在截切資料加速時間模式下的穩健排序估計方法

Abstract

存活分析中截切資料是很常見的一種資料型態，此資料的形成是因取樣的方式造成只能收到某些特性的樣本。例如左截切資料的事件時間必大於截切時間才可被收為樣本。若在可觀察範圍下事件時間與截切時間獨立則稱為類獨立，在此假設成立之下利用排序的方法來建構半母數加速事件時間模型的參數估計式已有成熟的發展。在很多情況下類獨立的假設並不成立，因此本文考慮當事件時間與截切時間相依時，以人工截切方式建立對完整存活時間的可比較配對和以設限的存活函數為權重調整因設限而未使用的資訊來建立U統計量型式迴歸參數的估計式。藉著模擬結果證實本文提出的參數估計式在事件時間與截切時間相依時所得到參數估計值具有一致性和穩健性，而對於須要類獨立假設成立的排序估計方法，在事件時間與截切時間相依時所得到的參數估計值可能有偏差。本文將所提出的參數估計方法運用在老人安養院及輸血感染愛滋病的資料上。此外，本文所提出的參數估計式為不可微函數，因此文中也會探討解不可微函數的兩段法和Nelder-Mead所提的方法等兩種解根演算法。

In observational studies, truncated survival data are often collected according to a certain sampling criterions in. For example, in left-truncated data, event time is observed only if it is larger than truncation time. In a semiparametrically accelerated failure time model, rank-based methods developed for estimating regression parameters for truncated data require the assumption of quasi-independence that the event time and truncation time are independent under the observable region. Quasi-independence assumption may fail to hold in many situations. Therefore, we develop a robust U-statistic-based estimating equation to estimate the regression parameters without relying on the quasi-independence assumption. In our proposed method, comparable pairs for uncensored cases are established and artificial truncation as well as inverse-censoring-probability weighted technique are used to modify truncation and censoring effects. Our simulation shows that our proposed estimators are consistent when event time and truncation time are dependent. However, the naive estimator from the rank-based estimating equation requiring the quasi-independence assumption is biased when event time and truncation time are strongly correlated. We apply our proposed method to the channing house data and transfusion-related AIDS data. Since our proposed estimating equation is a nondifferentiable function with respect to regression parameters, we also compare two root-finding algorithms for nondifferentiable function, bisection and Nelder-Mead methods, in this thesis.