指導教授：江金倉臺灣大學：數學研究所田婉廷Tien, Wan-TingWan-TingTien2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264039受惠於科技與醫學的進步，針對許多疾病已研發出能治癒病人的方法，譬如癌細胞經放射線治療後被完全消滅，康復的病患將不死於癌症，故有多數右設限資料記錄於觀測結束的時間點，由Kaplan-Meier存活函數的估計可觀察到長尾的平穩狀態，這些資料的特色是不論觀測時間多長，存活曲線永不趨近零，我們稱之為「治癒存活資料」，因此，藉由生物指標來判別病人治癒與否便成為一重要議題，這涉及到分類和真實狀況之間的關聯性。本論文目標主要將傳統真陽性率、偽陽性率與ROC曲線下面積的應用推廣到治癒存活資料上，並分析一筆心血管疾病的研究資料。Benefited from the advanced technology and medical science, more and more effective treatments for different kinds of incurable diseases have been invented. For instance, patients will not die of cancer if the radiation kills all cancer cells, so there are plenty of right-censored data at the end of the observation period. The Kaplan-Meier type estimator of survival curve shows a long and stable plateau in the tail. A characteristic of such survival data is that the survival function does not converge to zero as time goes to infinity. It is called "cure survival data". As a result, using biomarkers to discriminate uncured patients from all subjects becomes an important issue. It is related to the connection between classifications and the true status. Our primary research aim is to extend the application of true positive rate (TPR), false positive rate (FPR), and the area under receiver operating characteristic (ROC) curve (AUC) from classical survival data to cure survival data. And we will analyze the data of an angiography cohort study.誌謝 i 摘要 ii Abstract iii Table of Contents iv List of Figures v List of Tables vii 1 Introduction 1 2 Model and Estimation 5 2.1 Model 5 2.2 Estimation of the Survival Function 6 2.3 Estimation of ROC Curve and AUC 9 3 Monte Carlo Simulations 13 3.1 Simulation I – Univariate Marker 13 3.2 Simulation II – Multivariate Markers 20 4 Application to an Angiography Cohort 26 5 Discussion 31 Bibliography 321714686 bytesapplication/pdf論文公開時間：2014/08/01論文使用權限：同意有償授權(權利金給回饋學校)存活分析治癒存活資料生物指標真陽性率偽陽性率ROC曲線下面積[SDGs]SDG3thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264039/1/ntu-103-R01221025-1.pdf