在競爭風險下復發資料之無母數分析

Abstract

本論文的動機是來自分析一筆洗腎病患的資料。血液透析需要在病患體內植入瘻管，在長期的治療過程中，瘻管可能會發生兩類栓塞 (“急性”或“慢性”)，處理過後依然可能會再度復發。我們將問題納入可容許復發且存在競爭風險的事件史架構，針對兩次復發中的間隔時間 (gap time)，探討兩個重要的邊際函數：特定事件的累積發病比例函數 (cumulative incidence function) 和特定事件下的風險函數 (cause-specific hazard function)。類似的資料常見於生物醫學研究中，但相關的統計方法卻未臻成熟。為了處理分析間隔時間會引入的相關設限問題 (induced dependent censoring)，我們利用加權技巧來修正資訊的偏誤。此外我們亦推導了所提出估計量的大樣本性質，並建議以自助重抽法 (bootstrap) 處理後續的檢定問題。模擬分析顯示我們的方法有優良的表現。論文並呈現此筆洗腎資料的分析結果。

This project was motivated by a dialysis study in northern Taiwan. Dialysis patients, after shunt implantation, may experience two types (“acute” or “non-acute”) of shunt thrombosis, both of which may recur. We formulate the problem under the framework of recurrent events data in the presence of competing risks. In particular we focus on marginal inference for the gap time variable of specific type. The functions of interest are the cumulative incidence function and cause-specific hazard function. The major challenge of nonparametric inference is the problem of induced dependent censoring. We apply the technique of inverse probability of censoring weighting (IPCW) to adjust for the selection bias. Besides point estimation, we apply the bootstrap re-sampling method for further inference. Large sample properties of the proposed estimators are derived. Simulations are performed to examine the finite-sample performances of the proposed methods. Finally we apply the proposed methodology to analyze the dialysis data.