關於兩種或多種診斷方法,在診斷的預測上是否有顯著差異的檢定，在過去的文獻中已有一些研究，且對於一種診斷的正確性，通常利用ROC曲線下面積來評估。但在目前的診斷方法中，利用多個診斷方法同時評估某種疾病是常見的，例如糖尿病，但尚未有一個適當測度量可以評斷這些診斷方法的準確性。本論文主要提出一個整合的測度量來評估多種診斷方法同時使用下的準確性，在同時考慮多個診斷方法下，利用隨機效果模式架構了多變量ROC曲線下面積求法，及探討其性質。最後，將所導出的方法應用在一組糖尿病的資料上。

A statistical tool which is popular for describing the accuracy of diagnostic is the receive operating characteristic (ROC) curve. There has been an increased use of ROC curve for assessing the effectiveness of continuous diagnostic markers in distinguishing between diseased and healthy individuals. McClish (1989) recognized that the area under the ROC curve(AUROC) is a global measure of a test's accuracy because it includes the entire range of false-positive rates from 0.0 to 1.0.
In fact, it is possible that several diagnostic markers are used to detect a disease , e.g. diabetes, and how one can measure their simultaneous diagnostic accuracy. Based on the random effect model, we derive an estimate of the area under multivariate ROC curve. A model-based estimation and an approximated confidence interval are derived by combining the confidence intervals of two parameters using Bonferroni method. A nonparametric estimation will also be proposed and compared to the model-based estimate by a simulation study. Finally, this method is applied to a real data for example.

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