二元有序間隔時間之交叉分位數比分析

Abstract

序列事件常見於現代醫學和流行病學縱向研究中，而有序間隔時間資料常為研究者感興趣之主題。研究者欲了解病人的疾病進程而進行早期預防治療，而有序間隔時間之間相關性蘊含病人疾病歷程資訊，是自然的預測因子。本篇提出交叉分位數比 (cross quantile ratio，CQR) 測量隨時間改變之相依性，並以前兩段間隔時間為例。利用無母數方法，設限分位數迴歸估計交叉分位數比以及使用設限機率倒數權重調整相依設限，而不須額外假設聯合分布。本文另外討論交叉分位數比估計之一致性以及大樣本下共變異數估計。模擬結果顯示，交叉分位數比表現受限於設限率，在一定範圍的分位數相對偏誤都在5%以下；本文提供之標準差估計方法在大樣本下會有較好表現，最後以rhDNase資料為例，進行實際資料分析。

Serial event data are often encountered and of interest in the follow-up studies of chronic diseases and gap times between successive events. The relationship between serial gap times may provide predictive information on disease progression. In this thesis, the cross quantile ratio (CQR) is introduced to measure the time-varying dependence between the first and second gap times without specifying their joint distribution. Nonparametric estimation of cross quantile ratio can be carried out through censored quantile regression approach. In addition, the inverse probability of censoring weights is used to tackle the induced dependent censoring. The asymptotic properties of the proposed estimators are investigated and the corresponding asymptotic variance estimators are provided as well. Simulation results suggest good performance of the proposed methods within a certain range of quantile due to censoring. The rhDNase dataset is analyzed for further illustration of CQR method