左截切單一與二元間隔時間競爭風險資料之直接二項式迴歸估計方法

Abstract

生物醫學研究中，長期追蹤可觀察疾病的自然病程，或是可探討影響預後狀況的預後因子。考慮左截切的研究設計下，符合收案條件的個體必須在收案日期當下已發生起始事件且尚未發生觀察事件才能夠進入研究，故將導致抽樣偏差。當觀察到二元間隔時間而非單一事件時間時，即使假設間隔時間與右設限時間無關，第二間隔時間和對應之設限時間仍彼此相關，因此在分析時應處理此誘導性相依設限。當觀察時間為單一事件時間或是二元間隔時間時，最後事件可能有兩種以上的事件型態，而這些事件型態彼此競爭發生，針對此種競爭風險資料，Fine & Gray（1999）提出以累積發生函數為分析對象的比例次分布風險迴歸模型，Scheike等人（2008）則提出以直接二項式迴歸估計方法估計Fine & Gray（1999）的迴歸模型。本文希望能藉由Scheike等人（2008）的方法，將Fine & Gray（1999）的迴歸模型推廣至左截切單一事件時間以及左截切二元間隔時間資料。最後，本文模擬考慮左截切時間與右設限時間之間不同的相依結構，並將提出的方法應用在HIV以及大腸直腸癌的長期追蹤研究。

In biomedicine and epidemiology, a longitudinal study is commonly designed to explore natural history or to investigate prognostic factors of a certain disease. However, biased sampling may occur due to left truncation in which enrolled participants are those who have experienced initial event but have not had a certain event to the index date of study. Besides, when outcomes of interest are bivariate gap times instead of univariate event time, standard techniques for analyzing the second gap time are subject to dependent censoring induced by the dependence among the serial gap times. Moreover, if more than one type of events for univariate event time or the second gap time may occur in the disease process but only one of these events can be observed, then the event of interest will be competed by other event types. Cumulative incidence function (CIF), also known as the subdistribution, is the probability of failing from a certain cause and can be identifiable in competing risks data. Recently, Scheike et al. (2008) proposed direct binomial regression method as an alternative method to estimate the parameters in Fine & Gray (1999) proportional subdistribution hazards regression model which directly modeled cumulative incidence function by setting the appropriate link function. The aim of this thesis is to extend this method to left-truncated univariate and bivariate gap times data. Simulation studies are conducted under various dependence structures of truncation time and censoring time. Finally, we apply our proposed method to analyze a HIV cohort and a colorectal cancer cohort.