競爭風險下雙維度治癒模式

Abstract

本篇論文提出二維治癒模式，可用來探討複雜疾病在“發病與否” (disease incidence)與“發病時間”(age onset)的家族群聚性，模式考慮了死亡為發病的競爭風險，因此帶因者有可能在生前不發病。文章採混合模式架構以描述以上二種關聯性，對於發病時間的聯合分配，文章中假設copula模式，並提出以二階段法估計參數。第一階段目標為估計邊際函數，我們同時考慮Kaplan-Meier無母數估計法和給予母數模式的MLE方法，其中利用了EM演算法處理缺失值以簡化估計問題。在第二階段中將所得邊際函數估計量代入“擬概似函數”（pseudo-likelihood function）中，求其極值可得相關參數之估計量。我們透過電腦模擬評估所提出方法在有限樣本之表現。

In this thesis, we propose a bivariate cure model which describes two types of association, namely “disease incidence” and “onset ages”, between family members. Our model provides a systematic way to incorporate the effect of death by treating it as a competing risk for disease occurrence. We use a copula model to describe the joint distribution of the onset times for a susceptible pair. Another copula model is imposed to describe the joint distribution of competing risks due to death for the pair. For a susceptible person, whether the disease will actually occur depends on the order of the latent onset age and the competing risk. The parameters are estimated via a two-stage estimation procedure. In stage 1, nuisance parameters are estimated. The association parameters of interest are estimated in the second stage based on a pseudo-likelihood function. The EM algorithm is employed in both stages as a way to simplify the likelihood estimation. Properties of the estimators are examined via simulations.