在生物醫學的實驗中，實驗者都會有回診的動作，其收集到的資料為時間相依的資訊。一般傳統的接受者作業特徵曲線，是利用整體時間下的資料當作參數去估計。但這樣的做法不符合長期追蹤資料的性質。近期有許多學者提供了不同運算含時間相依共變數接受者特徵曲線面積的方法，在本篇論文比較最廣為人知的四種利用半母數模型做時間相依下接受者特徵曲線面積的方法，分別為Chambless & Diao (2006) 、Song & Zhou (2008) 、Uno, Cai, Tian & Wei (2007) 以及Heagerty & Zheng (2005) 。本篇以五筆有名的資料為實例，比較各方法的優劣。此五筆資料分別等待心臟移植資料、使用Didanosine以及Zalcitabine愛滋病患者資料、CD4與病毒乘載量對AIDS、原發性肝膽汁硬化(primary biliary cirrhosis)以及果蠅的產蛋數目與存活壽命的關係。最後發現Heagerty & Zheng的結果最佳，所得到的半母數模型做時間相依下接受者特徵曲線面積最為合理。;In biomedical research, many researchers have to follow up and collect patients’ information. In particular, the biomarkers are usually time-dependent data and of interest. In the traditional methods, Receiver Operating Characteristic curves are estimated by fixed covariates. Therefore, it cannot handle the longitudinal data. There are many recent scholars provide the methods which calculate the time-dependent area under the ROC curve. In this thesis, we explore the performance of four popular semi-parametric approaches for estimate of ROC curves possibly with time-dependent covariates. The four methods are Chambless & Diao (2006) , Song & Zhou (2008) , Uno, Cai, Tian & Wei (2007) and Heagerty & Zheng (2005) . We analyze five data sets to do comparison of these methods. The five data sets are Heart Transplant, ddI or ddC in patients, CD4 counts and viral load affect AIDS, primary biliary cirrhosis and total number of eggs laid during lifetime. Through these comparisons, we conclude that Heagerty & Zheng’s method provides fairly reasonable results in both simulation study and the real data sets. It provides the best performance of time-dependent semi-parametric AUC.
