study to investigate the PBB decay profile.
Table of Contents
1 Introduction
1.1 Background
1.2 Literature Review
1.2.1 Existing Work on Regression for Recurrent Event Data
1.2.2 Existing Work on Regression Analysis of Longitudinal Data
1.3 Outline
2 Accelerated Recurrence Time Analysis of Recurrent Event Data Observed in a Time Window
2.1 Regression Procedures
2.1.1 Data and Model
2.1.2 Two-Stage Estimation
2.1.3 Estimator Based on Counting Process
2.2 Simulation Studies
2.3 CFFPR Data Example
2.4 Remarks
2.5 Appendix
2.5.1 Proof of Theorems
3 Censored Quantile Regression Analysis of Longitudinal Data with an Informative Intermittent Missing Pattern
3.1 Regression Procedures
3.1.1 Data and Model
3.1.2 Estimation Procedure and Inference
3.1.3 Asymptotic Results
3.2 Simulation Studies
3.3 PBB Data Example
3.4 Remarks
3.5 Appendix
3.5.1 Examples of Estimator Satisfying Condition C 1
3.5.2 Proof of Theorems
4 Censored Quantile Regression Analysis of Longitudinal Data with Irregular Outcome-Dependent Follow-Up
4.1 Regression Procedures
4.1.1 Data and Model
4.1.2 Estimation Procedure
4.1.3 Asymptotic Properties
4.1.4 Inference
4.2 Simulation Studies
4.3 PBB Data Example
4.4 Remarks
4.5 Appendix
5 Summary and Future Works
5.1 Summary
5.2 Future Works
Bibliography
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