在醫學診斷中，通常會記錄病患回診所測量的共變數值，即為時間相依的 共變數值，有了長期追蹤資料的性質，即不適用一般的接受者作業特徵曲線下面積(AUC)來判斷生物指標對於疾病預測能力的程度，因此根據 Heagerty 和 Zheng (2005) 和 van Houwelingen, Putter (2012) 以及 Blanche, Dartigues 和 Jacqmin-Gadda (2013) 所提出的方法，皆可用來估計時間相依的AUC。由於上述的三種方法皆為依據 Heagerty 和 Zheng (2005) 的架構再分別透過不同的估計方法去計算時間相依的AUC，因此本論文主要針對 Heagerty 和 Zheng (2005) 的方法並進一步透過模擬和實例分析來探討隨著時間的不同，AUC 對於生物指標預測疾病能力的程度。由於 Heagerty 和 Zheng (2005) 是使用部分概似法，其需要完整的共變數歷史且不允許有測量誤差，因此本論文預期使用聯合模型可以解決部分概似函數的缺失問題， 使得時間相依的AUC可以有更精確的估計結果。;In the medical diagnosis, it usually recorded the measurements for covariates of patients with returning to clinic which also called time-dependent covariates. With the property of longitudinal data, it is not suitable for using traditional area under the Receiver Operating Characteristic curve (AUC) to distinguish the biomarkers for predicting ability of diseases. According to the methods in Heagerty & Zheng (2005), van Houwelingen, Putter (2012) and Blanche, Dartigues & Jacqmin-Gadda (2013), all can estimate time-dependent AUC. Since these three kinds of methods are mainly based on the approach in Heagerty & Zheng (2005), each method computes time-dependent AUC by different ways. Hence, we focus on the method in Heagerty & Zheng (2005) and explore AUC for biomarkers via simulation and case study. Due to Heagerty & Zheng (2005) using partial likelihood function to compute AUC that needs complete covariate history and doesn’t allow for measurement error. Consequently, this thesis tries to apply joint model approach to solve the problems of partial likelihood function to obtain a better prediction.
