利用生物標記判斷病人是否罹患疾病是一個重要的醫學研究問題。疾病的產生可能與數個生物標記有關，同時這些生物標記也可能互為相關，因此如何適當的組合這些生物標記，以便極大化其診斷疾病的能力就成為一個重要的醫學診斷問題。目前用以衡量生物標記診斷疾病效果的工具為受試者操作特徵曲線(Receiver Operating Characteristic Curve; 簡稱為ROC 曲線)，特別是此一曲線下的面積(Area under the ROC curve;簡稱為AUC)與Youden指數(Youden index)已經成為診斷醫學的兩個通用的衡量準則。本文將根據AUC與Youden指數研究文獻中常用的組合生物標記方法的優劣，其中包含Su and Liu(1993)提出的組合多元常態生物標記方法與Pepe et al.(2006)建議的無母數方法，因為這些方法僅考慮最佳化或極大化AUC。本文一方面提出資料冪轉換使其能適用需多元常態分布生物標記的方法；另一方面為加速無母數生物標記組合方法的操作，考慮多種選擇初值。最後，藉模擬方法研究在不同分布下，原來的方法與修正後的方法在組合不同個數生物標記情形下的疾病診斷能力及所需要的操作相對時間。;It is an important medical problem to diagnose a disease by many biomarkers. Several biomarkers might be related to the disease under study and they are correlated. Therefore, how to combined these biomarkers so that the combined one reaches its maximum capability for disease diagnosis becomes an important issue in medical diagnosis. The correct tool in use for medical diagnosis based on biomarkers is the Receiver Operating Characteristic(ROC) curve. In particular, the area under the ROC curve(AUC) and the Youden index are the two most widely used criteria for diagnostic biomarkers. The two criteria are need to evaluate, for example, the parametric method by Su and Liu(1993) and the non-parametric one by Pepe et al.(2006) for the two methods are constructed only based on the AUC. In this article, the power transformation of data is suggested so that the parametric methods can be used. On the other hand, to speed up the computation of non-parametric method, the choice of initial values is discussed. Finally, a simulation study is conducted to investigate the performance of the original and modified methods on disease, diagnostic, and the required relative operating time.
