Vary-Coefficient Models for Failure Time Data With Longitudinal Covariates

本文主要提出變異係數風險模式在不同型態之長期追蹤解釋變數下之參數函數估計方法。 不同於以往之估計方法，我們在此所提出之方法無須對解釋變數作太強之分配假設， 誠如在生物醫學及流行病學上所發生之長期追蹤資料，蒐集之解釋變數常有不同之量測尺度， 且變數間之相關性不易用簡易之分配模式解釋，因此，文獻上所提之模型及方法存在著許多限制且不實際。 在本論文中，我們除了提出一些合理之估計方法，並針對估計式推導其大樣本性質，此外，借助模擬 資料來檢視其有限樣本性質。最後，我們將討論估計方法延伸至遞迴性資料之可行性。In this thesis, more flexible varying-coefficient hazard models of Cox's type are considered for failure time data with different settings of longitudinally measured covariates. Here, a class of smoothing estimation methods are proposed for the parameter functions. Unlike the former approaches, no distribution assumption is required on the time-dependent covariates in our estimation methods. As we can see in many biomedical and longitudinal studies, the collected covariates might have different measured scales. It is impractical to model the complicated covariate processes, and, hence, the existing methods become very limited in application. In this study, the asymptotic risks of the proposed estimators are also established. To examine the finite sample properties of the proposed estimators, a Monte Carlo simulation is conducted. Finally, an extension of our methods to recurrent event data is discussed.Table of Contents ii List of Tables iii Abstract iv 摘要 v Acknowledgements vi 1 Introduction 1 2 Estimation Methods 4 2.1 Estimation Method under Model (2.1) . . . . . . . . . . . . . . . . . 5 2.2 Estimation Method under Model (2.2) . . . . . . . . . . . . . . . . . 7 2.3 Estimation of Asymptotic Variances . . . . . . . . . . . . . . . . . . 8 3 Asymptotic Properties 10 4 Numerical Study 23 5 Discussion 35 Bibliography 3