張淑惠Chang, Shu-hui臺灣大學:流行病學研究所傅宗襁Fu, Tsung-ChiangTsung-ChiangFu2010-05-052018-06-292010-05-052018-06-292009U0001-1508200920584100http://ntur.lib.ntu.edu.tw//handle/246246/180798在追蹤研究中，針對個體自起始事件後，可能發生的兩事件進行觀察而據此收集形成的資料型態稱為二元事件資料。分析二元事件資料時，過去文獻多考慮以下兩種時間尺度：事件發生時間及兩相鄰事件的間距時間。當兩事件有固定的時間順序時，則多以兩相鄰事件的間距時間，即間隔時間，為時間尺度進行分析。過去文獻中尚未有研究者針對二元有序間隔時間的相關性測度進行探討。一般來說，由於誘導訊息設限的問題，並不適合用分析事件發生時間的標準技巧分析第二段間隔時間。本文考慮以Kendall''s tau作為二元有序事件資料中兩間隔時間之相關性測度，並以設限時間的存活函數之倒數作為權重調整誘導訊息設限造成的偏差，建立二元有序間隔時間之Kendall''s tau的無母數估計量。運用U統計量的性質與平賭量的技巧，可以得到Kendall''s tau估計量的變異數為漸近常態。最後，經由模擬呈現本文所提供的估計量之估計表現。In follow-up studies, bivariate event data are often encountered when subjects may experience two events with different or the same types. In analyzing bivariate event data, two types of time scale are considered in the literature: the times to events and the times between adjacent events. When the occurrence of during follow-up two events is in a chronological order, the gap time, defined as the time between adjacent events, is often of interest in the study. In the literature, measures of association between bivariate event times have been studied, but not yet for two serial gap times. In general, standard techniques for analyzing the times to events are inappropriate for analyzing the second gap time due to the presence of induced informative censoring. In this paper, Kendall''s tau is considered as a measure of association between gap times. Nonparametric estimation of Kendall’s tau for two serial gap times is proposed in which inverse probability of censoring weights is used to accommodate the bias from induced informative censoring. Asymptotic normality of the proposed estimator of Kendall''s tau is obtained by employing the theory of U statistics along with martingale techniques. Finally, the performance of the proposed method is illustrated by a simulation study.致謝....................................................................................................................................i文摘要...........................................................................................................................ii文摘要..........................................................................................................................iii一章 導論 1.1 前言 1.2 研究動機 3二章 文獻回顧 7.1 以KENDALL’S TAU檢定其中一變數具右設限之二元資料的兩變數獨立性 7.2 CLAYTON的風險比 9.3 OAKES的交叉比 11.4 以倒數權重調整誘導訊息設限產生之偏差 16三章 方法 19.1 符號定義 19.2 二元有序間隔時間資料的KENDALL’S TAU估計與CLAYTON模式下的 風險比估計 20.3 KENDALL’S TAU估計量的變異數估計 25四章 二元有序間隔時間的模擬資料生成 29.1以CLAYTON二元指數分布生成模擬資料 29.1.1 Clayton二元指數分布生成 29.1.2 以Clayton二元指數分布生成資料之模擬結果 31.2以FRANK二元指數分布生成模擬資料 36.2.1 Frank二元指數分布生成 36.2.2 以Frank二元指數分布生成資料之模擬結果 38五章 結果與討論 43考文獻 46錄 48application/pdf496815 bytesapplication/pdfen-US間隔時間誘導訊息設限倒數權重有序事件U統計量Gap timesInduced informative censoringInverse weightedSerial eventsU statisticsKendall''s tauthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180798/1/ntu-98-R96842027-1.pdf