醫學上常利用幾個診斷方法一起來查出診斷疾病，但當疾病分類不是只分成有病和無病，而是分成三群時，本文研究如何估計此種診斷精確性的問題。本文利用多變量ROC曲面下體積來衡量三群下診斷的精確性，並推導出無母數方法的診斷精確性估計量和其變異數。由於在多變量常態分配下，有太多參數的問題，所以假設隨機效應模型以濃縮參數，並基於該模型推導出診斷精確性的估計量和其變異數。並利用模擬研究比較無母數方法和模型假設下兩估計量的均方誤，利用拔靴法計算拔靴信賴區間和診斷精確性的涵蓋機率。模擬結果顯示為模型假設下的均方誤會小於無母數估計的均方誤。最後，應用一個實例來說明此方法。

This paper studies the problem of estimating the diagnostic accuracy when several diagnostic markers are used to detect a disease. The volume under multivariate ROC surface is used to measure the diagnostic accuracy for three groups. A nonparametric estimator of the diagnostic accuracy and its variances will be proposed. Because there are many parameters under the assumption of multivariate normal distribution, a model-based estimate of the diagnostic accuracy and its variance will be derived based on the random effect model. The model-based estimate is compared with the nonparametric estimator by the mean square error. The approximated confidence intervals are derived and evaluated by the nominal coverage probability based on a simulation study. The simulation results show that the mean square error of the model-based estimator is smaller than that of the nonparametric estimator. Finally, the proposed methodology is applied to a real data for example.

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