相依性重覆事件與終止事件的間隔時間資料之聯合模式

Abstract

臨床上有許多疾病是需要接受反覆治療的；這些一系列的治療，實際上便構成了重覆事件。而根據病情需要，每次接受重覆治療和上一次治療之間間隔的時間可能都不同。因此這些治療，可以看作是彼此之間具有相依性的重覆事件發生。另一方面，臨床上可能發生某些事件使得治療必須中斷，這些事件便可被視作是所謂的終止事件。由於這兩種事件彼此相依無法切割，因此在資料分析時，我們必須同時處理重覆事件以及終止事件。此外，如果我們把病人從初次治療開始到任何重覆事件或是終止事件之間的事件時間當作有興趣的時間目標，這在臨床上會是不切合實際的。事實上，任何兩個連續發生的事件之間的間隔時間，才是和臨床上所關注更為貼切的。但這一系列間隔時間所伴隨的誘發性相依設限，則是在資料處理上必須處理的問題。在本研究中，我們介紹相依性重覆事件與終止事件的間隔時間資料之聯合模式，並在模式中加入過去事件歷史來捕捉一系列間隔時間之間的相依性。接著我們發展出模式中迴歸參數的估計方法，並討論其漸近性質。我們也會生成模擬數據，來驗證其分析有限樣本的表現。這些方法會用來分析一個實際資料；這資料是包含從2006年1月到2011年12月，在新北市某醫院接受後筋膜下注射曲安奈德來治療糖尿病黃斑部水腫的病人資料。

Clinically many diseases demand repeated treatments, which constitute of a series of repeated events. The gap times between two consecutive treatments may be variable due to the clinical conditions. Therefore, these repeated events will be mutually dependent. On the other side, some clinical events may hinder or interrupt further repeated treatments; these events then become so-called terminal events. Because the repeated events and terminal events are also mutually dependent, we have to deal with both events together when performing data analysis. Furthermore, it would be clinically impractical if we consider the periods between the initial diagnosis to each event, the event times, as the time outcomes of interest. In fact, it is more relevant clinically to study the gap times between any two successive events. In addition, the issue of induced dependent censoring must be tackled during the analysis of serial gap times. In this study, we introduce the joint models for gap time data of dependent repeated events and terminal event in which the event history is incorporated to capture the dependence among serial gap times. The estimation methods for regression parameters in the models are developed. Their asymptotic properties are also discussed. We also conduct numerical simulations to examine the finite-sample performance. These proposed methods are applied to the data including patients who received posterior subtenon injection of triamcinolone acetonide for diabetic macular edema in a hospital in New Taipei between January 2006 and December 2011.