長期追蹤及存活資料下潛藏因子結合模型

Abstract

本論文主要針對時間函數之反應值及存活時間建立一合理且具解釋性的變異係數潛藏因子模型。 藉由更廣泛之非參數化潛藏因子模式，反應值內部相關，反應值與存活時間之相關及觀測個體在此兩隨機變數之非齊一性質被建立。 在長期追蹤及存活資料結構下，我們利用參數函數之基底展式估計值做為參數函數之估計。 在此，我們更進一步推導所提出估計函數之大樣本性質，並借助模擬樣本檢視估計式之有限樣本性質。 最後，我們將討論衍生之有趣研究主題及所提出模式延伸之可行性。

In this thesis, a more flexible and easily explained joint latent varying-coefficient model is used to model the relationship between time-dependent responses and a failure time. Here, the dependence mechanism within time-dependent responses, between time-dependent responses and a failure time, and the heterogeneity among different subjects on time-dependent responses and failure times are established through a non-parametric latent process. Based on the longitudinally measured responses and survival time data, we mainly propose an estimation procedure for the time-dependent parameter functions. In our estimation approach, the parameter functions are first approximated via the corresponding basis function expansions. Trough the estimates of parameters in the basis function expansions, the estimated parameter functions are then obtained. Moreover, the asymptotic risks of the estimated functions are developed in this study. A Monte-Carlo simulation is conducted to examine the finite sample properties of the proposed estimated functions. Finally, some additional topics of interest are considered and a possible extension of our proposed model to more complicated joint processes is discussed.