多類復發事件之分析

Abstract

本計畫的動機來自於一筆台大醫院新竹分院所記錄洗腎病患之資料。許多病患發生 不只一次的瘻管栓塞（分急性與非急性），我們將其視為具有多個（兩個）發生型態的復 發事件史資料。我們針對復發事件的“間隔時間”，納入競爭風險的架構，討論重要參 數（函數）之建模與推論問題。因此類型資料受限於“訊息設限”，是推論分析中必須 克服的挑戰。兩年的計畫中，第一年的工作暫時不考慮解釋變數，把重點放在探討幾個 重要函數的無母數估計問題。所考慮的對象包含描述邊際行為的函數、與可反映出不同 階段相關性的聯合函數。我們擬利用動差關係去計算權數，以修正訊息設限在估計所造 成的偏誤。所提出的方法，將透過模擬實驗驗證其正確性，並用於分析此筆腎臟病資料。 第二年的計畫欲更進一步的把解釋變數納入分析裡，先建立（半母數）迴歸模型，再提 出參數估計方法。同步進行模擬驗證與資料分析以增進對數學模式之直覺感受。所提出 方法的大樣本理論會一併進行。我們會將資料分析的結果與新竹醫院醫師進行討論以作 為修正方向之參考。

Motivated by a real dataset from a medical study on dialysis patients, this project considers analysis of recurrence events data with multiple types. We focus on the gap times and incorporate the framework of competing risks in the analysis. A special characteristic of such data is the presence of induced informative censoring which will be a challenge for statistical inference. This two-year project contains two research directions. In the first year, we will consider nonparametric estimation of several descriptive functions. Some measures describe marginal behavior of the gap times while others provide information about the association. In the second year, we will focus on regression analysis which takes the effects of covariates into account. We will propose several regression models and investigate the plausibility of these models. Inference procedures will also be developed. All the proposed methods will be evaluated via simulations and applied to the data set. Their large-sample properties will also be derived. During the whole project, we will communicate with the doctors who provided the data to improve the applicability of our methods.