診斷醫學中經常利用生物指標診斷受試者是否罹患某一研究中的疾病。一般是根據病人與非病人的生物指標，建立受試者操作曲線 (Receiver Operating Characteristic curve; 簡稱為ROC曲線)。之後，計算此一曲線下的面積 (Area under the ROC curve; 簡記為 AUC )，評估該生物指標診斷疾病的鑑別能力；此外，也會計算其 Youden 指數，一併求出適當的臨界值。事實上，診斷醫學中也經常希望非病人的誤診率不宜過高。為研究非病人誤診率低於一定水準的部分 AUC 及部分 Youden 指數；分別記做 pAUC 及 J_p ，本文分別在生物指標有無分布假設下建構 pAUC 及 J_p 的有母數及無母數聯合信賴域。本文進一步利用模擬研究上述兩種聯合信賴域的涵蓋機率及信賴域面積，結果顯示在特定分布下所建構的有母數信賴域在維持信賴水準及信賴域面積表現皆佳；但是，當分布不符時，無母數的信賴域會有較為穩健的表現。本文最後分析一筆胰臟癌的資料說明所提方法的應用。

In medical disgnostics, biomarkers are usually employed to diagnosis if the subject suffers the disease under study. In general, the receiver operating characteristic curve (ROC) is constructed based on the biomarkers of diseased and non-diseased. The area under the ROC curve (AUC) is then calculated to evaluate the diagnostic ability of the biomarkers. In addition, Youden index is computed along with the cut off value. Note that, in practice, the false positive rate (FPR) should be controlled. Therefore, AUC and Youden index under the FPR constraint or partial AUC and partial Youden index are needed. In this thesis, we find the joint parametric and non-parametric confidence sets of the partial AUC and partial Youden index separately. A simulation study is conducted to investigate the coverage probability and area of the confidence set. Results show that the parametric confidence set is good on holding its confidence level and has reasonable area when the assumed distributions are correct. However, when the distributions are not feasible, the non-parametric confidence set is more robust on the level and area performance. A real data set is from a case-control study that includes pancreatic cancer subjects and pancreatic case-free subjects is finally illustrated to demonstrate the application of the proposed joint confidence sets.

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