在醫學診斷學中可以根據一個生物指標的受測者操作特徵曲線計算Youden指數，藉以決定此一生物指標的臨界值。上述的Youden指數考量真陽率與偽陽率的差異。鑒於醫學診斷的偽陽率不宜太高，Youden指數宜予修正。此外，實務上受測者除生物指標之外，經常也觀察或測量與此生物指標有關的共變數，因此，本文將考量這些共變數，並且在偽陽率有所限制之下推廣Youden指數，藉以決定與共變數有關的生物指標的臨界值。本文藉模擬研究所推廣的Youden指數和臨界值估計的偏差及誤差，最後利用一筆胰腺癌的資料說明所提方法的應用。

In medical diagnostics, we can find the cut-off point of a biomarker based on the Youden index computed from the corresponding
receiver operating characteristic curve. The Youden index considers the difference between the accurate positve rate and false positive rate.
Since, the false positive rate is usually undercontrol, the Youden index needs to be modified. In practice, however, covariates of each subject are often
available which maybe related to the biomarker under study. Therefore, in this thesis, an extention of the Youden index is proposed which produce covariate-dependent
cut-off point of the biomarker under a restriction of the false positive rate.
We then investigate the bias and the standard error of the estimated cut-off point and Youden index.
Finally, we apply the proposed methods to illustrate the data about pancreatic cancer.

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