三種資料結構下雙變數存活時間之迴歸分析

Abstract

雙變數存活分析已被廣泛應用於生物醫學的研究。早期的研究課題較偏向於探討兩個不同生物個體或器官組織存活時間之關連性。近年來的應用方向則拓廣到同一個體所發生不同事件的時間。後者在分析上，往往伴隨所探討的時間變數間彼此具有設限或截切關係，使得統計推論變得更為複雜。本論文包含兩個研究計劃，均在迴歸的架構下分析雙變數之存活時間。我們特別針對前面所述特殊的設限或截切資料，提出統計推論的方法。 第一個計劃針對半競爭風險資料，探討解釋變數對“中介事件發生時間”的影響。分析的難度在於所欲探討的時間長度受制於相關設限。大部分文獻所提出的方法均利用“人為設限”﹝artificial censoring﹞的技巧，以處理相關設限所造成的偏誤。不過這個方法因把部份觀測值捨棄而會產生估計效率上的損失，亦因添加了額外的模型假設而有缺乏穩健性的缺點。我們提出兩階段估計方法可改善前述方法的缺點。我們亦針對兩個所提出的假設，發展模型檢驗的方法。論文中並推導了大樣本性質，並且透過數值分析評估各推論方法在有限樣本下的表現。 在第二個計劃中，我們建構關聯性的迴歸模式，並且發展一套推論方法可以彈性的分析三種截然不同的資料結構。我們也針對此模式假設，提出模型檢驗的方法。論文中亦呈現大樣本分析與數值分析。

Bivariate survival analysis has received substantial attentions due to its wide applications. The variables of interest may represent failure times occurred to two different biological units or different event times measured from the same subject. In the latter situation, the two failure times may have censoring or truncation relationship which complicates statistical analysis. The thesis contains two projects, both of which consider regression analysis for bivariate survival data. The first project focuses on semi-competing risks data in which a terminal event censors a non-terminal event. In particular we investigate how covariates affect the marginal distribution of the time to a non-terminal event subject to dependent censoring. Most existing methods utilize the technique of artificial censoring to remove the sampling bias. However these approaches may result in efficiency loss and may not be robust under model mis-specification. We propose a two-stage procedure to tackle this problem. We also propose model selection methods to verify the two main assumptions. Large-sample properties are also proved. Numerical analysis is performed to evaluate finite-sample performances of the proposed methods. In the second part of the thesis, we consider the situation that covariates may affect the level of association. We propose a flexible regression model and then develop a unified inference procedure which can be applied to three different types of data structures. For this part, we also present a model checking method for assessing the appropriateness of the Clayton assumption. Large-sample analysis and numerical studies are also presented.