在競爭風險下，目標事件的累積發生機率的回歸分析

Abstract

許多疾病的病程包含數種以上的風險，例如乳癌患者可能會經歷癌細胞的復發，轉移甚至病情嚴重導致死亡。當研究者感興趣的主題事件為非終端事件時(例如癌細胞的復發)，若終端事件先發生，就無法觀察到主題事件。在存活分析的架構下，死亡被視為復發事件的競爭風險。此時如何推估主題事件的發生機率是個熱門的研究主題。本篇論文在迴歸的架構下探討自變數對主題事件發生機率的影響。

分析實證資料中常會因設限(censoring)而只能記錄到不完整的資訊。針對此現象，本論文提出兩種偏誤修正的方法以估計迴歸模式的參數。第一個方法利用設限機率的倒數做為權數以改正因設限造成的偏誤，稱之為 IPCW；第二個方法則以缺失值的條件期望值做為填補不完整的資訊，稱之為 Imputation。論文中我們推導迴歸參數估計量的大樣本性質，並藉由模擬以驗證所提出的估計方法在有限樣本時的表現。本論文亦將所提的迴歸模型和估計方法應用在史丹佛心臟移植資料和非典型肺炎(SARS)資料做為實例的佐證。

In the dissertation, we consider regression analysis for the cumulative incidence probability under the framework of competing risks. Instead of modeling the whole function which usually involves making stronger assumptions, we investigate the effect of covariates on the cumulative incidence rate at a pre-specified time point.

The information of incidence may be missing due to censoring. We apply two approaches to handle incomplete data. The first method utilizes the technique of the inverse probability of censoring weighting (IPCW) to correct the sampling bias. The other approach is to impute missing variables by an estimate of its conditional mean. Both methods are popular and useful tools in handling missing data. Large-sample properties of the proposed methods are also derived. Simulations are performed to examine finite-sample performances of the proposed methods. The Stanford Heart Transplant data and the severe acute respiratory syndrome (SARS) data are analyzed to illustrate the applicability of the proposed model and inference methods.