長期追蹤,重覆量測時間及存活時間之潛藏因子結合模型

Abstract

本論文主要針對時間函數之反應值，重覆量測時間及存活時間建立一變異係數潛藏因子模型。藉由半參數化之潛藏因子建立這些過程之內部相關，彼此之相關性以及非齊一性質。在長期追蹤以及存活資料結構下，我們利用基底展式估計值作為參數函數之估計。更進一步，我們推導所提出估計函數之大樣本性質，並藉助模擬檢視估計式之有限樣本性質。

In this thesis, a joint latent varying-coefficient model is proposed to establish the relationship among processes of time-dependent response, measurement time or recurrent event time, and terminal time. The dependence within and among these processes and the heterogeneity on each process are modelled through partially nonparametric latent variables. Based on the longitudinal and survival time data, an estimation approach is proposed for the parameter functions in the considered joint latent model. In our estimation procedure, each parameter function is first substituted by the corresponding basis function expansions, and, hence, the approximated likelihood function is induced. By implementing the expectation and maximization (EM) algorithm or directly using the integration technique, the estimates of parameters in the basis function expansions are obtained. It is naturally to use the estimated functions of basis function expansions as the estimators of the corresponding parameter functions. In this thesis, the asymptotic and finite sample properties of the estimated functions are also derived and examined through a Monte-Carlo simulation, respectively.